Hypothesis Testing, Logic of

From Sample to Population

If researchers had full data on the whole population of interest, making statistical inferences would be unnecessary. For example, if researchers wanted to know whether women were smarter than men and IQ scores for every man, woman, and child in the world were available, researchers could simply look at the average (mean) IQ score for women and the mean IQ score for men and easily determine which was higher. If researchers are comfortable making the assumption that those with higher IQ scores were smarter, they could use these averages to conclude whether women really were, on average, smarter than men.

Because it is almost never practical (or even possible) to collect full population information, researchers attempt to infer things about the population from a sample. Null hypothesis testing answers the question: If the relationship between two variables in the population were zero, what are the odds that researchers would have observed this nonzero relationship in their sample? If the odds are low, researchers often conclude that the relationship observed in the sample is probably not a result of chance. This is often interpreted as support for the research hypothesis (that the variables are related).

The Null Hypothesis

The null hypothesis is the default position that there is no relationship between two variables. [Page 678]The null hypothesis can be said to have presumption—researchers assume it is true until sufficient evidence is presented to overturn this presumption. Hence, the objective of null hypothesis testing is to generate sufficient evidence to overturn the presumption that there is no relationship between two variables.

For nominal (categorical) independent variables, the null hypothesis is typically expressed as a statement of equivalence. For example, if researchers wish to test whether there is an effect of sex on IQ, the null hypothesis would state that there is no effect of sex on IQ. However, if researchers measure sex as a categorical variable in which they assign everyone the sex of either “male” or “female,” their formal null hypothesis would be that male respondents would have the same IQ as female respondents. Stated otherwise, there will be no difference in IQ between males and females.

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