In a research on the effect of child-rearing practices on stress-proneness of…

Concept — how a research hypothesis is tested. A research (alternative) hypothesis is never tested directly. It is tested through its logical complement, the null hypothesis, which asserts that no effect or no relationship exists in the population. The level of significance is the ceiling the researcher fixes in advance on the probability of wrongly rejecting a true null hypothesis. Because the two statements are complementary claims about the same population parameter, evidence strong enough to discard one is evidence in favour of the other.

Applying it to this study

1. Research hypothesis: child-rearing practices do influence stress-proneness — that is, an effect exists in the population.

2. Its complement, the null hypothesis: child-rearing practices have no influence on stress-proneness — no effect exists.

3. The researcher fixes the level of significance at 0.01, so the null hypothesis will be discarded only if the observed result, or one more extreme, would occur in fewer than 1 sample in 100 when the null hypothesis is true.

4. The available evidence meets that standard and the null hypothesis is rejected at 0.01.

5. Discarding "no effect" leaves its complement, "an effect exists", as the statement the data support. The research hypothesis is therefore accepted at the 0.01 level of significance.

Cross-check

• The null hypothesis and the research hypothesis are complementary claims about the same population parameter, so a single set of evidence can never discard both: rejecting the null hypothesis is precisely what leaves the research hypothesis standing.

• Rejecting the null hypothesis is itself the decision rule of the test, so the analysis does not end undecided — the whole purpose of advancing the null hypothesis was to make this decision possible.

• 0.01 is a stricter standard than the commonly used 0.05, so a result significant at 0.01 is significant at 0.05 as well; the conclusion holds a fortiori.

• "Accepted" here means supported at the stated level of significance. The 0.01 level is the long-run rate at which a true null hypothesis would be wrongly rejected — a standard of evidence fixed before the data were seen, and not a proof.

• The decision is not symmetric in the other direction: had the evidence failed to reach the 0.01 standard, the null hypothesis would only have been retained for want of evidence, and would not thereby have been established as true.

Result: the research hypothesis that child-rearing practices influence stress-proneness is accepted at the 0.01 level of significance.