Introductory Statistics

# Formula Review

### 13.2The F Distribution and the F-Ratio

$S S total = ∑ ​ x 2 − ( ∑ ​ x ) 2 n S S total = ∑ ​ x 2 − ( ∑ ​ x ) 2 n$

$S S within =S S total −S S between S S within =S S total −S S between$

dfbetween = df(num) = k – 1

dfwithin = df(denom) = nk

MSbetween = $S S between d f between S S between d f between$

MSwithin = $S S within d f within S S within d f within$

F = $M S between M S within M S between M S within$

F ratio when the groups are the same size: F = $n s x ¯ 2 s 2 pooled n s x ¯ 2 s 2 pooled$

Mean of the F distribution: µ = $df(num) df(denom)−2 df(num) df(denom)−2$

where:

• k = the number of groups
• nj = the size of the jth group
• sj = the sum of the values in the jth group
• n = the total number of all values (observations) combined
• x = one value (one observation) from the data
• $s x ¯ 2 s x ¯ 2$ = the variance of the sample means
• $s 2 pooled s 2 pooled$ = the mean of the sample variances (pooled variance)

### 13.4Test of Two Variances

F has the distribution F ~ F(n1 – 1, n2 – 1)

F = $s 1 2 σ 1 2 s 2 2 σ 2 2 s 1 2 σ 1 2 s 2 2 σ 2 2$

If σ1 = σ2, then F = $s 1 2 s 2 2 s 1 2 s 2 2$ Do you know how you learn best?
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