Explaining Psychological Statistics by Cohen Barry H.;

Author:Cohen, Barry H.;
Language: eng
Format: epub
Publisher: John Wiley & Sons, Incorporated
Published: 2013-11-12T05:00:00+00:00

Interpreting Significant Results

Had we rejected the null, we could have concluded that the population means are not all the same, but we could not conclude that they are all different. We would need to conduct follow-up t tests to determine which pairs of population means are significantly different from each other (this will be explained in the next chapter). Moreover, because the three conditions were not created by the experimenter, rejecting the null would not mean that parental death causes changes in optimism. Alternative explanations are possible. For instance, pessimism may run in families, and pessimism may lead to poor health and early death. According to this hypothetical explanation, both the child's pessimism and the early parental death are caused by a third variable—that is, the parents' pessimism.

If the independent variable had involved an experimental manipulation (e.g., all subjects are given a “test” and then given randomly chosen feedback suggesting that their future job prospects are good, fair, or poor), significant differences in optimism between the (randomly assigned) groups could be attributed to the feedback manipulation. In this case, we might talk of the underlying population means being different, but we are not referring to actual populations; we are referring to theoretical populations (e.g., the mean of the population if everyone in the population had received positive feedback, the mean if everyone in the population had received negative feedback, etc.). To conclude that the population means are not all the same (i.e., reject the null hypothesis in a one-way ANOVA) in this case would be to say that the manipulation had some effect on optimism. To quantify the size of that effect, you will need to calculate an effect-size meaure like the ones described later in this section.

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