6.1 The Logic of Hypothesis Testing

Ten Facts About Hypotheses and Hypothesis Testing

1. A hypothesis is a statement about a population, not a sample. This is because a researcher wants to draw a conclusion about the larger population and not about the specific sample being studied.

2. There will be two hypotheses—one called the null hypothesis, H₀, and the other called the alternative hypothesis, H₁.

3. The two hypotheses must be all-inclusive, which means they cover all possible outcomes. For example, if one hypothesis said that all cars in the world were white and the other that all cars were black, those two hypotheses wouldn’t be all-inclusive because red and green and yellow cars also exist. However, if one hypothesis stated, “All cars are white” and the other hypothesis, “Not all cars are white,” then the two hypotheses would be all-inclusive.

4. The two hypotheses must be mutually exclusive, which means that only one hypothesis at a time can be true. For example, a coin can land on heads or on tails, but not on both sides at once. Heads and tails are mutually exclusive outcomes.

5. The null hypothesis is a negative statement. The null hypothesis says that in the population the explanatory variable does not have an impact on the outcome variable. For example, if a researcher were testing a technique to improve intelligence, the null hypothesis would state that the technique does not improve intelligence. Because the null hypothesis makes a specific prediction, it would say that the technique has zero impact and does not improve intelligence at all.

6. The alternative hypothesis is what the researcher believes is true; it states that, in the population, the explanatory variable has an impact on the outcome variable. For the researcher testing the intelligence-improving technique, the alternative hypothesis would state that the technique has some impact on intelligence. Notice that the alternative hypothesis doesn’t specify how much impact. Unlike the null hypothesis, the alternative hypothesis doesn’t make a specific prediction.

7. A negative statement, like the null hypothesis, can’t be proven true. Suppose an adult wants to prove the negative statement “There are no unicorns” to a child who believes in unicorns. No matter what evidence the adult offers (e.g., “I looked all through Ohio and didn’t find one”), the child will counter that the adult wasn’t looking in the right place, or that the unicorns heard the adult coming and fled. A negative can’t be proven.

8. However, a negative can be disproven. It just takes one example. If the child ever walks up leading a unicorn on a leash, the adult can no longer claim, “There are no unicorns.” Because the null hypothesis makes a specific prediction, it is used to predict how a researcher’s experiment will turn out. If the experiment doesn’t turn out as the null hypothesis predicted, the researcher disproves, or “rejects,” the null hypothesis. The null hypothesis can be nullified.

9. If the null hypothesis is rejected, then one has to accept the mutually exclusive alternative hypothesis as true. This happens because the null hypothesis and the alternative hypothesis are all-inclusive and mutually exclusive. If one hypothesis is not true, then the other hypothesis has to be true. As the researcher usually believes that the alternative hypothesis is true, the objective of a study is almost always to reject the null hypothesis.

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10. However, if a researcher fails to disprove the null hypothesis, he or she can’t say that the null hypothesis is true. Remember, a negative statement, like the null hypothesis, can’t be proven true. The best the researcher can say is that he or she hasn’t found enough evidence to reject the null hypothesis. This is different from saying the null hypothesis is true, just as a not guilty verdict in a trial is different from saying that the defendant is innocent. Not guilty just means that there wasn’t enough evidence to persuade the jury that the defendant was guilty.