Statistics Tests and Concepts: T-Tests, ANOVA, Chi-Square, Regression, and Effect Sizes

Z-Test

Compares one group to a known population mean when the population standard deviation is known and the sample size is large.

One-Sample t-Test

Compares one group to a known average when the population standard deviation is unknown.

Two-Independent Samples t-Test

Compares the averages of two completely different groups.

Dependent (Paired) Samples t-Test

Compares the same group measured at two different times.

One-Way ANOVA

Compares three or more groups using one independent variable.

Two-Way ANOVA

Examines the effect of two different independent variables on one dependent variable.

Correlation

Measures the strength and direction of the relationship between two variables.

Regression

Uses one variable to predict another variable.

One-Way Chi-Square

Tests whether the frequencies of one categorical variable are evenly distributed.

Two-Way Chi-Square

Tests whether two categorical variables are related.

η²

Effect size for a one-way ANOVA.

Coefficient of determination

r².

s

Sample standard deviation.

Sample correlation

r

R²

Percent of variance accounted for by the regression.

se

Average difference between predicted and actual scores.

s²

Sample variance.

Sample mean symbol

M.

Population variance symbol

σ².

Alpha

Type I error rate.

sMD

Standard deviation of difference scores

M

Sample mean.

σ²

Population variance.

sM

Standard error of the mean.

Intercept symbol

a.

Sample size symbol

n.

µ

Population mean.

Population standard deviation

σ.

Regression slope symbol

b.

Sample standard deviation

s.

Sample variance

s².

MD

Mean of difference scores.

SS

Sum of squares.

Variance if SD = 4

→ 16.

n

Group size, N = total sample size.

Nonparametric test

Chi-square.

Population mean symbol

µ.

sD

Standard deviation of difference scores.

sample correlation symbol

r.

Sp²

Pooled variance.