Use of Statistical Tables and Critical Values in Interpretation of Significance

How do you interpret the result from the statistical test?

To interpret the result from a statistical test, the calculated value is compared to the

appropriate critical value from a critical values table to determine whether the calculated

value is significant (reject the null hypothesis) or not significant (accept the null hypothesis).

What pieces of information must be known in order to select the appropriate critical value?

1. Whether the test is one-tailed (directional hypothesis) or two-tailed (non-directional).

2. Level of significance (for most studies this is p≤0.05).

3. The number of participants in the condition(s) (N) or the degrees of freedom (df).

Explain one tailed and two tailed test

A one-tailed test is used for a directional hypothesis which states a specific outcome (e.g.

more, slower, greater, positive, negative, etc.). A two-tailed test is used for a non-directional

hypothesis, which does not state a specific outcome (e.g. difference, correlation).

Explain the level of significance

The standard level of significance used in Psychology is p≤0.05. If the outcome has potential

implications for society, a stricter level may be selected (e.g. p≤0.01). If the study is a

replication of previous research, a more lenient level may be selected (e.g. p≤0.1).

Explain the number of participants or degrees of freedom

Each statistical test requires knowledge of the number of participants/scores or degrees of

freedom. Details of how to calculate these are listed below but will be provided in the exam:

• Chi Square: df = (number of columns – 1) x (number of rows – 1).

• Sign Test: N (total number of + signs and − signs).

• Mann Whitney: N1, N2 (number of participants/scores in conditions 1 and 2).

• Wilcoxon: N (number of participants/pairs of participants).

• Spearman’s Rho: N (number of participants/related co-variables).

• Unrelated t-test: df = N1 + N2 – 2.

• Related t-test: df = N – 1.

• Pearson’s: df = N – 2.

Explain how to compare the calculated value and critical value

The calculated value must be compared to the appropriate critical value to assess its

significance. The rules listed below are provided in the exam next to the critical values table:

• The calculated value must be greater than or equal to the critical value for significance to

be shown for: Spearman’s Rho (ignore the – sign), Chi-Squared, t-tests, Pearson’s r.

• The calculated value must be less than or equal to the critical value for significance to be

shown for: Sign test, Mann Whitney, Wilcoxon

Explain how to report the result of a Statistical Test

Ultimately, the outcome of a statistical test is reported in a specific way. This should include

all the information looked up in the critical values table and a statement of whether to accept

or reject the null hypothesis. The example template below is one way of doing this:

For a one/two-tailed test when p≤_______ and N/N1,N2/df = _______, the calculated value

(_______) is greater than/equal to/less than the critical value (_______) so the result is

significant/not significant. The null hypothesis is therefore accepted/rejected and the

alternative hypothesis is accepted/rejected.