Use statistical tables to determine significance (to include: using an…

The idea

An inferential test produces an observed value, and a table of critical values decides whether that value is unlikely enough to count. Reading the table needs three facts from the study: the level of significance, normally 0.05, whether the hypothesis was directional and so one tailed or non directional and so two tailed, and either the number of participants or of pairs or the degrees of freedom. Then the comparison runs in a direction fixed by the test. Chi Square, Spearman's rho, Pearson's r and both t tests need the observed value to be equal to or greater than the critical value. Mann Whitney U, Wilcoxon and the sign test need the observed value to be equal to or less than the critical value before the null hypothesis can be rejected.

What earns the marks

• Selecting the right cell of the table: the column for p less than or equal to 0.05, the one tailed side for a directional hypothesis, and the row for the degrees of freedom or the value of N that the test uses.
• Working out degrees of freedom where the test needs them, so Chi Square uses (rows - 1)(columns - 1) and the related t test uses the number of pairs minus one.
• Stating the comparison in full with both figures, for example that an observed Chi Square value of 7.82 is greater than the critical value of 3.84 for one degree of freedom at p less than or equal to 0.05.
• Concluding in the language of hypotheses: the result is significant, the null hypothesis is rejected, and the probability that the difference arose by chance is five percent or less.

Common mistakes and how to put them right

• Reading the two tailed column when the hypothesis predicted a direction, which applies a stricter critical value and can turn a significant result into a non significant one.

• Applying the greater than rule to every test, so an observed Wilcoxon value of 8 against a critical value of 21 is called non significant when the result is in fact significant.

• Using the number of participants where the table asks for degrees of freedom, or reading the row for a related test when the design was unrelated.

• Writing that the result proves the hypothesis, and leaving out the level of significance at which the decision was made.

Exam tips

• The paper prints the extract from the tables, so every number you need is on the page and the marks come from choosing the right cell and stating the comparison, not from memorising critical values.
• Write the comparison as a sentence containing both values and the level of significance, because the mark scheme credits observed against critical rather than the bare word significant.
• If the stem says the researcher predicted that one group would score higher, that is a directional hypothesis and the one tailed column is the one to use.
• Expect a follow up mark for saying what rejecting the null hypothesis means for the study, so write about the actual variables and participants rather than about hypotheses in the abstract.