Expectations

In statistical analysis you compare what you observe with what you expected to observe. This step is often overlooked by people who are trying to interpret data.

For example, let's suppose that 60% of the purchases of one of the products you sell are made by women. Do you conclude that the product appeals more to women?

That would depend on the numbers of men and women who have the opportunity to buy your product. If women make 70% of the purchases in the stores where your product is sold, then you must reject the idea that the product is more appealing to women.

What if women made only 50% of the purchases in these stores? Then the answer depends on the size of the sample you used to estimate the percentage of women among purchasers.

If the sample consists of 50 purchasers, then a statistical test would tell you that the percentage of purchasers who are women is not sufficiently different from 50% for you to conclude the difference is anything other than accidental variation (assuming, of course, that the sample is representative). If the sample consists of 100 purchasers, then the most lenient commonly used criterion for statistical significance would say the difference was improbable enough that you could concluded that your product was more likely to appeal to women. The certainty with which you can draw this conclusion increases as the sample size increases above 100.