W5 T-Tests

One-sample t-test

A statistical test used to compare the mean of a single sample to a known or hypothesised population mean to see if they differ significantly.

Matched-sample t-test

A test comparing two related groups — often the same participants measured twice (before/after) or matched participants — to see if their means differ significantly.

Independent-sample t-test

A test comparing the means of two unrelated groups (e.g., control vs. experimental) to see if there is a statistically significant difference.

Pooled variance

An average of the variances from two samples, weighted by their sample sizes, used when we assume both groups have equal variances.

Welch’s t

A variation of the independent-sample t-test that does not assume equal variances between groups; adjusts degrees of freedom accordingly.

Cohen’s d

A standardised measure of effect size that expresses the difference between two means in terms of standard deviations.

Absolute t statistic

The magnitude of the t-value, ignoring its sign; the sign only shows direction, not the size of the effect.

t-test statistic

The calculated value from a t-test that reflects the ratio of the difference between sample means (or a sample mean and a population mean) to the variability of the data.

Standard error

A measure of how much sample means vary from the true population mean; calculated as the standard deviation divided by the square root of the sample size.

Central Limit Theorem

A statistical principle stating that, for large enough samples, the sampling distribution of the mean will be approximately normal — and that the standard error is the standard deviation divided by the square root of the sample size.

Z-test

A statistical test similar to the t-test but used when the population variance is known (or sample size is large enough) and data are assumed to follow a normal distribution.

Confidence limit

The upper or lower boundary of a confidence interval, representing the range within which we expect the population parameter to fall at a given confidence level.

Levene's Test

A statistical test used to check if two or more groups have equal variances — often run before deciding whether to use pooled variance or Welch’s t in a t-test.