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Ratuiszt

Answered question

2022-09-30

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

Answer & Explanation

Cullen Kelly

Beginner2022-10-01Added 7 answers

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

S D = \sqrt{\frac{(S D_{1}^{2} + S D_{2}^{2})}{2}}

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

S D = \sqrt{\frac{(n_{1} - 1) S D_{1}^{2} + (n_{2} - 1) S D_{2}^{2}}{n_{1} + n_{2} - 2}}

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.

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