” . Then follow up with something exceptional and specific that makes you differentiate themselves from other candidates ie. “I am certified on Database Platform An and B and in my newest position, reduced database downtime by 23%. “.

Maybe, it had been their day, after they were able to close sales through telephone. Maybe, just maybe, everything relies on your know-how about what you’re doing additionally what strategies make use of, don’t you think that – This goes to indicate that the rationale why talking to does not use other people is because perform not just know how to make calls, important concept of talking to, and the things that need to be considered before produce a cold call. Therefore, for those people who are not yet convinced that cold calling works and it’s just depending on some circumstances that cold calling can not work for a number of people here is an inventory of some problems that will inform you that talking to really does work1. It works when the one who does cold calling knows who your customer or clients are.

Unlock The Game shows you ways to be incredibly effective in cold calling without triggering rejection from potential clients. Learn to Let Your Language Match Your Thinking – If you’ll be able to center yourself the place where you may let go of feeling that you have to go on using traditional talking to “scripts” and behaviors, you’ll discover youself to be spontaneously using language that you simply would utilization in a natural conversation. Using natural text — speaking exactly the way you would with someone you recognize, can modify cold calling a new refreshing and productive experience. And, as you let go of that old-school contacting model, during which your product or service is your best of generating a mobile phone conversation that has a prospect, you’ll make probably the most crucial transition of you’ll begin thinking about approaching customers not from your perspective, however from theirs.

Each and every PlayStation three owner must have some collection of their favored games but they nevertheless have question that what are the very best PS3 games ever released for the program. Considering all these gamers need and attempting to fulfill their curiosity we are right here mentioning some critically acclaimed very best games.

ACCESSORIES:

The PlayStation three has many accessories that can be used in a large variety of games. The very first controller was the “SIXAXIS”. It was used from the release of the console till 2008, when DualShock three took his location. The principal difference of the two controllers is that DualShock 3′s vibration function doesn’t interfere with the motion sense. As we all know a controller is just not sufficient for the gamers of the 21st Century. That’s why the PS3 also has a “racing wheel” for racing simulation games. This wheel was developed by Logitech. PS3 users can also interact with specific games through motions using the PlayStation Eye. This is a webcam with a constructed in microphone, and it can be employed for games like “EyePet”, “Tiger Woods PGA Tour 08″ and “The Eye of Judgment”.

RELIABILITY:

Sony made an extremely trustworthy console with only ten% failure in a time period of two many years. Even if the console is 1 of the most reliable out there on the market is has it’s issues. A handful of of these problems are the “yellow light of death”, which is a non-particular hardware difficulty. This problem occurred mostly in the UK, so occasionally a console repair is needed. PS3 repairs can be annoying if you do not know a store which can fix the difficulty near you. Also not too long ago there was a huge error with the PlayStation Network. Somebody hacked the servers and accessed the user database. This leaked the personal info of about 77 million users including passwords, addresses, and payment background. Apparently no credit card information was stolen. Following this Sony gave a totally free month membership to all PSN users with a new identity theft program.

GAMES ON PLAYSTATION 3:

There are a couple of PlayStation three exclusives like “LittleBigPlanet”, the “Infamous” series and possibly the most well-liked PS3 game, “Uncharted”. Of course there are tons of multi-console games like the “Devil May well Cry” series, “Mortal Kombat” and the “Call of Duty” series. Right now game developers are much more most likely to publish a game on consoles like the PS3 and the Xbox 360 than on a Pc.

Doing it on your own is a lot quicker and will expense you much less. Some on the internet applications supply detailed video instructions that walk you by way of it in much less than an hour and some will even supply some additional bonuses that make your system a lot more functional the moment the difficulty is fixed.

The only purpose to ever pay the shipping to Sony is if you have a valid warranty that will pay for the repairs fully. Otherwise, you can do it less costly and significantly, significantly quicker by making use of a great online program with video instruction.

If these three suggestions didn’t help you to fix your PS3 red light error, then it’s substantial most likely that you need to have to open up your console, and fix the problem from inside of. I actually can’t support you with that, since you will want step by step guidelines that’s coming along with either videos or images. But, you’ve got three choices to get your hardware problems solved.

Are you enthusiastic to understand how to sew but afraid to commit errors? No more worries for there are sewing machines for newbies obtainable in the industry. And there are surely quite a few of them courtesy of premier maker makes this kind of as Brother, Singer, and Janome. Sadly, the range only would make the range procedure even harder. Now right here are some guiding recommendations that will absolutely arrive helpful along the range method.
Long lasting Exterior Layout

As the exterior layout takes place to be the frontline of any unit, it would be very best to scrutinize the form. In contrast to regular sewing machines, those ones for novice generally seem in compact layout. Much more generally than not, these are likewise light-weight in kind consequently enabling you to consider the sewing exercise just everywhere. Amongst other individuals nevertheless, exterior engineering need to be offered meticulous interest as it defines the longevity capabilities. Acquire note that it is expected to house the fragile method hence it ought to be rough to endure standard use and tear.

Simplified Operations

An additional major worry is the operation as newbie sewists are not properly acquainted with the procedure. In turn, simplified sewing exercise is inimical to facilitate thorough sewing procedure. Studying the ropes is manufactured a lot easier when you are not confronted by complicated sewing procedure. Consequently, mechanical sewing would be favourable more than computerized procedure utilized by amateurs and specialists. In the exact way, single or dual features integration would be finest for multi-useful models can only confuse initially timers who are even now on their way to finding acquainted with sewing particulars. In addition to, practically nothing beats the basic sewing strategies when it comes to neophyte practitioners.
Consumer-Helpful Controls

Conceivably you have witnessed stitching machines armed with as well numerous buttons. You could possibly be fascinated by these sight but it really is different when you are requested to use them. Mere familiarization of these keys may possibly even give you a headache. No wonder, it is not sensible for beginners to grab an unit fancied by so a lot of knobs. And so never get overcome by too quite a few buttons for you may finish up apprehensive on how to use them all.

Stitch width can be modified for specific stitches up to 7mm and duration up to 5mm. The stitch reference guide is quickly readily available beneath the hinged cover on the major of the sewing device.
Janome DC5100 Presser FeetA entire of 11 snap-on presser feet are included in the box and these feet are intended for earning complex stitch work a breeze: Zigzag, Zipper, Blind Hem, Hemmer, Overedge, Even Feed, Satin Stitch, Cording foot, Overcasting, Basting foot, and an Automatic Buttonhole Foot.

Janome DC5100 Attributes and PerformanceThe set of functions on the Janome DC5100 involve all the very best sewing machine automation along with the flexibility to utilize very fine-tuned enhancements to your stitches.
For fast set up and effective sewing, there is a drop-in bobbin with see-as a result of cover, a programmable needle up/down button, precision thread stress management, an automated needle threader, a seven point feed dog, drop feed puppy handle, Start out/End button, speed command, conveniently found reverse button, stitch pattern memory, and horizontal thread delivery.

For precision and energy, the device operates on a DC motor which gives you much more force to the needle arm. Stretch stitches can be modified with the stretch stitch adjustment dial. There is even a buttonhole pitch adjustment dial for perfectly aligned sides on each and every buttonhole.

The computerized management panel sits under a backlit LCD screen and the buttons are flat and responsive.
The Janome DC5100 sewing device draws you in with its vibrant colour accents, then it taunts you with beautiful stitches and an beautiful command panel but it’s the electric power and precision hiding underneath that certainly supply like an easy sewing experience.

what is on the marketplace these days.what is on the industry these days.

Time for them to grab your Secret Secret agent Attack Finn McMissile and travel the globe to thwart evil at every turn! Or at least take a trip to your best pals house and fire Finn’s skyrocket launchers at his children sister. Ok! Just kidding that! (said with just a new soft spy type laugh to let’s you know that I really wasn’t! ) Whenever you feast your eyes about this latest release from Mattel and Disney, you will see precisely why the Secret Spy Attack Finn McMissile will be another one of the toys in your Cars 2 lineup that should have kids everywhere wishing to become an international awesome spy.

Now just should you don’t have a good deal of background intel (a strategy spy word for being familiar with who’s who) on Finn McMissile, he is the super suave and sophisticated British master spy who have sniffed out an evil plot regarding the World Grand Prix in your upcoming movie Cars 2. Not to mention naturally, like any superior spy would do, he embarks on an adventure of saving the day! Now exactly like in the movie, the Secret Spy Attack Finn McMissile comes with a variety of high tech weaponry to assist him succeed in his / her daring mission.

So just how cool is the Automobiles 2 Secret Spy Encounter Finn McMissile? Well let’s begin with the fact that he talks and claims some his signature lines on the movie. To make Finn chat, all your child has got to do is press over the hood, where there is known as a sticker conveniently located who says “press”, and Finn will become talking. But wait! There’s a great deal more!

If you fully depress that hood on Finn out and about will pop 2 ultra modern spy type missile launchers with the top of each fender that are willing to launch missiles at ones own nearest adversary! And the uniqueness when using the Secret Spy Attack Finn McMissile gets a better choice. If your child presses down around the rear bumper, another missile launcher appears from the trunk and then a super secret infra green spy screen from your roof. When you’re done with your mission all you want to do is push them last and Finn is right back to normal and happy to mingle unnoticed.

With includes like these, along with the attention to detail that Mattel has been doing with the Secret Criminal Attack Finn McMissile, that is surely going to be certainly one of your kids favorite fresh toys to play through. In fact, Finn could in all likelihood turn into a surprise best seller after the Cars 2 movie hits the big screens.
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LEGO joins in in the Cars frenzy

The Spy Jet Escape LEGO 8638, together with the Big Bentley Bust Apart LEGO 8639, are LEGO sets where kids reach play out a favorite scene belonging to the movie with the models and characters make build themselves.

You may find lots of Cars products available in existence but the LEGO sets are actually unique as they don’t come out of the box ready to get played just yet. You need to do the hard work yourself before you’re able enjoy the fruits on your labor.

Building the models yourselves

What’s great concerning the Spy Jet Escape is that you will have to build the models along with the characters yourself. Getting a toy that you may play with just right right out of the box can be a bit boring. Why not challenge your children by letting them put together the toys for themselves?

It also will teach your children some skills that they’ll certainly use in the future. It teaches them the extra worthiness of patience, building the models surely would devote some time; and it teaches them the quality of hard work.

Aside because of this, Spy Jet Escape LEGO 8638 at the same time gives them more creativity to construct their own models and create their own storylines for playtime

Lots involving characters included

There are lots of characters as part of the Spy Jet Escape establish. Almost all of these products are new characters with the second movie will always be included. How cool is usually that?

The characters integrated are Finn McMissile, law enforcement car; Holly Shiftwell, any British Spy car; and the lemons Grem and Aide. An old character in the first movie is equally included, everyone’s favorite Mater.

One downside to the set is that the most crucial character Lightning McQueen is not really included, but the last character surely accounts for for it. Siddeley, the huge spy jet is roofed. Siddeley measures an remarkable 11 inches long and 11 inches wide.

Kids have many options with the Secret agent Jet Escape LEGO 8638 arranged. They can play with the 6 Cars characters, play out their favorite scene from the video clip, or make out a story of their own. The most beneficial part of all is which they get to create the models as well as characters from scratch.

They get a choice in construction the models, they can strictly follow the instructions for making exact same thing as seen in the package or they may establish totally new models. They are brag to friends that they made the toys independently.
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Fisher-Price Protein shake ‘n Go! Disney/Pixar Cars 2 – Entire world Grand Prix is an absolute must have, especially if your children are hooked on the Cars 2 Dvd movie. Lightning McQueen and Francesco, two of the very memorable characters from this movie, race to the finish in this awesome need to have 2011 hot Christmas squeaky toy.

