Читать книгу Statistical Analysis with Excel For Dummies - Joseph Schmuller - Страница 18

Consider once again the coin tossing study I mention in the preceding section. The sample data are the results from the 100 tosses. Before tossing the coin, you might start with the hypothesis that the coin is a fair one so that you expect an equal number of heads and tails. This starting point is called the null hypothesis. The statistical notation for the null hypothesis is H₀. According to this hypothesis, any heads-tails split in the data is consistent with a fair coin. Think of it as the idea that nothing in the results of the study is out of the ordinary.

An alternative hypothesis is possible: The coin isn’t a fair one, and it's loaded to produce an unequal number of heads and tails. This hypothesis says that any heads-tails split is consistent with an unfair coin. The alternative hypothesis is called, believe it or not, the alternative hypothesis. The statistical notation for the alternative hypothesis is H₁.

With the hypotheses in place, toss the coin 100 times and note the number of heads and tails. If the results are something like 90 heads and 10 tails, it's a good idea to reject H₀. If the results are around 50 heads and 50 tails, don't reject H₀. Similar ideas apply to the reading speed example I give earlier, in the section “Samples and populations.” One sample of children receives reading instruction under a new method designed to increase reading speed, and the other learns via a traditional method. Measure the children's reading speeds before and after instruction and tabulate the improvement for each child. The null hypothesis, H₀, is that one method isn't different from the other. If the improvements are greater with the new method than with the traditional method — so much greater that it's unlikely that the methods aren't different from one another — reject H₀. If they're not greater, don't reject H₀.

Notice that I did not say “accept H₀.” The way the logic works, you never accept a hypothesis. You either reject H₀ or don't reject H₀.

Here’s a real-world example to help you understand this idea. Whenever a defendant goes on trial, that person is presumed innocent until proven guilty. Think of innocent as H₀. The prosecutor’s job is to convince the jury to reject H₀. If the jurors reject, the verdict is guilty. If they don’t reject, the verdict is not guilty. The verdict is never innocent. That would be like accepting H₀.

Back to the coin tossing example. Remember I said “around 50 heads and 50 tails” is what you could expect from 100 tosses of a fair coin. What does around mean? Also, I said if it’s 90-10, reject H₀. What about 85-15? 80-20? 70-30? Exactly how much different from 50-50 does the split have to be for you to reject H₀? In the reading speed example, how much greater does the improvement have to be to reject H₀?

I don't answer these questions now. Statisticians have formulated decision rules for situations like this, and you explore those rules throughout the book.