Inferential Statistics

Inferential statistics

Statistical tests used to determine whether results are significant and not due to chance.

Significance

A statistical judgement about whether the findings are unlikely to have occurred by chance.

p-value

The probability that results occurred by chance.

5 percent significance level

The standard p-value of 0.05 used in psychology.

Critical value

A value from a statistical table used to judge whether the observed result is significant.

Observed value

The result of the statistical test calculated from the data.

Observed value rule

Whether observed value must be higher or lower than critical value depending on the test.

Significance decision

If observed value meets the critical value rule, the result is significant.

Rejecting the null hypothesis

If results are significant, the null hypothesis is rejected.

Accepting the null hypothesis

If results are not significant, the null hypothesis is accepted.

Type I error

False positive; rejecting the null hypothesis when it is true.

Type II error

False negative; accepting the null hypothesis when it is false.

When Type I errors occur

Using too lenient a significance level (e.g. p = 0.10).

When Type II errors occur

Using too strict a significance level (e.g. p = 0.01).

Parametric test

A statistical test requiring normal distribution and interval data.

Non-parametric test

A statistical test used for non-normal data or ordinal/nominal data.

Level of measurement

Nominates whether data is nominal, ordinal or interval/ratio.

Nominal data

Data in categories with no numerical meaning.

Ordinal data

Ranked data with inconsistent intervals.

Interval data

Data with equal numerical intervals but no absolute zero.

Ratio data

Interval data with an absolute zero point.

Test selection

Depends on design, level of measurement and correlation vs difference.

Correlation test

Used when exploring relationships between two co-variables.

Difference test

Used when comparing two groups or conditions.

Related design

A repeated measures or matched pairs design.

Unrelated design

An independent groups design.

Directional hypothesis

Predicts the direction of the effect; requires a one-tailed test.

Non-directional hypothesis

Predicts a difference but not the direction; requires a two-tailed test.

Chi-square test

A test used for nominal data with independent groups.

Chi-square requirement

Data must be frequencies, not scores.

Chi-square hypothesis type

Used for tests of association or difference with nominal data.

Sign test

A non-parametric test for repeated measures design with nominal data.

Sign test calculation

Count number of pluses and minuses; smallest number is observed value.

Mann-Whitney U test

A test for unrelated design with ordinal or interval data.

Mann-Whitney requirement

Independent groups; measuring difference.

Wilcoxon signed-rank test

A test for related design with ordinal or interval data.

Wilcoxon requirement

Repeated measures or matched pairs design.

Spearman’s rho

A correlation test for ordinal data or non-parametric conditions.

Spearman’s requirement

Measures strength and direction of correlation.

Pearson’s r

A correlation test for interval data with parametric assumptions.

Parametric test requirement

Normally distributed data and equal variances.

HOLY GRID purpose

Helps choose correct statistical test based on design, data type and hypothesis.

HOLY GRID difference, unrelated, ordinal

Mann-Whitney U.

HOLY GRID difference, related, ordinal

Wilcoxon signed-rank test.

HOLY GRID difference, unrelated, nominal

Chi-square.

HOLY GRID difference, related, nominal

Sign test.

HOLY GRID correlation, ordinal

Spearman’s rho.

HOLY GRID correlation, interval

Pearson’s r.

One-tailed test

Uses directional hypothesis and one critical value region.

Two-tailed test

Uses non-directional hypothesis and splits critical region across two tails.

Degrees of freedom

A number calculated for some tests to consult critical values.

Sign test critical value rule

Observed value must be less than or equal to critical value.

Mann-Whitney critical value rule

Observed value must be less than or equal to critical value.

Wilcoxon critical value rule

Observed value must be less than or equal to critical value.

Chi-square critical value rule

Observed value must be greater than or equal to critical value.

Spearman’s critical value rule

Observed value must be greater than or equal to critical value.

Pearson’s critical value rule

Observed value must be greater than or equal to critical value.

Wilcoxon ties

Equal ranks must be handled according to procedure.

Spearman coefficient range

Values between -1 and +1 indicating strength of correlation.

Pearson coefficient range

Values between -1 and +1 but requires interval data.

Normal distribution requirement

Parametric tests require normally distributed data.

Critical region

The area beyond the critical value where results are considered significant.

Significance in psychology

A result is significant if p < 0.05 unless otherwise stated.

Data ranking

Required for ordinal data in Mann-Whitney, Wilcoxon and Spearman tests.

Frequency data requirement

Chi-square requires data in frequency counts, not means or scores.

Observed frequencies

The actual recorded frequencies for Chi-square analysis.

Expected frequencies

Frequencies expected if null hypothesis is true.

Chi-square formula

(sum of (O - E²) ÷ E) across all categories.

Effect size

A measure showing the strength of the effect beyond significance.

Inferential test rationale

Ensures results reflect genuine effects, not random variation.