The game consists for taking the Shake ‘n Visit cars, shaking them up and placing them over the track and letting these go. Your child controls the force and speed of the cars based on how much they move them up. The more they beveled the faster and longer they’ll go!

Children watch for the reason that cars race round everything Grand Prix through London, Tokyo and Italy. And, just like the flick, the racetrack also comes including the camera. This camera will let you knock the cars off of the track by turning the particular camera around. This 2011 hot Christmas time toy keeps children occupied and happy all day.

The racecars that are widely-used on the track don’t include any switches or buttons to jog. The power comes with the child who simply shakes your car to get it running. And going they can, up to twenty legs per shake.

The World Grand Prix racetrack incorporates two collectible cars, Super McQueen and Francesco. Yet, the play set won’t be complete if you do not collect Finn McMissile, Master, Nigel Gearsley and Teacher Z. The beauty of that set is that the child can play alone and / or with other children of their class or neighborhood.

Children aged three to eight 8 desire to make things go round and round. This track gives children all of the excitement they can bear action, thrill and the speed of this game. And, there’s a learning element built into this toy: cause and additionally effect. You shake this hard and you go this far. The actual harder you shake, the daddy it goes. Additionally, just a little competition among friends educates sportsmanship.

We all know that a majority of children love to engage in with other children compared to playing by their selves. That’s why the Tremble ‘n Go cars perfect for group play as effectively. Not only does a child have to be the “racer” on your track, they can be part of the pit crew, much too. Then, to change it up rather, they can switch placements and take turns being racer. This type of execute teaches both teamwork not to mention cooperation thereby emphasizing cooperation and fun instead of only competition.
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The initial Disney Pixar Cars movie brought us one of the most remembered and easily established movie characters of contemporary times. Most children, along with numerous adults, will be able to call at least one or two the Disney Pixar New or used cars characters without hesitation, personalities like Lightning McQueen, up to date hotshot racing rookie sense, Tow Mater, the loveable rustic tow truck, or Macintosh, the superliner truck exactly who transports Lightning’s trailer, these along the rest of the cast of Cars possess all become household names world wide and with the sequel, Cars 2, releasing throughout 2011, the thrill of a race and magic within the movie is set to take place all over again.

Disney Pixar are keeping many plot to the Automobiles 2 movie pretty close to their chests, but it truly is thought that the picture will centre around two of the main characters from the Cars movie, Lightning McQueen and additionally Mater, who travel all over to take part within the new race, the contest of champions, which is due to take place over a few different race circuits around five different countries, united kingdom, Italy, France, Germany plus Japan.

The remaining Disney Pixar Cars characters in the original movie, characters for example Sally Carrera, Radiator Springs’ legal practitioner and Lightning’s love attention, Doc Hudson, the villages judge and previous victorious of three piston keyrings, sheriff, the mercury pub coupe police car, Luigi, Guido, Filmore and Sarge to name just a couple of, we feel, will accompany Lightning and Mater given that the pit crew and helping keep the pair for line, and it is believed that no less than one new character by all the name of Finn McMissile is usually to be introduced and who realizes, hopefully we will be introduced to way more new Disney Pixar Automobiles characters.

How Does This Copying PS3 Computer software Perform?

The Easy Backup Wizard works very simply. You only want to carry out three methods in order to effectively backup, copy and burn the Playstation 3 game.

1) Insert the original game to your Pc.

two) Load the game and begin making a backup from it.

3) When that’s completed, you can begin to copy the Playstation three game by clicking on “burn”

The Playstation 3 yellow light of death, YLOD, is very appropriately named! When you go to turn on your method and view that small yellow light flip to a blinking red light it is quite frustrating. You press the button above and more than attempting to get the method to boot, but it does no excellent. Although numerous people presume their console has really died and there is absolutely nothing to do but replace it, this is totally untrue.

It would certainly be less difficult and quicker to just throw away the method out and obtain a new one particular, but anybody who does that would be stupid adequate due to the fact the PS3 Yellow Light Of Death is a fixable problem! Plus, it is really likely that the new console will just develop the same Playstation 3 yellow light issue, and you can’t continually replace it over and over.

In most instances, the flashing yellow light of death of PS3 is triggered by internal failures due to overheating. Numerous users notice that their console sounds a lot louder than typical and/or feels very warm to the touch prior to the Playstation 3 yellow light issue developing. These are truly very good indicators that the method is overheating and if you can repair the difficulty proper away the flashing lights may possibly really be avoided!
When you have cleaned dust off of your console and placed it in an place wherever it is not obstructed, it is time to attempt a couple fast fixes:

Unplug the console from the wall for half an hour, then plug it back in.

Get rid of the difficult drive and replace.

Check all wires and connections to the console.

If you can get a tough drive from an individual else which you know works, you will decide appropriate away if you can replace the hard drive to fix yellow light of death difficulty. In most situations, there will be a lot more substantial damage internally which will demand you to either send the console in to Sony or understand how to fix the Playstation three yellow light blinking difficulty on your very own.

Undertaking it on your very own is much more quickly and will expense you much less. Some online programs offer you in depth video directions that walk you through it in less than an hour and some will even supply some extra bonuses that make your technique more functional as soon as the dilemma is fixed.

The only purpose to ever pay the shipping to Sony is if you have a valid warranty that will pay for the repairs fully. Otherwise, you can do it less expensive and a lot, significantly quicker by using a good online program with video instruction.
If you don’t know how to repair your ps3 yellow light of death error, than it is really tough to repair it. But, if you know how to repair the problem, it’s getting easier. For these who do not know how you can repair the error, take an appear below. I’ve put up ideas and options for you and all work to fix the issue you got on your playstation 3.

How to fix ps3 yellow light of death three. guidelines initial

1)Turn off your playstation 3. If you feel your ps3 has been caught by the heat, then wait at least 20 minutes and put it back on once again

2) Examine if there’s any loose cable.

3) Attempt to put out your playstation’s hard-drive, and put it back in. You may want to repeat this 2-three times for much better final results.

If this did not perform, then there are two options left for you on how to fix your ps3 secure and quickly!

Send your playstation three back to Sony

You might think that this is an excellent alternative, but take a look at some statistics. Most users had to wait at least 4-six weeks ahead of they had their Console back. And also, if your warranty is expired, you have to spend a large fat $150,- to get the job done! Does this still sound as a good option?

The last alternative is to repair your console by yourself.

When you fix the yellow light error by your self, you will take control in your own hands. Meaning that you choose how much it charges and that you choose how lengthy it will take to fix it. This is the greatest and most suggested way to fix your ps3 savefully and quick! Users who didn’t know an issue about Hardware, have fixed it within 1 hour with the use of a repair guide. You should really use a manual due to the fact if you don’t, it will be guess perform.

Because recession began in 2008, flexibility has been key to keeping continuous employment for many mixed up in property industry. For some it has meant being pragmatic about standard of appointment, for example choosing a position a rung or maybe two below your last job to stay gainfully employed. For others it really is has meant utilising transferable skills within related sub sectors therefore we have seen former auctions try their hand concerning selling new homes directly on a developer and vice versa. Selling new homes or selling second-hand; what’s the difference?

Office versus showhouse
For several new homes sales negotiators work is really a lonely place. Most sites are solo manned and interaction come primarily from potential clients visiting the site and check in calls on interested occasions. They see the sales manager now and again but their immediate peers are on other sites surrounding the region. Compared to the estate agents office this is a quiet working existence. You don’t have office banter or watercooler discuss last nights TV.

New versus second hand

Similarly, an agent will usually get generous kickbacks once they pass buyers onto lawyers and surveyors they can regularly work with. An added advantage regarding using lawyers and surveyors referred to by the agent is that they may tend to overlook difficulty with properties to enable sales to check. In any town or even just areas of a locale, most agents, lawyers and surveyors may have worked together prior to now and none will want to upset many of the others. So even every time a buyer believes their legal representative and surveyor are representing their interests, it’s likely that this lawyer and surveyor may well be more sensitive about ensuring continuing a very good relationship with the estate agent and not just worrying about the needs of a buyer that they will probably never deal by means of again. When I started to question both my attorney at law and surveyor about things that were there apparently ‘overlooked’, the legal counsel paid me ? 6, 000 plus the surveyor ? 2, 500 – this could have been because they were terribly nice people and really liked me; or it seemed to be because they realised its cosy little arrangement while using estate agent had been rumbled and so were keen to avert any possibly embarrassing explanations. Any buyer who gets caught from the spider’s web of the agent’s business associates could find it a very steeply-priced experience.

Remember OEAs offer all the same services as High Street agents and they also advertise on all the particular major online property forums. There is no change in quality or services. Just in price.

Even if a buyer has fund available, an agent might show buyers that ‘it’s company policy’ so all buyers get the best quality loan deals available thus, whether you want the idea or not, the agent makes an appointment for one to meet a mortgage jeweler with business connections to your agency.
Similarly, an agent will most likely get generous kickbacks once they pass buyers onto lawyers and surveyors them to regularly work with. An added advantage of using lawyers and surveyors known to the agent is that they’ll tend to overlook reactions to properties to enable sales to plod through. In any town or maybe even areas of a locale, most agents, lawyers and surveyors should have worked together historically and none will want to upset many of the others. So even every buyer believes their lawyer and surveyor are which represent their interests, it’s likely that the lawyer and surveyor will be more sensitive about ensuring continuing a good quality relationship with the estate agent in lieu of worrying about the hobbies and interests of a buyer that they need to probably never deal along with.
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Cold calls will bring you success on the markets; it is as simple as that. The more calls you will make the better you’ll be at the process and before long you’ll have converted more appointments so because of this more listings.

Show me an effective salesperson making 25 or further real cold calls to new contacts per day, and I will tell you someone who is earning or gonna earn big commissions because of good property listings.

So the time does this success receive? You will start to discover results from cold calling from month or so just like you get more meetings through fresh prospects. Importantly it’s important to keep up the calling process without stop. This is at which most salespeople struggle; they furnish up or lack the discipline you need to do it every day.

When one make cold calls to help you anyone, the reality is that you’re most likely an interruption to your partner, and most of us don’t especially like to be seen for being an interruption. That is why most salespeople are able to return a call right from an enquiry, but less happy to make an outbound call to come up with a prospect or a gathering.

To be successful at cold calling you might want to develop the following:
A mindset that you will be calling to see that the person has a legitimate need or wants assist. If they do not then that may be fine, you simple go forward.
A professional dialogue to create the call that is founded on the words that you receive and not some script that arises from others and is uncomfortable if you want to talk through.
A relaxed approach to conversation and calling. With regard to this process try upright at the telephone any time you make your calls. It may help greatly with the conversation as well as the conversions.

A confident tool for turning around negative responses once you will almost always find some in each call. It takes about 2 or 3 negatives to arrive at a positive point of discussion within the cold call. When you’re free to a positive you can generate a meeting to talk further.

Do not sell your services on the telephone; simply try for a gathering and only if your partner has an interest or perhaps a need. You do not envy meeting with people that might waste your time.

Out of 6 to 8 appointments you need to be converting at least you to a new listing. Should you have more listings you convey more sales and commissions.
Most salespeople will agree they have little time to spare around the average business day. Hence, and to be prosperous in cold calling cautious very diligent and encouraged yourself. The only person who can build success on and from cold phone is you. It takes you about 21 days to construct your calling process into every day and keep it effective.

A person has a fabulous personality; a person is a positive reminder of another, since it is claimed that experience just triggers a memory of the similar experience, so we’re never really experiencing a little something new. A friendly, insightful, salesperson or cold naming person, who makes one smile with her satisfied demeanor, wit and identity style, is probably going to undertake a bigger impact on you than a banner on a web site.

