The following summary table presents the results from an ANOVA comparing four tr

Question

The following summary table presents the results from an ANOVA comparing four treatment conditions with n=10 participants in each condition. Complete all missing values. ( Start with the df column)

Source                   SS                          df                        MS

Btw treatments      -----                         -----                     10             F= __

Within treatment    ___                        ___                     ___

Total                     174                          ------

Please show work.

Explanation / Answer

Degrees of freedom:

Nunber of treatments (k) = 4

So,

Btw treatment degrees of freedom = k - 1 = 4 - 1 = 3

Number of observations (n) = 10

So,

Total degrees of freedom = n - 1 = 10 - 1 = 9

Error degrees of freedom

= Total degrees of freedom - Btw treatment degrees of freedom

= 9 - 3

= 6

Sum of squares (SS):

MS = SS/df

In case of between treatments, MS = 20 and df = 3

So,

20 = SS / 3

SS = 60

Given,

Total SS = 174

So,

Within treatment SS = 174 - 30 = 144

Mean sum of Squares (MS):

MS = SS/df

For within treatment, SS = 144, df = 6

So,

MS = 144 / 6

MS = 24

F Value:

F = MS (Btw treatment) / MS (Within Treatment)

F = 10 / 24

F = 0.4167 (Rounded off to 4 decimal places)

The ANOVA table will be:

Source SS df MS F Btw Treatments 30 3 10 0.4167 Within Treatments 144 6 24 - Total 174 9 - -

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