Statistics for People Who (Think They) Hate Statistics

by Neil J. Salkind

First, for a bit of review, the two types of hypotheses differ in that one (the null hypothesis) usually states that there is no relationship between variables (an equality), whereas the research hypothesis usually states that there is a relationship between the variables (an inequality). This is the primary difference. Second, null hypotheses always refer to the population, whereas research hypotheses usually refer to the sample. We select a sample of participants from a much larger population. We then try to generalize the results from the sample back to the population. If you remember your basic philosophy and logic (you did take these courses, right?), you’ll remember that going from small (as in a sample) to large (as in a population) is a process of induction. Third, because the entire population cannot be directly tested (again, it is impractical, uneconomical, and often impossible), you can’t say with 100% certainty that there is no real difference between segments of the population on some variable. Rather, you have to infer it (indirectly) from the results of the test of the research hypothesis, which is based on the sample. Hence, the null hypothesis must be indirectly tested, and the research hypothesis can be directly tested. Fourth, in statistics, the null hypothesis is written with an equal sign, while the research hypothesis is written with a not equal to, greater than, or less than sign.