There are the odd occasions were an advertisement is indeed hugely phenomenal that it blows almost everything else out of the stream… but those occasions are rare.
I would imagine that the best way forward is to hit the prospective from all angles. The item. the Internet and your letterbox… but use intelligent campaigns, relational, dynamic telemarketers and lead generation companies to uncover the target for you.

With a great many options and businesses bored with being bombarded with freezing callers: the fad within the 80′s and 90′s, prospecting companies are your best advance. They find your target groups and provide you with data of potential customers that genuinely wish to hear from you. Laying the groundwork some people literally pave the technique to close that deal.
Things have got over them from cold calling, to telemarketing yourself with random data also now towards lead generation

corporations… the Internet cannot kill the human require for interaction, in a way them promotes it but

Fine, you did your homework and got the ideal kayak – now it’s good to make another decision. How can you transport your new kayak?
Some kayaks really are heavy and cumbersome – certainly rigged fishing kayaks.

You’ll need to position some thought into what is the best transport method available for you, your kayak, and your car. Various vehicles will construct different situations to take care of. For instance, if you have an incredibly tall vehicle it most likely is not practical for you to be able to load your kayak on top – maybe a trailer is the ideal solution, or a Hullavator. Maybe you have a health problem or a personal injury that will prevent anyone from lifting a kayak. Or you just don’t think lifting a 60+ lb kayak over your mouth.

All of these issues might be addressed.

Let’s go over several of the different methods to carry around your kayak(s).

Transport Methods

Rack Systems

Most kayak transport needs are usually satisfied by adding any after-market rack system. A rack system comprises the bars and little feet (adapters) that attach the device to your particular automobile. The bars can be used alone or they can serve when the base for additional kayak carriers and accessories. The preferred systems are made just by Thule and Yakima. A majority of these racks offer the most weight capacity so are the safest way to move kayaks on a car.

Factory Racks

Many vehicles incorporate factory bars (usually typically the flat oblong shaped ones) and these can do fine to transport your kayak and can usually be fitted together with most kayak carriers, however lack the carrying capacity and long term strength of a decent after-market rack system. So whenever you carry multiple kayaks or maybe even one heavy single kayak, getting a good rack system could be your best option.

Rack Pads

Rack Pads were originally devised for surfboards but work properly for kayaks. The pads wrap close to your factory or after-market bars and so are held in place by Velcro straps. Rack pads are a very good choice if you carry around you kayak face along (the seat area dealing with the roof), by carrying face down you might be placing the load relating to the gunwales (the strongest an area of the kayak) and it stands out as the way many kayak companies recommend to sling the kayak to hinder distorting or damaging any hull.

Pros: Like polyurethane foam blocks, it can manifest as a very economical set together, especially if you already have bars on your used car. Unlike foam blocks stand pads can’t fly away from the vehicle.

Cons: Pads usually don’t have numerous cushion and can damage some kayaks if transported when using the hull down or if you over tighten the tie-down connectors.

Cradles and Saddles: An awfully popular way to carry a kayak that will carry the kayak most suitable side up (just enjoy it is on the water). Some examples of these are the Thule Set-To-Go and then the Malone Seawing.
Pros: These have a tendency to keep kayak in destination and protect the hull with damage. These systems usually are very effective with other parts that aid in delivering your kayak on your used car like rollers and glide pads (we will talk over these later).

Cons: These set-ups are made to transport your kayak ideal side up, not the ideal method for preventing distortion, but with care this isn’t going to be an issue. Also, if you’ll transport 2 kayaks, cradles do limit the usable space for your rack bars.
J-Carriers: These work by carrying your kayak(s) on their side in J-shaped shelving.

Many people assume that when the weather commences acquiring wintry and also the
actually leaves start to autumn, it really is set aside the actual farming resources and also delay
until finally subsequent early spring to your workplace with their backyard garden again. Completely wrong. The winter season is definitely an
vital time for you to take care of your garden’s health and reassure your own beneficial
crop intended for the coming year. It might seem that might decide to try lengthy to get ready ones
garden, but the truth is that it takes lower than at some point to ready your own
backyard for any upcoming winter months.

In the event the night time heat shed so that you can fewer than forty-five qualifications
Fahrenheit more than some a short time consecutively, or maybe ice is forecast to get
your city (generally all-around overdue March or December) you realize its time so that you can
begin planning garden. Make sure you start with checking a garden
layout, check out that plant life increased effectively prior to now period, plus which will flowers
didn’t do well. Slide is a great time and energy to pick which crops will always be in
you back garden next season, in addition to which ones runs.

It’s also fun to determine which usually completely new facilities you intend to develop. In order to
build your backyard much more colorful plus healthy, make certain only to vegetable the more
sturdy vegetation during the slide so that they can resist winter months. Several
plants that can carry out fine getting rooted within drop are: rudbeckia, Aster
Novi-belgii, Anemone Japonica, panicle hyandea, endive, escarole, in addition to
Brussels pals. You can get many of these and a lot more within gardener
magazines as well as the local baby’s room.

After you have done this kind of make sure you start clearing garden.
Begin with pulling out weeds which could include clipped in place, as well as raking gone down
departs. Unwanted weeds in addition to rotten departs can contain pests and also ailments which may
always be bad for your garden. It’s also wise to remove your garden of put in once-a-year
plant life, and also reap your produce along with vegetation that cannot resist
the wintertime weather conditions. Immediately after autumn originates along with eliminated, the foliage might be out of
the trees and you may begin to see the spoiled offices. Cutting over undesired
offices through your trees isn’t really necessary to a person’s back yards health, yet may well
help down the line by way of not necessarily falling organizations for your plant life without blocking as well
much of sunshine.

Should you have newer woods consider covering these along with supporting
them pegs to assist them pull through a bitterly cold winter the wind and cool. Placing
compost around the backyard for the wintertime generally is a handy technique to shield
facilities coming from abrupt temps changes and heavy ideal. With regard to compost you are able to
employ about a few inches width connected with shredded bark, wood fine needles, or simply a variety of
other materials. You have to be cautious to never compost too early, because
a few insect pests might still be alive as well as capable of taking shelter within it to the
winter season.

Thoughts is broken finished a person’s farming gear you must fresh these folks as well as
get them to be within a safe place where by they don’t decay and also you learn
exactly where they will be to get buy. Before the winter season happens you should arranged
outside slug resilient, while slugs are some of the worst insects to own in your
back garden. If you have a swimming pool and also fountain in the lawn, you’ll want to take out
every bass that you have inside them and produce these on the inside. There’s next to nothing
sadder than just a bass iced in a very block involving glaciers.

Blow up or inflatable whitewater kayaks are the perfect choice for whitewater kayaking sports. They are easy to carry, comfortable and convenient for the whole family to use. There are a myriad of choices for inflatable whitewater kayaks depending on your budget and how many people you want to sit in the boat. And of course, the seaworthiness of the vessel must be taken into consideration. Brands such as Sevylor and Sea Eagle offer sturdy vessels that last a long time and feature innovative designs that can be used in whitewater. There are kayaks that are as low as $120+ and as high as $1000+.

Inflatable whitewater kayaks are growing in popularity because are known for their durability and their easy carry feature. If we were to compare inflatable kayaks to the traditional hard-shell kayaks, you don’t have to worry about the space your kayak will take in the car because it is inflated and deflated with an action pump. That also saves money and instead of paying for a locker for a hard-shell kayak, the inflatable can be taken home. The user can put the kayak away into a neat compact bag and its weight ranges from 25-30 pounds. The user can even bring the deflated kayak onboard an airplane. Inflatable kayaks have the convenience of being inflated within a few minutes and deflate it just as easy once done.

Most blowup whitewater kayaks are made of sturdy PVC plastic and high grade nylon that can hold up to capacities of as much as 400 pounds. Aside from the weight the kayak can carry, certain blow up whitewater kayaks such as the Sea Eagle 330 can handle Class III whitewater. The Sea Eagle model as well as the Innova K1 whitewater canoe have self-bailing properties that prevent water from filling the boat.

Inflatable kayaks may have several drawbacks in that its lightweight feature causes the vessel to be easily caught by the air, making the maneuverability of the vessel quite difficult for the user. This is expected of a lightweight vessel. Some boats come with a skeg but some require the separate purchase of one. The skeg will increase the trackability of the vessel as well as the maneuverability and decrease the unwanted wandering and weaving of the vessel.

Extensive research of each brand and product will help in choosing the correct model and type that corresponds to use and budget. There are a few things to keep in mind when purchasing an inflatable kayak. The size and shape, stability and speed and maneuverability of the kayak will determine the purchase. For whitewater kayaking, look for a river running style inflatable with self-bailing holes and knee-strap anchors to handle the harshness of whitewater. Recreational kayaks are used on a more flat-water, calm and slow-moving rivers so check the quality and durability of the materials.

The design of the hull will determine the stability and stability affects speeds. A wider boat is more stable than a narrow-bodied vessel. A V-shaped hull will aid in tracking. A high air pressure or multiple side tubes on the inflatable makes a stiffer hull for better performance. Tie-down gear, net bags, rope lacing and storage compartments are useful for long distant trips. Spray skirts must be included to keep dry and protected. An outdoor patio provides additional rigidity and dryness and warmth is guaranteed for the trekker in nastier conditions.

Know the kayak’s controllability and how easily the boat will turn and track. It can get rough in the water and high quality inflatable kayaks with good hull designs and high air pressure will hold the inflatable kayak’s shape and have stable and controllable performance.

Whitewater kayaking needs a certain level of precaution and safety. Whitewater rafting is a challenging recreational outdoor activity and the inflatable whitewater kayak that is purchased must match the challenge. Whitewater rafting is considered an extreme sport and it can be dangerous. An awareness of the boat’s dynamics and basic safety knowledge will aid the kayaker in staying safe while having fun.

Inflatable kayaks do stand the test of time with the proper use and storage. Taking care of the vessel must be practiced so that the blowup whitewater kayak will last. Allowing the vessel to dry out completely before storing prevents the formation of mildew which can further erode the material and damage it.

In general, for individuals that have a love for the outdoor, a purchase of an inflatable whitewater kayak is worth the purchase. An extensive research of each brand and product will help in choosing the correct model and type that corresponds to use and budget. But as far as popular brands go – names such as Advanced Elements, Sea Eagle and Sevylor – all produce quality inflatable whitewater kayaks that can be enjoyed by the kayak enthusiast.

Seeking at riding lawnmowers from a buyer’s angle, I tried to list my expectations. Firstly, the mower ought to do what it’s meant to do, i.e., mow lawns efficiently. Subsequent, it need to fulfill the promise the seller can make to potential customers. And most importantly, the price should be reasonable and competitive.

Cutting a prolonged story quick, I zeroed in on a common brand of lawn mowers – Husqvarna.If you are lazy, the auto mower may truly make you lazier nevertheless, as it does every thing for you. You do not have to walk behind or ride a mower. All you have to do is make a boundary by pinning a wire to the ground. Then you place the car mower in the middle and it mows.

If you believe a tree on your lawn specifically with roots above the ground may possibly harm your automobile mower, the manufacturer assures not to worry. The collision sensors, they say, not only stop it, but also support reverse the mower when it comes lightly in contact with objects. (I invite anyone with actual expertise to testify this.

The operating price is relatively low. Depending on the size of the lawn it may possibly price up to $25 per year for electrical energy. Also, it is emission-cost-free and tends to make nearly no noise.

What About Upkeep? Warranty? Accessories?

