Test (Stats)

A hypothesis test using the standard normal distribution to determine if a sample mean or proportion differs significantly from a known value.

When the population variance is known or the sample size is large enough for the central limit theorem.

Whether observed data are unlikely under the null hypothesis using the normal distribution.

A test used to compare means when the population standard deviation is unknown or the sample is small.

Independent (two-sample), paired (before/after), and others.

Whether two groups differ in their averages in a statistically meaningful way.

A measure of how asymmetric a distribution is around its mean.

The right tail is longer.

The left tail is longer.

A measure of how heavy or light the tails of a distribution are.

More data in the tails and more outliers.

Lighter tails and fewer extremes.

A hypothesis test predicting a specific direction, using only one tail of the distribution.

A hypothesis test checking for differences in either direction, using both tails.

It affects interpretation of p-values and critical regions.

A test comparing the means of three or more groups.

By separating variability into between-group and within-group variance.

It controls Type I error more effectively.

Post-hoc tests to identify which groups differ.

A measure of linear relationship strength and direction between two continuous variables.

-1 to +1, with 0 meaning no linear correlation.

Correlation does not imply causation.

A non-parametric alternative to one-way ANOVA for comparing three or more independent groups.

By using ranked data rather than raw values.

Whether at least one group’s distribution differs from the others.

A non-parametric alternative to repeated-measures ANOVA.

When analyzing three or more related/matched samples without assuming normality.

By ranking data within each subject and comparing conditions.

A non-parametric test for paired data considering only the direction of change.

The magnitude of differences.

When assumptions about difference sizes cannot be made or data are ordinal.

A non-parametric test for paired data using both rank and direction.

It includes magnitude information through rankings.

When assumptions of the paired t-test are violated or data aren’t normally distributed.