Used Audi TT - How to compare Audi tt dealers scientifically

Car dealers often claim  best quotes, best offers on new and used cars, cheapest prices, etc., etc. They offer price comparison and extensive search within their own offers. There is no real service that compares internet car sales mainly because it is strictly forbidden to use their data for anything but private purpose. So, even if technically possible, such service will never exist due to legal issues. However, we are able to compare car dealers on our own. With statistical test, we can do it with really small data set.  And that means fast!

Since Audi TT is one of my passions I've decided to use it as example car for comparing two dealers. I'm quite sure anyone who goes to buy a car knows exactly what he/she wants. But, how to find best deal? Believe it or not, it is very simple and free. Takes about half an hour, but can save you couple of 1000$! What follows is real example, with real quotes for very real car.

What is important to know is that you should only compare same things under different conditions. For instance, you should not mix prices for different Audi TT models in test. If you choose to test with Auti TT Coupe, then it should be same model, year and all other factors same. So, it is OK to test only Audi TT 1.8 Quattro Coupe AWD year 2006 from different dealers, but it would be wrong to test Audi TT Quatro Coupe 1.8 year 2006, Audi TT Quatro Coupe 3.2 year 2008, Audi TT roadster 2.0 year 2008 at once because you compare mixture of very different items. Not to say that mileage would be probably very different foreach item. What's also important: take at least 3 different quotes from EACH dealer you compare. t-test will not work for single items. The more quotes you compare, the more sure you will be. But 3 should do.

In this example, I've compared two dealerships on used Audi TT. I picked Audi TT 1.8 Coupe model year 2006 to make shure whether or not two dealers offer same price. Then I wrote down data in a table (you don't need lot's of data, in this example, I am able to statisticaly prove difference with only three prices from each dealer). Table looks like this:

I've included mileage in order to check if miles influence evaluation result. If you typed results in Excel like in this table, you should open Tools>Data Analysis. In newly opened box choose t-Test: Two Sample Assuming Unequal Variances. In Variable 1 range select all data from Dealer1/Price and in Variable 2 range select all data from Dealer2/Price. Labels box should be unchecked. It looks like on the following image.

After you click OK, you get result:

t-Test: Two-Sample Assuming Unequal Variances
	Variable 1	Variable 2
Mean	20323.67	23327.33
Variance	2310065	334336.3
Observations	3	3
Hypothesized Mean Difference	0
df	3
t Stat	-3.19925
P(T<=t) one-tail	0.02468	SIGNIFICANT! (<0.05)
t Critical one-tail	2.353363
P(T<=t) two-tail	0.04936	SIGNIFICANT! (<0.05)
t Critical two-tail	3.182446

What we read here is that dealer 1 has price for the same thing 3000$ lower in comparison to dealer 2! (Mean value fo variable 1 and 2). But is it just a glitch or is it really so? So called P-value gives us significance. When P value is lower than 0.05 (here is 0.024 for one tail and 0.04936 for two tails of distribution) than we can say that our results significantly differ. We are confident that dealer 1 offers better price.

Since we also wanted to check if mileage has influence on the result, we test for the opposite. Namely, we need P value higher than 0.05. Than it means that both sets of that are equivalent and that they don't cause difference in price.

Following same procedure as before, we make t-test on miles. Again we go through menu Tools>Data Analysis and choose t-Test: Two-Sample Assuming Unequal Variances. Since Excel remembers what we did last time, we'll have to go inside the boxes for Variable range 1, change selection to highlight miles for dealer 1 and do the same for Variable range 2. Leaving Labels box unchecked, we also place Output range so that we don't overwrite the results for prices. Select cell somwhere beneath existing results, click OK and you should get following result:

t-Test: Two-Sample Assuming Unequal Variances
	Variable 1	Variable 2
Mean	41382.67	29597.33
Variance	4.59E+08	1.09E+08
Observations	3	3
Hypothesized Mean Difference	0
df	3
t Stat	0.856933
P(T<=t) one-tail	0.22724	NOT SIGNIFICANT! (>0.05)
t Critical one-tail	2.353363
P(T<=t) two-tail	0.454481	NOT SIGNIFICANT! (>0.05)
t Critical two-tail	3.182446

There you go! P-values are 0.22724 for one-tail and 0.454481 for two-tails proving that there is not much difference on mileages for selected prices. Now we are sure that this part of information is NOT what is causing difference.

If you don't have Excel, you can use free page like (or search for "t-test online) http://www.graphpad.com/quickcalcs/ttest1.cfm?Format=50. Just type your data under Group 1 and Group 2 (Rename them to Dealer 1/ Dealer 2 if you like) press calculate and you get the result with nice explanations.

What is amazing with this result is that dealers have really different quotes (3000$ was real surprise to me!), so, before buying an used Audi TT car or any car other whatsoever, check offers between dealer so you can be shure to make best sale from it.