Northern Tool delivers toll totally free tech assistance via its 50 outlets in 11 states. So, you have spares and service within straightforward reach, with a 2 – 3 many years extendable warranty, for parts and labor. Also, you can pick from a wide assortment of accessories: lawn aerators, tail mowers, tow behind sprayers, tow behind lawn sweeps, manure spreaders and industrial tools trailer carts.

How very good are they truly, taking all aspects into account?

Well-liked Mechanics has rated Husqvarna the greatest mower of 20011.

When you are seeking to buy a lawnmower, you really should consider hunting at utilised riding lawnmowers. There are three substantial causes to consider acquiring used more than new.

1. Time Cost savings. Employing a riding mower allows you to mow the lawn in a fraction of the time you would want if you were using a push mower. Whilst you won’t get the exercise you would if you had been employing a push mower, the shorter volume of time essential to comprehensive the job implies that you are a lot more likely to get out there and mow your lawn.

2. Price. Expense is an issue when acquiring any item, specifically big ticket products. Utilized riding lawnmowers are a fraction of the cost of new mowers. Given that the new mowers can expense over $five,000, it can make sense to consider acquiring an employed riding lawnmower as a substitute of purchasing new.

Yard function is a truth of life for most homeowners. If you are in the marketplace for a mower, you need to think about utilised riding lawnmowers. A riding mower will alter your life for the far better.

And best of all they are about to come out with a ride on electrical mower with as considerably electrical power as a conventional petrol mower, with only half the noise. Itcan be charged in 16 hours which will run the mower for 1.five hours. This is the first electrical ride on mower on the market and plans to be sold for $3,299 at Home Depot shops and Ariens dealerships starting in May 2009. Ariens’ market research showed that customers desired an all-electrical riding mower, for environmental factors, and they also wanted a mower that was quieter and made less vibration, stated Dan Ariens, organization president.”Those shoppers are all over the place.

I do not consider that regulations have to drive the alternatives that folks make,” he mentioned.

A lawn mover is a machine that is utilised to cut lawn evenly. The report covers brief synopsis on stroll behind mowers that incorporate push gas mowers and self propelled, along with corded electric, cordless, and manual reel mowers. Evaluations advocate stroll behind lawn for locations up to about half an acre in size. Robotic mowers can take care of larger lawns. For the greatest lawns, riding mowers and lawn tractors are best.
According to not long ago conducted best lawn mower evaluations at Australian consumer reports, where fifty electrical and gas mowers went by way of rigorous tests, the assessment rates each lawn mower on its functions and capability to cut grass at an even length, as properly as its performance in handling grass clippings this kind of as bagging, mulching, and side-discharging. In addition, the mowers are tested for adaptability and rated for overall use. The brand repair records are primarily based on annual poll of readers.

Mowers can final for decades and need far much less upkeep than any form of powered mower.
They are the least expensive and extremely tough option. They are very best for the surroundings as well. When kept oiled and sharpened, they can serve you for decades. Nonetheless, mostly users say that they are suggested for extremely tiny yards.

Among gas lawn mowers, Toro, Honda, and, Lawn-Boy normally rank near the best in reviews. Craftsman and MTD produced manufacturers like Cub Cadet, Bolens, Troy-Bilt, or Yard Machines normally rank reduce. The fairly new Troy-Bilt XP series is fetching good reviews.
Comparison reviews are dependable guides to lawn mowers performance, reliability, noise, and ease of use. They also propose that lawn mowers though priced the identical: with similar attributes, but vary enormously in handling grass clippings in different modes. With numerous mowers available in the industry, it is essential to examine the various brands to choose the proper 1 for your individual requirements. Reliability, efficiency, and durability are the most crucial elements that you should consider when hunting for a gardening power tool for your lawn. It will aid in producing a final determination on which mower to choose.
The Husqvarna riding lawn mower is developing in popularity, and there are basically a number of various variations and models of this brand of lawn mower as nicely. The Husqvarna lawn mower is reasonable and reasonably priced in cost, and there are a lot of spots in which these mowers can be purchased.

So if you are looking for a mower that will do the task and final a prolonged time then the Husqvarna lawn mower could be the one for mowing your yard.

Randomized (complete) block design: An experimental design in which the treatments in each block are assigned to the experimental units in random order. Blocks are all of the same size and each treatment appears in the same number of times within each block (usually once). A different level of the factor is assigned to each member of the block randomly. The data can be analyzed using the paired t-test (when there are two units per block) or by randomized block ANOVA (in blocks of any size). The results are substantially more precise than a completely randomized design of comparable size. In studies with a block design more assumptions are required for the model: no interactions between treatments and blocks and constant variance from block to block.

Random sampling: A method of selecting a sample from a target population or study base using simple or systematic random methods. In random sampling each subject in the target population has equal chance of being selected to the sample. Sampling is a crucially important point in selection of controls for a case-control study. By randomization systematic effects are turned into error (term) and there is an expected balancing out effect: known and unknown factors that might influence the outcome are assigned equally to the comparison groups. One disadvantage of randomization is generation of a potentially large error term. This can be avoided by using a block design. See Basic Concepts of Sampling and

R2 (R-squared): See Multiple regression correlation coefficient and Pearson’s correlation coefficient (for r2).

Quantitative: Quantitative variables are variables for which a numeric value representing an amount is measured. They may be discrete (for example taking values of integers) or continuous (such as weight height blood pressure). If a quantitative variable is categorized it becomes an ordinal variable.

Qualitative: Qualitative (categorical) variables define different categories or classes of an attribute. Examples are gender blood groups or disease states. A qualitative (categorical) variable may be nominal or ordinal. When there are only two categories it is termed binary (like sex dead or alive).

Proportional odds ratio: When the response variable in an ordered/ordinal logistic regression model has more than two ordered response categories odds ratio obtained for each category is called a proportional odds ratio. See UCLA Stata: Ordinal Logistic Regression; Lecture note on Logistic Regression.

Probability vector: Any vector with non-negative entries whose sum is equal to 1.0. See Wikipedia.

Probability distribution function: A function which gives for each number x the probability that the value of a continuous random variable X is less than or equal to x. For discrete random variables the probability distribution function is given as the probability associated with each possible discrete value of the variable.

Probability density function: When a curve is used to model the variation in a population and the total area between the curve and the x-axis is 1 then the function that defines the curve is a probability density function.

Probability: The ratio of the number of likely outcomes to the number of possible outcomes.

Prevented fraction: The amount of a health problem that actually has been prevented by a prevention strategy in real world.

Predictive value: The probability that a person with a positive test if affected by the disease (positive predictive value) or the probability that a person with a negative test does not have the disease (negative predictive value). Estimation requires sensitivity specificity and disease prevalence.

Predictor (explanatory independent) variable: The variable already in hand

Power of a statistical test: See Statistical Power.

Post hoc test: A test following another one. The most common example is performing multiple comparisons between groups when the overall comparison between groups shows a significant difference. For example when an ANOVA analysis yields a small P value post hoc tests (such as Newman-Keuls Duncan’s or Dunnett’s tests) are done to narrow down exactly which pairs differ most significantly (similarly Dunn’s test is done in a non-parametric ANOVA setting) (

Positive predictive value: Probability of a true positive as in a person identified as diseased by a test is really diseased (see also negative predictive value).

Population stratification (substructure):

Population attributable risk: The proportion of a disease in a specified population attributable to a specific factor (such as a genetic risk factor).

Population: The population is the universe of all the objects from which a sample could be drawn for an experiment.

Polytomous variable: A variable with more than two levels. If there are two levels it is called dichotomous (as in the most common form of logistic regression).

Polynomial: A sum of multiples of integer powers of a variable. The highest power in the expression (n) is the degree of the polynomial. When n=1 for example f(x)=2×1+3 this is a linear expression. If n=2 it is quadratic (for example x2 + 2x + 4); if n=3 it is cubic if n=4 it is quartic and if n=5 it is quintic.

Poisson regression: Analysis of the relationship between an observed count with a Poisson distribution (i.e. outcome variable) and a set of explanatory variables. In general it is appropriate to fit a Poisson model to the data if the sample size is > 100 and the mean for the occurrence of the event is <0.10xN.

Poisson distribution: The probability distribution of the number of (rare) occurrences of some random event in an interval of time or space. Poisson distribution is used to represent distribution of counts like number of defects in a piece of material customer arrivals insurance claims incoming telephone calls or alpha particles emitted. A transformation that often changes Poisson data approximately normal is the square root. See

Pharmacoepidemiology: Application of epidemiological reasoning methods and knowledge to the study of the uses and effects (beneficial and adverse) of drugs in human populations. A relatively new field in epidemiology becoming more closely related to pharmacogenetics. See a review on statistical analysis of pharmacoepidemiological case-control studies (Ashby 1998).

Pearson’s correlation coefficient (r): A measure of the strength of the ‘linear’ relationship between two quantitative variables. A major assumption is the normal distribution of variables. If this is not met (for example due to outliers) the non-parametric equivalent Spearman’s rank correlation should be used. The r represents

Parsimonious: The simplest plausible model with the fewest possible number of variables.

Parameter: A numerical characteristic of a population specifying a distribution model (such as normal or Poisson distribution). This may be the mean variance degrees of freedom the probability of a success in a binomial distribution etc.

Overmatching: When cases and controls are matched by an unnecessary non-confounding variable this is called overmatching and causes underestimation of an association. For example matching for a variable strongly correlated with the exposure but not with the outcome will cause loss of efficiency. Another kind of overmatching is matching for a variable which is in the causal chain or closely linked to a factor in the causal chain. This will also obscure evidence for a true association. Finally if a too strict matching scheme is used it will be very hard to find controls for the study. See BMJ Statistics Notes: Matching.

Overfitting: In a multivariable model having more variables than can be justified from sample size. The statistical rule of thumb is to have at least ten subjects for each variable investigated.

Overdispersion: Dispersion is a measure of the extent to which data are spread about an average. Overdispersion is the situation that occurs most frequently in Poisson and binomial regression when variance is much higher than the mean (normally it should be similar). It is evident with a high (>2) residual mean deviance (which should normally be around one) and the presence of too many outliers. The reasons for overdispersion may be outliers misspecification of the model variation between the response probabilities and correlation between the binary responses. It distorts standard error and confidence interval estimations. In the analysis overdispersion may be taken into account by estimating a dispersion parameter.

Outlier: An extreme observations that is well separated from the remainder of the data. In regression analysis not all outlying values will have an influence on the fitted function. Those outlying with regard to their X values (high leverage) and those with Y values that are not consistent with the regression relation for the other values (high residual) are expected to be influential. The test the influence of such values the Cook statistics is used.

Outcome (response dependent) variable: The observed variable which is shown on y axis. A statistical model shows this as a function of predictor variable(s).

Ordinal variable: An ordered (ranked) qualitative/categorical variable. The degree of HLA matching (one two three or four antigen matching in two loci) in transplant pairs or HLA sharing in parents (one-to-four shared antigens) are ordinal variables although the increments do not have to be equal in magnitude (see interval and ratio variables). An ordinal variable may be a categorized quantitative variable. When two groups are compared for an ordinal variable it is inappropriate to use ordinary Chi-squared test but the trend test or its equivalents must be used.

One-way ANOVA: A comparison of several groups of observations all of which are independent and subjected to different levels of a single treatment (such as cells exposed to different dosage of a growth factor). It may be that different groups were exposed to the same treatment (different cell types exposed to a new agent). The main interest focuses on the differences among the means of groups.

Omnibus test: If the chi-square test has more than one degree of freedom (larger than 2×2 table) it is called an ‘omnibus’ test which evaluates the significance of an overall hypothesis containing multiple sub-hypotheses (these multiple sub-hypotheses then need to be tested using follow up tests).

