INTRODUCTION TO THE NULL HYPOTHESIS

Suppose we drew random samples of engineers and psychologists, administered a selfreport measure of sociability, and computed the mean (the most commonly used average) for each group. Furthermore, suppose the mean for engineers is 65.00 and the mean for psychologists is 70.00. Where did the five-point difference come from? There are three possible explanations:

1. Perhaps the population of psychologists is truly more sociable than the population of engineers, and our samples correctly identified the difference. (In fact, our research hypothesis may have been that psychologists are more sociable than engineers which now appears to be supported by the data.)

2. Perhaps there was a bias in procedures. By using random sampling, we have ruled out sampling bias, but other procedures such as measurement may be biased. For example, maybe the psychologists were contacted during December, when many social events take place and the engineers were contacted during a gloomy February. The only way to rule out bias as an explanation is to take physical steps to prevent it. In this case, we would want to make sure that the sociability of both groups was measured in the same way at the same time.

3. Perhaps the populations of psychologists and engineers are the same but the samples are unrepresentative of their populations be cause of random sampling errors. For instance, the random draw may have given us a sample of psychologists who are more sociable, on the average, than their population.

The third explanation has a name - it is the null hypothesis. The general form in which it is stated varies from researcher to researcher. Here are three versions, all of which are consistent with each other:

Version A of the null hypothesis:

The observed difference was created by sampling error. (Note that the term sampling error refers only to random errors-not errors created by a bias.)

Version B of the null hypothesis:

There is no true difference between the two groups. (The term true difference refers to the difference we would find in a census of the populations, that is, the difference we would find if there were no sampling errors.)

Version C of the null hypothesis:

The true difference between the two groups is zero.

Significance tests determine the probability that the null hypothesis is true. (We will be considering the use of specific significance tests in Topics 41-42 and 48-50.) Suppose for our example we use a significance test and find that the probability that the null hypothesis is true is less than 5 in 100; this would be stated as p < .05, where p obviously stands for probability. Of course, if the chances that something is true is less than 5 in 100, it's a good bet that it's not true. If it's probably not true, we reject the null hypothesis, leaving us with only the first two explanations that we started with as viable explanations for the difference.

There is no rule of nature that dictates at what probability level the null hypothesis should be rejected. However, conventional wisdom suggests that .05 or less (such as .01 or .001) is reasonable. Of course, researchers should state in their reports the probability level they used to determine whether to reject the null hypothesis.

Note that when we fail to reject the null hypothesis because the probability is greater than .05, we do just that: We "fail to reject" the null hypothesis and it stays on our list of possible explanations; we never "accept" the null hypothesis as the only explanation-remember, there are three possible explanations and failing to reject one of them does not mean that you are accepting it as the only explanation.

An alternative way to say that we have rejected the null hypothesis is to state that the difference is statistically significant. Thus, if we state that a difference is statistically significant at the .05 level (meaning .05 or less), it is equivalent to stating that the null hypothesis has been rejected at that level.

When you read research reported in academic journals, you will fmd that the null hypothesis is seldom stated by researchers, who assume that you know that the sole purpose of a significance test is to test a null hypothesis. Instead, researchers tell you which differences were tested for significance, which significance test they used, and which differences were found to be statistically significant. It is more common to find null hypotheses stated in theses and dissertations since committee members may wish to make sure that the students they are supervising understand the reason they have conducted a significance test.

As we consider specific significance tests in the next three parts of this book, we'll examine the null hypothesis in more detail.

EXERCISE ON TOPIC

1. How many explanations were there for the difference in sociability between psychologists and

engineers in the example in this topic?

2. What does the null hypothesis say about sampling error?

3. Does the term sampling error refer to random errors or to bias?

4. The null hypothesis says that the true difference equals what value?

5. What is used to determine the probabilities that null hypotheses are true?

6. For what does p < .05 stand?

7. Do we reject the null hypothesis when the probability of its truth is high or when it is low?

8. What do we do if the probability is greater than .05?

9. What is an alternative way of saying that we have rejected the null hypothesis?

10. Are you more likely to find a null hypothesis stated in a journal, article or in a thesis?