Formula Review

if δ₀=1 then

Test statistic is :

$S{S}_{\text{between}}={{\displaystyle \sum }}^{\text{}}\left[\frac{{(s_j)}^2}{n_j}\right]-\frac{{\left({{\displaystyle \sum }}^{\text{}}{s}_j\right)}^2}{n }$

$S{S}_{\text{total}}={{\displaystyle \sum }}^{\text{}}{x}^2-\frac{{\left({{\displaystyle \sum }}^{\text{}}x\right)}^2}{n}$

$S{S}_{\text{within}}=S{S}_{\text{total}}-S{S}_{\text{between}}$

df_between = df(num) = k – 1

df_within = df(denom) = n – k

MS_between = $\frac{S{S}_{\text{between}}}{d{f}_{\text{between}}}$

MS_within = $\frac{S{S}_{\text{within}}}{d{f}_{\text{within}}}$

F = $\frac{M{S}_{\text{between}}}{M{S}_{\text{within}}}$

• k = the number of groups
• n_j = the size of the j^th group
• s_j = the sum of the values in the j^th group
• n = the total number of all values (observations) combined
• x = one value (one observation) from the data
• $s_{\bar{x}}{}^2$ = the variance of the sample means
• $s^2{}_{pooled}$ = the mean of the sample variances (pooled variance)