Offset: A fixed already known regression coefficient included in a generalized linear model (which does not have to be estimated).

Odds ratio (OR): Also known as relative odds and approximate relative risk. It is the ratio of the odds of the risk factor in a diseased group and in a non-diseased (control) group (the ratio of the frequency of presence / absence of the marker in cases to the frequency of presence / absence of the marker in controls). The interpretation of the OR is that the risk factor increases the odds of the disease ‘OR’ times. OR is used in retrospective case-control studies (relative risk (RR) is the ratio of proportions in two groups which can be estimated in a prospective -cohort- study). These two and relative hazard (or hazard ratio) are measures of the strength/magnitude of an association. As opposed to the P value these do not change with the sample size. OR and RR are considered interchangeable when certain assumptions are met especially for large samples and rare diseases. Odds ratio is calculated as ad/bc where abcd are the entries in a 2×2 contingency table (hence the alternative definition as the cross-product ratio). In logistic regression the coefficient

Odds multiplier: In logistic regression

Odds: The odds of a success is defined as the ratio of the probability of a success to the probability of a failure (p/(1-p)). If a team has a probability of 0.6 of winning the championship the odds for winning is 0.6/(1-0.6) = 3:2. Similarly the odd in a case-control study is the frequency of the presence of the marker divided by the frequency of absence of the marker (in cases or controls separately). The link function logit (or logistic) is the loge of the odds.

Number needed to treat:

Null model: A model in which all parameters except the intercept are 0. It is also called the intercept-only model. The null model in linear regression is that the slope is 0 so that the predicted value of Y is the mean of Y for all values of X. The F test for the linear regression tests whether the slope is significantly different from 0 which is equivalent to testing whether the fit using non-zero slope is significantly better than the null model with 0 slope.

Normal probability plot of the residuals: A diagnostic test for the assumption of normal distribution of residuals in linear regression models. Each residual is plotted against its expected value under normality. A plot that is nearly linear suggests normal distribution of the residuals. A plot that obviously departs from linearity suggests that the error distribution is not normal.

Normal distribution(Gaussian distribution) is a model for values on a continuous scale. A normal distribution can be completely described by two parameters: mean (

Nonparametric methods(distribution free methods): Statistical methods to analyze data from populations which do not assume a particular population distribution. Mann-Whitney U test Kruskal-Wallis test and Wilcoxon’s (T) test are examples. Such tests do not assume a distribution of the data specified by certain parameters (such as mean or variance). For example one of the assumptions of the Student’s t-test and ANOVA is normal distribution of the data. If this is not valid a non-parametric equivalent must be used. If a wrong choice of test has been made it does not matter very much if the sample size is large (a non-parametric test can be used where a parametric test might have been used but a parametric test can only be used when the assumptions are met). For a small sample size non-parametric tests tend to give a larger P value. In general parametric tests are more robust more complicated to compute and have greater power efficiency. Parametric tests compare parameters such as the mean in t-test and variance in F-test as opposed to non-parametric tests that compare distributions. Nonparametric methods are most appropriate when the sample sizes are small. In large (e.g. n > 100) data sets it makes little sense to use nonparametric statistics (a tutorial on Parametric vs Nonparametric Methods; Review of Nonparametric Tests in Intuitive Biostatistics; Nonparametric Tests for Ordinal Data at Vassar).

Nonlinear Regression: Regression analysis in which the fitted (predicted) value of the response variable is a nonlinear function of one or more X variables. GraphPad Guide to Nonlinear Regression Introduction to Nonlinear Regression A GraphPad Practical Guide to Curve Fitting.

Nominal variable: A qualitative variable defined by mutually exclusive unordered categories such as blood groups races sex etc. (see also ordinal variable).

Nested model: Models that are related where one model is an extension of the other.

Negative predictive value: Probability of a true negative as in a person identified healthy by a test is really free from the disease (see also positive predictive value).

Natural (raw) residuals: The difference between the observed (Yi) and fitted values (Yi-hat) of the response variable in regression. To obtain the standardized residual this value is divided by its estimated standard deviation. Other residual types are Pearson residual deviance residual and deletion residual. In all cases a relatively large residual indicates an observation poorly fitted by the model. The one that is most closely related to maximum likelihood estimation (i.e. generalized linear models) is the standardized deviance residual (which is equal to the standardized Pearson residual in normal linear models).

Multivariate analysis of variance (MANOVA): An extension of Hotelling’s T2 test to more than two groups with related ‘multiple’ outcome measures. Groups are compared on all variables simultaneously as a global test (rather than one-by-one as ANOVA does). See also multivariate analysis; MANOVA on Stata.

Multivariate analysis: Methods to deal with more than one related ‘outcome/dependent variable’ (like two outcome measures from the same individual) simultaneously with adjustment for multiple confounding variables (covariates). When there is more than one dependent variable it is inappropriate to do a series of univariate tests. Hotelling’s T2 test is used when there are two groups (like cases and controls) with multiple dependent measures (may be more than two) and multivariate analysis of variance (MANOVA) is used for more than two groups. Wilks’ lambda is the most common parameter used to quantitate the significance of the result of a multivariate procedure (others are Roy’s largest criterion Hotelling-Lawley trace and Pillai-Bartlett trace). Unfortunately the word ‘multivariate’ is most frequently used instead of ‘multivariable’ analysis (which means multiple independent/explanatory variables but one outcome/dependent variable;

Multivariable analysis: As opposed to univariable analysis statistical analysis performed in the presence of more than one explanatory variable to determine the relative contributions of each to a single event is (or should be) called multivariable analysis (in practice however it is called univariate and multivariate analysis more frequently). It is a method to simultaneously assess contributions of multiple variables or adjust for the effects of confounders. Multiple linear regression multiple logistic regression proportional hazards analysis are examples of multivariable analysis which has no similarity whatsoever to multivariate analysis

Multiplication rule: The probability of two or more statistically independent events all occurring is equal to the product of their individual probabilities. If the probability of having trisomy 21 is a and trisomy 6 is b assuming independence of these two events for a baby the probability of having both trisomies is (a x b). One of the most critical errors of judgment in the use of independence assumption relates to a court case in the UK (Watkins 2000). (See also addition rule.)

Multiple regression correlation coefficient (R2 – R-squared): R2 is a measure of the proportion of variability explained by or due to the regression (linear relationship) in a sample of data (equal to the percentage of variance accounted for). It is a measure of the effect of X in reducing the uncertainty in predicting Y. The R2 statistic is given by R2 = s.s. (regression) / s.s. (total) [i.e. ESS/TSS] where s.s. is the sum of squares. It is also called the coefficient of determination. When all observations fall on the fitted regression line then s.s. (residual) = 0; and ESS=TSS; thus R2 = 1. When the fitted regression line is horizontal (

Multiple regression: To quantify the relationship between several independent (explanatory) variables and a dependent (outcome) variable. The coefficients (

Multicolinearity: In multiple regression two or more X variables are colinear if they show strong linear relationships. This makes estimation of regression coefficients impossible. It can also produce unexpectedly large estimated standard errors for the coefficients of the X variables involved. This is why an exploratory analysis of the data should be first done to see if any collinearity among explanatory variables exists. Multicolinearity is suggested by non-significant results in individual tests on the regression coefficients for important explanatory (predictor) variables. Multicolinearity may make the determination of the main predictor variable having an effect on the outcome difficult.

Monte Carlo trial: Studying a complex relationship difficult to solve by mathematical analysis by means of computer simulations. An online book on

Model building: The traditional approach to statistical model building is to find the most parsimonious model that still explains the data. The more variables included in a model (overfitting) the more likely it becomes mathematically unstable the greater the estimated standard errors become and the more dependent the model becomes on the observed data. Choosing the most adequate and minimal number of explanatory variables helps to find out the main sources of influence on the response variable and increases the predictive ability of the model. Ideally there should be more than 10 observations for each variable in the model. The usual procedures used in variable selection in regression analysis are: univariate analysis of each variable (using

Mode: The observed value that occurs with the greatest frequency. The mode is not influenced by small numbers of extreme values.

Metropolis-Hastings algorithms: These algorithms are a class of Markov chains which are commonly used to perform large scale calculations and simulations in Physics and Statistics. See Metropolis-Hastings Applet. See Markov Chain Monte Carlo methods.

Meta-analysis: A systematic approach yielding an overall answer by analyzing a set of studies that address a related question. This approach is best suited to questions which remain unanswered after a series of studies. Meta-analysis provides a weighted average of the measure of effect (such as odds ratio). The rationale is to increase the power by analyzing the sets of data. The selection of studies to include in a meta-analysis study is the main problem with this approach. Funnel Plot is an informal method to assess the effect of publication bias in this context. See also Introduction to Meta-Analysis by the Cochrane Collaboration; Meta-Analysis in Epidemiology by Stroup et al (2000); Methods for Meta-Analysis in Medical Research

Median test: This is a crude version of the Kruskal-Wallis ANOVA in that it assesses the difference in samples in terms of a contingency table. The number of cases in each sample that fall above or below the common median is counted and the Chi-square value for the resulting 2xk samples contingency table is calculated. Under the null hypothesis (all samples come from populations with identical medians) approximately 50% of all cases in each sample are expected to fall above (or below) the common median. The median test is particularly useful when the scale contains artificial limits and many cases fall at either extreme of the scale. In this case the median test is the most appropriate method for comparing samples (Online Median Test).

Median: Another measure of location just like the mean. The value that divides the frequency distribution in half when all data values are listed in order. It is insensitive to small numbers of extreme scores in a distribution. Therefore it is the preferred measure of central tendency for a skewed distribution (in which the mean would be biased) and is usually paired with the interquartile range (dQ) as the accompanying measure of spread. See Martin Bland’s page for calculation of confidence intervals for a median.

Measures of central tendency: These are parameters that characterize an entire distribution. These include mode median and mean.

Measures of association: These measures include the Phi coefficient of association Cramer’s contingency coefficient (C) and V Kendall’s tau-b and (Stuart’s) tau-c Somers’ D (a modification of Kendall’s tau-b) Yule’s Q gamma Spearman’s rank correlation coefficient (rho) Pearson’s correlation coefficient lambda (symmetric and asymmetric) uncertainty coefficients (symmetric and asymmetric) Guttman’s coefficient of predictability (lambda)/Goodman-Kruskal’s lambda Goodman-Kruskal’s gamma and Goodman-Kruskal’s tau (concentration coefficient). See also Measures of Effect-Size & Association; Measures of Association for Cross-tabulations; Measures on SAS STATA SYSTAT; Ennis 2001; Morton 2001.

