Chapter 12 Formulas

df_between = N_groups − 1

df_within = df₁ + df₂ +…+ df_last (in which df₁, df₂, etc., are the degrees of freedom, N − 1, for each sample) [formula for a one-way between-groups ANOVA]

df_total = df_between + df_within [formula for a one-way between-groups ANOVA]

df_total = N_total − 1

SS_total = ∑(X − GM)²

SS_within = ∑(X − GM)² [formula for a one-way between-groups ANOVA]

SS_between = ∑(M − GM)²

SS_total = SS_within + SS_between [alternative formula for a one-way between-groups ANOVA]

[formula for a one-way between-groups ANOVA]

, if equal sample sizes

, for any two sample means

, if unequal sample sizes

Chapter 12 Symbols

F

df_between

df_within

MS_between

MS_within

df_total

SS_between

SS_within

SS_total

GM

R²

HSD

N′