Test The Hypothesis

Assuming that the sample of Nova Scotia beer drinkers is not biased, can you now conclude that Keith's is the most popular brand?

To answer this question, consider a related question: If you were to obtain another sample of Nova Scotia beer drinkers, would you expect to see exactly the same results? Realistically, you would expect some variability in the observed outcomes from sample to sample.

Given this expected sampling variability, you might wonder whether the observed brand preferences might be better accounted for by random sampling variability rather than by reflecting real differences in the population of interest. In statistical terminology, this sampling variability explanation is called the null hypotheses. (The null hypothesis is designated by the symbol H_o.) In this instance, formulate it as the statement that the expected number of responses is the same accross all categories of response:

H_o: # Keiths = # Olands = # Schooner = # Other

If you can rule out the null hypothesis, then you will make some progress towards answering the original question about whether Keith's is the most popular brand. The alternative hypothesis that you can then entertain is that the proportions are different in the population of interest.

This test-the-null-hypothesis-first logic applies at multiple stages in the analysis of poll data. Ruling out the null hypothesis so you have no overall differences in your data, you may then proceed to test a more specific null hypothesis, namely that no difference exists between Keith's and Schooner or between Keith's and all other brands.

The reason you proceed by testing the null hypothesis rather than directly assessing the alternative hypothesis is because it is easier to statistically model what one would expect to observe under the null hypothesis. Next, I'll demonstrate how to model what would be expected under the null hypothesis so that I can compare the observed results to what would be expected under the null hypothesis.