Mean squares: A sum of squares divided by its associated df is a mean square. In ANOVA the regression (explained) mean square is ESS/k-1 and the residual (error) mean square is RSS/N-k. Note that the mean squares are not additive i.e. they do not add up to TSS/N-1. Importantly the residual (error) mean square is an unbiased estimator of the variance (

Mean(or average): A measure of location for a batch of data values; the sum of all data values divided by the number of elements in the distribution. Its accompanying measure of spread is usually the standard deviation. Unlike the median and the mode it is not appropriate to use the mean to characterize a skewed distribution (see also standard deviation) (

McNemar’s test: A special form of the Chi-squared test used in the analysis of paired (not independent) proportions. This non-parametric test compares two correlated dichotomous responses and finds its most frequent use in situations where the same sample is used to find out the agreement (concordance) of two diagnostic tests or difference (discordance) between two treatments. If the pairs of data points are the measurements on two matched people (such as affected and unaffected siblings) in a case-control study or two measurements on the same person the appropriate test for equality of proportions is the McNemar’s test. It can be used to assess the outcome of two treatments applied to the same individuals or the significance of the agreement between two detection methods of a physical sign. If there are more than two periods of data collection (such as pretest posttest and follow-up) Cochran’s Q test should be used (

Maximum likelihood: This method is a general method of finding estimated values of parameters. It yields values for the unknown parameters which maximize the probability of obtaining the observed values. The estimation process involves considering the observed data values as constants and the parameter to be estimated as a variable and then using differentiation to find the value of the parameter that maximizes the likelihood function. First a likelihood function is set up which expresses the probability of the observed data as a function of the unknown parameters. The maximum likelihood estimators of these parameters are chosen to be those values which maximize this function. The resulting estimators are those which agree most closely with the observed data. This method works best for large samples where it tends to produce estimators with the smallest possible variance. The maximum likelihood estimators are often biased in small samples (see

Markov Chain Monte Carlo(MCMC random walk Monte Carlo) methods: See Wikipedia: MCMC; MCMC Applet; Markov Chain Simulation Applets; Buffon’s Needle Applet; Monte Carlo Methods Links; MCMC Tests of Genetic Equilibrium (Lazzeroni & Lange 1997); Markov Chain Monte Carlo in Practice (Book) and Virtual Labs: Markov Chain (requires MathPlayer). See also Metropolis-Hastings algorithms.

Mantel-Haenszel(also called Cochran-Mantel-Haenszel (CMH) test): Test for a null hypothesis of no overall relationship in a series of 2×2 tables for stratified data derived either from a cohort or a case-control study. It allows analysis of confounding and gives an adjusted odds ratio or relative risk. It can be used on categorical or categorized continuous data. The test is only valid when the variance of observed data is

Mann-Whitney (U) test: A non-parametric test for comparing the distribution of a continuous variable between two independent groups. It is analogous to the independent two-sample t-test so that it can be used when the data are ordinal or not normally distributed. The Wilcoxon signed ranks T-test for independent samples is another non-parametric alternative to the t-test in this context (for paired samples Wilcoxon matched pairs signed rank test should be used) (online Mann-Whitney Test).

Longitudinal data: Data collected over a period of time as in cohort studies. These data are usually analyzed by using survival analysis techniques. See Longitudinal Studies Chapter in Epidemiology for the Uninitiated.

Loglinear model: Multinomial data (from contingency tables) can be fitted by using a generalized linear model with a Poisson response distribution and a log link function. The resulting models for counts in the cells of a contingency table are known as loglinear models in which the logarithm of the expected value of a count variable is modeled as a linear function of parameters. Loglinear models try to model all important associations among all variables. In this respect they are related to ANOVA models for quantitative data. Loglinear modeling allows more than two discrete variables to be analyzed and interactions between any combination of them to be identified. Associations between variables in log-linear models are analogous to interactions in ANOVA models. The aim is to find a small model which achieves a reasonable fit (small residual). Data sets with a binary response (outcome) variable and a set of explanatory variables that are all categorical can be modeled either by logistic regression or by loglinear modeling. More on Loglinear Models and Online Loglinear Test at Vassar College.

Logit transformation: The logit (or logistic) transformation Y of a probability p of an event is the logarithm of the ratio between the probability that the event occurs (p) and that the event does not occur (1-p): Y = ln (p/(1-p)). Thus it is a transformation of a binary (dichotomous) response variable. The logit transformation of p is also known as the log odds of p since it is the logarithm of the odds. There are other link functions for binary response variables.

Logistic (binary) regression: A statistical analysis most frequently models the relationship between a dichotomous (binary) outcome variable (such as diseased or healthy; dead or alive; relapsed or not relapsed) and a set of explanatory variables of any kind (such as age HLA type blood pressure kind of treatment disease stage etc). It can also be used when the outcome variable is polytomous (several categories of the prognosis; including ordinal response ‘ordinal logistic regression’ or ‘proportional odds ratio model’) and when there are several outcome variables (multinomial logistic regression – a special class of loglinear models). Analysis of data from case-control studies via logistic regression can proceed in the same way as cohort studies. See Logistic Regression Lecture Note

Log transformation: This transformation pulls smaller data values apart and brings the larger data values together and closer to the smaller data values (shrinkage effect). Thus it is mostly used to shrink highly positively skewed data.

Log-rank test (of equality across strata): A non-parametric test of significance for the difference between two survival curves (for categorical data). It is a special application of the Mantel-Haenszel test. It can be adjusted for confounders (not preferable to Cox proportional hazard regression which is a semi-parametric model) or performed for trend (for details and parametric alternatives see Lee & Go 1997). It was developed by Mantel and Haenszel as an adaptation of the Mantel-Haenszel

Log 0is undefined. If we need to use a log transformation but some data values are 0 the usual way to get round this problem is to add a small positive quantity (such as 1/2) to all the values before taking logs.

LOD Score: Stands for the logarithm of odds. It is a statistical measure of the likelihood that two genetic markers occur together on the same chromosome and are inherited as a single unit of DNA (co-segregation). The LOD score serves as a test of the null hypothesis of free recombination versus the alternative hypothesis of linkage. Determination of LOD scores requires pedigree analysis and a score of >3 is traditionally taken as evidence for linkage. Linkage is between two genetic loci but not alleles. An example is the linkage between the hemochromatosis gene (HFE) and HLA-A. This means that within the same family all affected subjects will have the same HLA-A allele but not necessarily a particular one i.e. there will be no recombination between HFE and HLA-A. LOD score has nothing to do with linkage disequilibrium.

Link function: A particular function of the expected value of the response variable used in modeling as a linear combination of the explanatory variables. For example logistic regression uses a logit link function rather than the raw expected values of the response variable; and Poisson regression uses the log link function. The response variable values are predicted from a linear combination of explanatory variables which are connected to the response variable via one of these link functions. In the case of the general linear model for a single response variable (a special case of the generalized linear model) the response variable has a normal distribution and the link function is a simple identity function (i.e. the linear combination of values for the predictor variable(s) is not transformed).

Linkage disequilibrium: Also called gametic association which is more appropriate. It means increased probability for two or more alleles to be on the same chromosome at the population level. In a population at equilibrium haplotype frequency is obtained by multiplying the allele frequencies x2. When there is linkage disequilibrium the observed frequency (say by family analysis or sperm typing) is different from the expected frequency. The difference gives the

Linear regression models: In the context of linear statistical modeling ‘linear’ means linear in the parameters (coefficients) not the explanatory variables. The explanatory variables can be transformed (say x2) but the model will still be linear if the coefficients remain linear. When the overall function (Y) remains a sum of terms that are each an X variable multiplied by a coefficient the function Y is said to be linear in the coefficients. A non-linear model is different in that it has a non-constant slope (a tutorial on

Linear logistic model: A linear logistic model assumes that for each possible set of values for the independent (X) variables there is a probability p that an event (success) occurs. Then the model is that Y is a linear combination of the values of the X variables: Y = b

Linear expression: A polynomial expression with the degree of polynomial being 1. It will be something like f(x)=2x

Likelihood ratio test: A general purpose test of hypothesis Ho against an alternative H1 based on the ratio of two likelihood functions one derived from each of Ho and H1. The statistics

Likelihood distance test (likelihood residual deletion residual): This test is based on the change in deviance when one observation is excluded from the dataset. It uses the difference between the log-likelihood of the complete dataset and the log-likelihood when a particular observation is removed. A relatively large difference indicates that the observation involved is an outlier (poorly fitted by the model).

Likelihood: The probability of a set of observations given the value of some parameter or set of parameters. For example the likelihood of a random sample of n observations (x1 to xn) with probability distribution f(x;

Leverage points: In regression analysis these are the observations that have an extreme value on one or more explanatory variable. The leverage values indicate whether or not X values for a given observation are outlying (far from the main body of the data). A high leverage value indicates that the particular observation is distant from the centre of the X observations. High-leverage points have the potential to dominate a regression analysis but not necessarily influential. If the residual of the same data point and Cook’s distance are also high then it is an influential point. See also influential points.

Least squares method: A method of fitting a straight line or curve based one minimization of the sum of squared differences (residuals) between the predicted and the observed points. Given the data points (x

Large sample effect: In large samples even small or trivial differences can become statistically significant. This should be distinguished from biological/clinical importance.

Kurtosis:

Kruskal-Wallis test(One-way ANOVA by ranks): It is one of the non-parametric tests equivalent to one-way ANOVA that are used to compare multiple (k > 2) independent samples. This test assesses the hypothesis that the different samples in the comparison were drawn from the same distribution or from distributions with the same median. It can be used to analyze ordinal variables. It is an extension of the Mann-Whitney (U) test (for two independent samples). The interpretation of the Kruskal-Wallis test is identical to that of one-way ANOVA but is based on ranks rather than means (

Kolmogorov-Smirnov two-sample test: A non-parametric test applicable to continuous frequency distributions. It is considered to be the equivalent of the

Interval variable(equivalent to continuous variable)

Interquartile range (dQ): dQ is a measure of spread and is the counterpart of the standard deviation for skewed distributions. dQ is the distance between the upper and lower quartiles (Q­U-QL).

Interpolation: Making deductions from a model for values that lie between data points. Making deductions for values beyond the data points is called extrapolation and the results are not valid.

Intercept: In linear regression the intercept is the mean value of the response variable when the explanatory variable takes the value of zero (the value of y when x=0).

Interaction: If the effect of one factor depends on the level of another factor the two factors involved are said to interact and a contrast involving all these levels is called their interaction. Factors A and B interact if the effect of factor A is not independent of the level of factor B. For example when there are two main effects on a response variable if their combined effect is higher than the sum of their main effects due to a bonus (say the effects of a kind of exercise and a kind of diet on blood lipid levels) they have an interaction (meaning a simple additive model is not sufficient to account for the observed data and a multiplicative term must be added). Briefly interaction is a deviation from additivity. Also there would be an interaction between the factors sex and treatment if the effect of treatment was not the same for males and females in a drug trial. Interaction is closely linked with effect modification in epidemiology (see Genetic Epidemiology Glossary; Wikipedia: Statistical Interaction).

Influential points: Observations that actually dominate a regression analysis (due to high leverage high residuals or their combination). The method of ordinary least squares gives equal weight to every observation. However every observation does not have equal impact on the least squares results. The slope for example is influenced most by the observations having values of the independent variable farthest from the mean. An observation is influential if deleting it from the dataset would lead to a substantial change in the fit of the generalized linear model. High-leverage points have the potential to dominate a regression analysis but not necessarily exert an influence (i.e. a point may have high leverage but low influence as measured by Cook statistics). Cook statistics is used to determine the influence of a data point on the model.

Inferential statistics: Making inferences about the population from which a sample has been drawn and analyzed.

Index plot: An index plot plots each residual leverage or Cook’s distance against the corresponding observation (row) number (i or index) in the dataset. In many cases the row number corresponds to the order in which the data were collected. If this is the case this would be similar to plotting the residuals (or another diagnostic quantity) against time. The index plot is a helpful diagnostic test for normal linear and particularly generalized linear models. Both outliers and influential points can be detected by the index plot. It is particularly useful when the data is in time order so that pattern in the residuals etc. over time can be detected. If a residual index plot is showing a trend in time then they are not independent (violation of a major assumption of linear regression).

Hypergeometric distribution: A probability distribution of a discrete variable generally associated with sampling from a finite population without replacement. An example may be that given a lot with 25 good units and five faulty. The probability that a sample of five will yield not more than one faulty item follows a hypergeometric distribution.

Hotelling’s T2 test: This is a generalization of Student’s t-test for multivariate data. Designed to provide a global significance test for the difference between two groups with simultaneously measured multiple dependent/outcome variables and multiple explanatory/independent variables. It can also be used for one group with simultaneously measured multiple dependent outcome variables (another test similar to Hotelling’s T2 test is Mahalanobis’s D2 test). See multivariate analysis.

