The Difference Statistic:

We need to ANALYZE our data. In order to do this you need to reduce your findings down to a single number, which you can then determine the significance of. How can you do this? Good question.

First of all, what is it that you are interested in about the taste-test?
Put another way, would the taste-test have been interesting at all if the results had all been the same? Probably not.
So the interesting thing about any preference test is that there are differences in the obtained values. You will use this difference to get one number from the several votes that you obtained. You will call it the difference statistic, or the d-statistic for short.

Beginning with the assumption that people do not have any preferences for their soft drinks, you need to see how different your observations were from what you expected, which would be equal votes for all of the soft drinks.

For example if 34 people voted, and there was no preference for any soft drink in the group, to find the expected number of votes for each beverage you would take the number of voters and divide by the number of beverages (in this case 4). The result here is 34/4 which is 8.5.
How can there be 8.5 votes for each beverage!?! It doesn't matter, you don't have to expect a whole number for your outcomes, it will work out in the end.

Using your results for the taste test, fill out the rest of the table from the earlier page.

Modeling:

Now what? You have a d-statistic. What good does it do you?
None yet, but with a little thought it will be invaluable.

Remember the d-statistic is a measure of how far your results were from what you would expect them to be with no preference. But even with no preference, if you randomly selected from the four beverages you would rarely get exactly the same results, or even close. Let's try it.

You will need:
A six-sided die
A piece of paper to keep track of results

Roll your die and keep track of the results like this:
If you get a 1 then mark a vote for Cola 1
If you get a 2 then mark a vote for Cola 2
If you get a 3 then mark a vote for Cola 3
If you get a 4 then mark a vote for Iced Tea
If you get a 5 or 6, don't write anything, and roll again.

Side Question: Why can you ignore the 5 and 6 and roll again? Click Here to explore this phenomenon.

Roll as many times as were votes in your taste test.

How do the results of your random taste test compare to your actual one?
Copy another table for finding the d-statistic and find out what the d-statistic is for this data. Everyone in the class should do the same. Record all of the answers on the board in order from least to greatest. You should see that there are very few numbers that are very large. That is because there should not be a large difference between the observations and what you expect (even votes) in a random study.

Find where your real taste test d-statistic falls in the table of randomly found d-statistics. Count the number of values higher than your d-statistic and divide that by the total number of values. If this number is smaller than .1 then you can declare the highest vote getter the winner of the taste test. This is because that means there is less than a 10% chance that your value could have happened by chance, which means more than likely that there was some difference in the preference of the people polled. You may congratulate the victorious soda company by e-mail.