# How do you find the pooled standard deviation in an ANOVA table?

How do you find the pooled standard deviation in an ANOVA table?
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Cullen Kelly
Note that a pooled standard deviation assumes that the population variances are equal. Now, there are two formulas for pooled standard deviation depending if the factors tested in ANOVA have the same group size.
For same group size, the pooled standard deviation can be computed as
$SD=\sqrt{\frac{\left(S{D}_{1}^{2}+S{D}_{2}^{2}\right)}{2}}\phantom{\rule{0ex}{0ex}}$
where $S{D}_{1}$ is the standard deviation of the first group and $S{D}_{2}$ is thestandard deviation of the second group.
For unequal group size, the pooled standard deviation can be computed as
$SD=\sqrt{\frac{\left({n}_{1}-1\right)S{D}_{1}^{2}+\left({n}_{2}-1\right)S{D}_{2}^{2}}{{n}_{1}+{n}_{2}-2}}\phantom{\rule{0ex}{0ex}}$
where
$S{D}_{1}$ is the standard deviation of the first group.
$S{D}_{2}$ is the standard deviation of the second group.
${n}_{1}$ is the group size of the first group.
${n}_{2}$ is the group size of the seconf group.