Homoscedasticity (homogeneity of variance):Normal-theory-based tests for the equality of population means such as the t-test and analysis of variance assume that the data come from populations that have the same variance even if the test rejects the null hypothesis of equality of population means. If this assumption of homogeneity of variance is not met the statistical test results may not be valid. Heteroscedasticity refers to lack of homogeneity of variances.

Hetereoscedastic data: Data that have non-constant (heterogeneous) variance across the predicted values of y. In this case residual graph will show varying variability across the fitted values. This is a regression diagnostic problem and should be fixed by transforming the data. See also

Hazard Ratio (Relative Hazard): Hazard ratio compares two groups differing in treatments or prognostic variables etc. If the hazard ratio is 2.0 then the rate of failure in one group is twice the rate in the other group. The computation of the hazard ratio assumes that the ratio is consistent over time and that any differences are due to random sampling. Before performing any tests of hypotheses to compare survival curves the proportionality of hazards assumption should be checked (and should hold for the validity of Cox’s proportional hazard models). (See also Log-rank test).

Hazard Rate: It is a time-to-failure function used in

Hazard function(instantaneous failure rate conditional failure intensity or force of mortality function): The function that describes the probability of failure during a very small time increment (assuming that no failures have occurred prior to that time). Hazard is the slope of the survival curve – a measure of how rapidly subjects are having the event (dying developing an outcome etc).

Harmonic mean: Of a set of numbers (y1 to yn) the harmonic mean is the reciprocal of the arithmetic mean of the reciprocal of the numbers [H = N / (1/(y1 + y2 + .... yn))]. The harmonic mean is either smaller than or equal to the arithmetic mean. It is a measure of position.

Haplotype Relative Risk method: This method uses non-inherited parental haplotypes of affected persons as the control group and thus eliminates the risks and bias associated with using unrelated individuals as controls in case-control association studies as well as the higher cost (see Falk & Rubinstein 1987; Knapp 1993; Terwilliger & Ott 1992).

Half-normal plot: A diagnostic test for model inadequacy or revealing the presence of outliers. It compares the ordered residuals from the data to the expected values of ordered observations from a normal distribution. While the full-normal plots use the signed residuals half-normal plots use the absolute values of the residuals. Outliers appear at the top right of the plot as distinct points and departures from a straight line mean that the model is not satisfactory. It is appropriate to use a half-normal plot only when the distribution is symmetrical about zero because any information on symmetry will be lost.

Geometric mean: G = (x1.x2…x

Genetic Distance Estimation by PHYLIP: The most popular (and free) phylogenetics program PHYLIP can be used to estimate genetic distance between populations. Most components of PHYLIP can be run online. One component of the package GENDIST estimates genetic distance from allele frequencies using one of the three methods: Nei’s Cavalli-Sforza’s or Reynold’s (see papers by Nei et al 1983 Nei M 1996 and a lecture note for more information on these methods). GENDIST can be run online using the default options (Nei’s genetic distance) to obtain genetic distance matrix data. The PHYLIP program CONTML e

Generalized linear model (GLM): A model for linear and non-linear effects of continuous and categorical predictor variables on a discrete or continuous but not necessarily normally distributed dependent (outcome) variable. (Note that in the general linear model the dependent (outcome) variable should be normally distributed). Normal binary (or linear logistic; when the outcome variable is a proportion) binomial or Poisson (when the outcome variable is a count) exponential and gamma (when the outcome variable is continuous and non-negative) models are different versions of generalized linear models. Particular types of models arise by specifying an appropriate link function variance and distribution. For example normal linear regression corresponds to an identity link function constant variance and a normal distribution. Logistic regression arises from a logit link function and a binomial distribution (the variance of the response (npq) is related to its mean (np): variance = mean (1 – (mean/n)). Loglinear models are used for binomial or Poisson counts. Standard techniques for analyzing censored survival data such as the Cox regression can also be handled within the GLM framework (

General linear model: A group of linear regression models in which the response variable is continuous and normally distributed the response variable values are predicted from a linear combination of predictor variables and the linear combination of values for the predictor variables is not transformed (i.e. there is no link function as in generalized linear models). Linear multiple regression is a typical example of general linear models whereas simple linear regression is a special case of generalized linear models with the identity link function.

G Statistics: An application of the log-likelihood ratio statistics for the hypothesis of independence in an r x c contingency table. It can also be used to test goodness-of-fit. The G-test should be preferred over Chi-squared test when for any cell in the table

Gaussian distribution: Another name for the normal distribution (GraphPad Gaussian Distribution Calculator).

Game theory: The theory of contests between two or more players under specified sets of rules. The statistical aspect is that the game proceeds under a chance scheme such as throwing a die.

Gambler’s ruin: A classical topic in probability theory. It is a game of chance related to a series of Bernoulli trials. There are variations of the game theory associated with problems of the random walk and sequential sampling.

F test: The F test for linear regression tests whether the slope is significantly different from 0 which is equivalent to testing whether the fit using non-zero slope is significantly better than the null model with 0 slope. See also mean squares.

Friedman test: This non-parametric test is an extension of Wilcoxon matched pairs signed ranks test which is concerned with more than two time periods of data collection or conditions and groups of three or more matched subjects (

F distribution: A continuous probability distribution of the ratio of two independent random variables each having a Chi-squared distribution divided by their respective degrees of freedom. The commonest use is to assign P values to mean square ratios (variance ratios) in ANOVA. In regression analysis the F-test can be used to test the joint significance of all variables of a model. (Tables of critical values of t F and Chi-square).

Factorial analysis of variance: An analysis in which the treatments differ in terms of two or more factors (with several levels) as opposed to treatments being different levels of a single factor as in one-way ANOVA.

Factorial experiments: In some data the explanatory (predictor) variables are all categorical (i.e. factors) and the response variable is quantitative. When there are two or more categorical predictor variables the data are called factorial. The different possible values of the factors are often assigned numerical values known as levels.

Factor: A categorical explanatory variable with small number of levels such that each item classified belongs to exactly one level for that category. If the factor is ‘sex’ the levels are ‘male’ and ‘female’; if the factor is ‘drug received’ the levels are ‘drug A’ ‘drug B’ ‘drug C’ etc. A set of factor levels uniquely defining a single treatment is called a cell. A cell may have just one observation (no replication) or multiple observations (replications).

Exposure: In an epidemiologic study exposure may represent an environmental exposure an intervention or the presence of a marker (biomarker/genetic marker).

Exponential family: A family of probability distributions in the form

Exponential distribution: The (continuous) distribution of time intervals between independent consecutive random events like those in a Poisson process.

Exploratory data analysis: An initial look at the data with minimal use of formal mathematics or statistical methods but more with an informal graphical approach. Scatter plots correlation matrices and contingency tables (for binary data) can be used to get an initial idea for relationships between explanatory variables (for collinearity) or between an explanatory variable(s) and a response variable(s) (correlation). In ANOVA normality can be checked by box-plots. It gives some indication of which variables should be in the model and which one of them should be put into the model first and whether linear relationship is adequate.

Explained (regression) sum of squares (ESS): The measure of between treatments sum of squares (variability) in ANOVA. If the means of treatment groups are different the ESS would be greater than RSS to yield a high variance ratio. The bigger the ESS the better explained the data by the model.

Error terms: Residuals in regression models. Shown as Wi or

Epi-Info: An epidemiologic data management and analysis package freely available from the CDC website. Originally a DOS program the latest version (3.3.2) is designed for Microsoft Windows 95-XP (release date: Febr 9 2005). There are also tutorials available online: CDC Nebraska University Dalhousie University and Henry Ford Health Systems.

Epidemiologic flaws and fallacies: Beware of confounders selection bias response bias variable observer Hawthorne effect (changes caused by the observer in the observed values) diagnostic accuracy bias regression to the mean significance Turkey nerd of nonsignificance cohort effect ecological fallacy Berkson bias (selection bias in hospital-based studies) and others (discussed in M Michael III et al. Biomedical Bestiary. Little Brown and Company 1984; and in Bias & Confounding in Molecular Epidemiology).

Empirical rule: In variables normally distributed 68% of the data values are within 1SD of the mean; 95% are within 2SD of the mean; and 99.7% (nearly all) are within 3SD of the mean.

Empirical P value: A P value obtained by a simulation program such as Monte Carlo statistics. This is less likely to be affected by multiple comparisons.

EM Algorithm: A method for calculating maximum likelihood estimates with incomplete data. E (expectation)-step computes the expected values for missing data and M (maximization)-step computes the maximum likelihood estimates assuming complete data. It was first used in genetics (Ceppellini R et al 1955) to estimate allele frequency for phenotype data when genotypes are not fully observable (this requires the assumption of HWE and calculation of expected genotypes from phenotype frequencies). For a brief overview see ARC CIGMR: EM Algorithm. Arlequin implements EM algorithm in haplotype construction and frequency analysis.

Eigenvalues(latent values): In multivariate statistics eigenvalues

Effect modification: The situation in which a measure of effect changes over values of another variable (the association estimates are different in different subpopulations of the sample). The relative risk or odds ratio associated with exposure will be different depending on the value of the effect modifier. For example if in a disease association study the odds ratios are different in different age groups or in different sexes age or sex are effect modifiers. Effect modification is highly related to statistical interaction in regression models. If where an exposure decreases risk for one value of the effect modifier and increases risk for another value of effect modifier this is called crossover. See Thompson 1991 and Effect Modification in Encyclopedia of Biostatistics.

Edwards’ test:

Ecological fallacy:The aggregation bias which is the unfortunate consequence of making inferences for individuals from aggregate data. It results from thinking that relationships observed for groups necessarily hold for individuals. The problem is that it is not valid to apply group statistics to an individual member of the same group. See an essay on Ecological Fallacy.

Ecological study: Analyses based on data grouped to the municipal provincial or national level. See Ecological Studies Chapter in Epidemiology for the Uninitiated.

Dunnett’s test: When ANOVA shows a significant difference between groups if one of the groups is a control (reference) group Dunnett’s Test is used as a post hoc test. This multiple comparison test can be used to determine the significant differences between a single control group mean and the remaining treatment group means in an analysis of variance setting. It is one of the least conservative post hoc tests.

Dunn’s Test: This test is used when a difference between the groups is found in a non-parametric ANOVA test. Dunn’s test is a post hoc test that makes pairwise (multiple) comparisons to identify the different group. See GraphPad Prism Guide: K-W and Dunn’s Test (for an example see

Dummy variables: A binary variable that is used to represent a given level of a categorical variable. In genetic data analysis for example it is created for each allele at a multiallelic locus. The most common choices as dummy variables are 0 and 1. For each level of the variable 1 denotes having the feature and 0 denotes all other levels. Also called indicator variables. If an indicator variable is used the regression coefficient gives the change per unit compared to the reference value. Creating dummy variables on Stata: Stata & UCLA Statistics: STATA Dummy Variables.

Discrete variable: A variable of countable number of integer outcomes. Examples include -ordinal multinomial- several prognostic outcomes (such as poor median and good) as a function of treatment modalities stage of the disease age etc. or -multinomial- peoples choices of hospitals (hospital A B or C) as a function of their income level age education etc. A discrete variable may be binomial: diseased or non-diseased in a cohort or case-control study. The nature of the outcome variable as discrete or continuous is crucial in the choice of a regression model (see the generalized linear model).

