The Taste Test Module

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## Day 2-3: The Difference Statistic and Modeling

#### 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.