Deviance difference: In generalized linear modeling models that have many explanatory variables may be simplified provided information is not lost in this process. This is tested by the difference in deviance between any two nested models being compared:

Deviance: A measure for judging the degree of matching of the model to the data when the parameter estimation is carried out by maximizing the likelihood (as in GLMs). The deviance has asymptotically a Chi-squared distribution with df equal to the difference in the number of parameters in the two models being compared. The total deviance compares the fit of the saturated model to the null model thus expresses the total variability around a fitted line which can be decomposed to explained and unexplained (error) variability. The residual deviance in a GLM analysis of deviance table corresponds to RSS in an ANOVA table and regression deviance corresponds to ESS. The residual deviance measures how much fit to the data is lost (in likelihood terms) by modeling compared to the saturated model. This will be a small value if the model is good (and it will be zero for the saturated model containing all main effects and all interactions). The regression deviance measures how much better is the model taking into account the explanatory variables compared to the simplest model ignoring all of them and only containing a constant (the mean of the responses). This measurement is again made in terms of log-likelihood and the bigger the regression deviance the better fits the model (i.e. the regression effect is strong). In likelihood terms the residual deviance can be expressed as follows:

Descriptive statistics: Summary of available data. Examples are male-to-female ratio in a group; numbers of patients in each subgroup; the mean weight of male and female students in a class etc. Only when the distribution is symmetric mean and standard deviation can be used. Otherwise (as in survival data) mean and percentiles/range should be used to describe the data. See GraphPad guide to Interpreting Descriptive Statistics.

Deletion (or deleted) residual: A modified version of the standardized residual which uses an estimate of

Degrees of freedom (df): The number of independent units of information in a sample used in the estimation of a parameter or calculation of a statistic. In the simplest example of a 2×2 table if the marginal totals are fixed only one of the four cell frequencies is free to vary and the others will be dependent on this value not to alter the marginal totals. Thus the df is only 1. Similarly it can easily be worked out that in a contingency table with r rows and c columns the df = (r-1)(c-1). In parametric tests the idea is slightly different that the n bits of data have n degrees of freedom before we do any statistical calculations. As soon as we estimate a parameter such as the mean we use up one of the df which was initially present. This is why in most formulas the df is (n-1). In the case of a two-sample t-test with n1 and n2 observations to do the test we calculate both means. Thus the df = (n1 + n2 – 2). In linear regression when the linear equation y =

Cross-sectional data: Data collected at one point in time (as opposed to longitudinal/cohort data for example). See Cross-Sectional Studies Chapter in Epidemiology for the Uninitiated.

Crossover design: A clinical trial design during which each subject crosses over from receiving one treatment to another one.

Cramers V: A measure of the strength association for any size of contingency tables. It can be seen as a correction of the Chi-squared value for sample size. The transformation of the chi-squared value provides a value between 0 and 1 for relative comparison of the strength of the association. For a 2×2 table Cramer’s V is equal to the Phi coefficient. Cramers V is most useful for large contingency tables. It can also be used as a global linkage disequilibrium value for multiallelic loci (See GOLD-Disequilibrium Statistics; Online Cramers V calculation.)

Cramers coefficient of association(C): Also known as contingency coefficient. While Chi-squared is used to determine significance of an association (and varies by sample size for the same association) Cramers C is a measure of association varying from 0 (no association) to 1 (perfect association) that is independent of the sample size. However it seldom reaches its upper limit. It allows direct comparison of the degree of association between different contingency tables. It is calculated directly from the Chi-squared value and the total sample size as (

Covariance models: Models containing some quantitative and some qualitative explanatory variables where the chief explanatory variables of interest are qualitative and the quantitative variables are introduced primarily to reduce the variance of the error terms. [Models in which all explanatory variables are qualitative are called analysis of variance -ANOVA- models.] Analysis of covariance -ANCOVA- combines features of ANOVA and regression. It augments the ANOVA model containing the factor effects with one or more additional quantitative variables that are related to the response variable. The intention is to make the analysis more precise by reducing the variance of the error terms. Each continuous quantitative variable added to the ANOVA model is called a concomitant variable (and sometimes also covariates). If qualitative variables are added to an ANOVA model to reduce error variance the model remains to be ANOVA. By adding extra variables the results are said to be controlled or adjusted for the additional variables (like age or sex).

Covariance (covariation): It is a measure of the association between a pair of variables: the expected value of the product of the deviation of two random variables from their respective means. It is also called a measure of ‘linear dependence between the two random variables. If the two variables are independent (no linear correlation) then their covariance is zero but for non-zero values covariance is unstandardized (unlike correlation coefficient); there is no limit to possible values. Because of this it is difficult to compare covariances. A negative value means that for small values of X there are large values of Y (inverse association). It is calculated as the mean sum-of-products using each x

Covariate: Generally used to mean explanatory variable less generally an additional explanatory variable is of no interest but included in the model. More specifically it denotes a ‘continuous’ explanatory variable which is unaffected by treatments and has a linear relationship to the response. The intention is to produce more precise estimates of the effect of the explanatory variable of main interest. In the analysis a model is first fitted using the covariate (and the blocking factor if any). Then the main explanatory variable is added and its additional effect is assessed statistically. Whether the use of a covariate is wise can be judged by checking its effect on the residual (error) mean square (variance). If the addition of covariate reduces it remarkably it will improve the analysis. See also covariance models.

Cox proportional hazards model: A regression method described by D.R. Cox (J Royal Stat Soc Series B 1972;34:187-220; JSTOR-UK) for modeling survival times (for significance of the difference between survival times log-rank test is used). It is also called proportional hazards model because it estimates the ratio of the risks (hazard ratio or relative hazard). As in any regression model there are multiple predictor variables (such as prognostic markers whose individual contribution to the outcome is being assessed in the presence of the others) and the outcome variable (e.g. whether the patients survived five years or died during follow-up etc). The model assumes that the underlying hazard rate (rather than survival time) is a function of the independent variables and consistent over time (proportionality assumption i.e. the survival functions of the groups are approximately parallel). There is no assumption for the shape and nature of the underlying survival function. Cox’s regression model has been the most widely used method in survival data analysis regardless of whether the survival time is discrete or continuous and whether there is censoring (Lee & Go 1997). Cox regression uses the maximum likelihood method rather than the least squares method (Online Cox Proportional Hazards Survival Regression; a Superlectures on survival analysis; Cox’s proportional hazards model; an example of Model Building).

Correspondence analysis: In population genetics a complementary analysis to genetic distances and dendrograms. It displays a global view of the relationships among populations (Greenacre MJ 1984; Greenacre & Blasius 1994; Blasius & Greenacre 1998). With its visual output it supplements more formal inferential analyzes. This type of analysis tends to give results similar to those of dendrograms as expected from theory (Cavalli-Sforza & Piazza 1975) but is more informative and accurate than dendrograms especially when there is considerable genetic exchange between close geographic neighbors (Cavalli-Sforza et al. 1994). Cavalli-Sforza et al concluded in their enormous effort to work out the genetic relationships among human populations that two-dimensional scatter plots obtained by correspondence analysis frequently resemble geographic maps of the populations with some distortions (Cavalli-Sforza et al. 1994). Using the same allele frequencies that are used in phylogenetic tree construction correspondence analysis can be performed on ViSta (v7.0) VST Statistica SAS but most conveniently on MultiVariate Statistical Package (MVSP). Link to a Tutorial; Course Notes; StatSoft Textbook: Correspondence Analysis Chapter.

Correlation Coefficient: See

Cook statistics: A diagnostic influence statistics in regression analysis designed to show the influential observations. Cook’s distance considers the influence of the i th value on all n fitted values and not on the fitted value of the i th observation. It yields the shift in the estimated parameter from fitting a regression model when a particular observation is omitted. All distances should be roughly equal; if not then there is reason to believe that the respective case(s) biased the estimation of the regression coefficients. Relatively large Cook statistics (or Cook’s distance) indicates influential observations. This may be due to a high leverage a large residual or their combination. An index plot of residuals may reveal the reason for it. The leverages depend only on the values of the explanatory variables (and the model parameters). Cook statistics depends on the residuals as well. Cook statistics may not be very satisfactory in binary regression models. Its formula uses the standardized residuals but the modified Cook statistics uses the deletion residuals.

Contrast: A contrast is combinations of treatment means which is also called the main effect in ANOVA. It measures the change in the mean response when there is a change between the levels of one factor. For example in an analysis of three different concentrations of a growth factor on cell growth in cell culture with means

Conservative test: A test where the chance of type I error (false positive) is reduced and type II error risk is increased. Thus these tests tend to give larger P values compared to non-conservative (liberal) tests for the same comparison.

Confounding variable: A variable that is associated with both the outcome and the exposure variable. A classic example is the relationship between heavy drinking and lung cancer. Here the data should be controlled for smoking as it is related to both drinking and lung cancer. A positive confounder is related to exposure and response variables in the same direction (as in smoking); a negative confounder shows an opposite relationship to these two variables (age in a study of association between oral contraceptive use and myocardial infarction is a negative confounder). The data should be stratified before analyzing it if there is a confounding effect. Mantel-Haenszel test is designed to analyze stratified data to control for a confounding variable. Alternatively a multivariable regression model can be used to adjust for the effects of confounders. See Bias & Confounding Lecture Note; a review by Greenland 2001.

Conditional (fixed-effects) logistic regression: The conditional logistic regression (CLR) model is used in studies where cases and controls can be matched (as pairs) with regard to variables believed to be associated with the outcome of interest. The model creates a likelihood that conditions on the matching variable. It is the preferred method for the analysis of nested case-control studies when matching is done at the individual level (there may be more than one control per case). In economic analysis it is called fixed-effects logit for panel data. See Preisser & Koch 1997.

Concomitant variable: See covariance models.

Cohort effect: The tendency for persons born in certain years to carry a relatively higher or lower risk of a given disease. This may have to be taken into account in case-control studies.

Coefficient of variation: It is a measure of spread for a set of data. It is a measure of variation in relation to the mean. Calculated as standard deviation divided by the mean (x100). (Online Calculator for Coefficient of Variation and Other Descriptive Statistics).

Cochran’s Q Test: A nonparametric test examining change in a dichotomous variable across more than

Chi-squared test: The most commonly used test for frequency data and goodness-of-fit. In theory it is nonparametric but because it has no parametric equivalent it is not classified as such. It is not an exact test and with the current level of computing facilities there is not much excuse not to use Fishers exact test for 2×2 contingency table analysis instead of Chi-squared test. Also for larger contingency tables the G-test (log-likelihood ratio test) may be a better choice. The Chi-square value is obtained by summing up the values (residual2/fit) for each cell in a contingency. In this formula residual is the difference between the observed value and its expected counterpart and fit is the expected value. See

Chi-squared distribution: A distribution derived from the normal distribution. Chi-squared (

Central limit theorem: The means of a relatively large (>30) number of random samples from any population (not necessarily a normal distribution) will be

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Censored observation: O

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Categorical (nominal) variable: A variable that can be assigned to categories. A non-numerical (qualitative) variable measured on a (discrete) nominal scale such as gender drug treatments disease subtypes; or on an ordinal scale such as low median or high dosage. A variable may alternatively be quantitative (continuous or discrete). See GraphPad QuickCalc: Categorical Data Analysis.

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Causal relationship: It does not matter how small it is a P value does not signify causality. To establish a causal relationship the following non-statistical evidence is required: consistency (reproducibility) biological plausibility dose-response temporality (when applicable) and strength of the relationship (as measured by odds ratio/relative risk/hazard ratio). See Hills’s criteria of causality

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Case-control study: A design preferred over cohort studies for relatively rare diseases in which cases with a disease or exposure are compared with controls randomly selected from the same study base. This design yields odds ratio as opposed to relative risk from cohort studies. See Case-control Studies Chapter in Epidemiology for the Uninitiated.