Question

The following table shows the results of a repeated-measures analysis of variance comparing two treatment conditions with a sample of n = 12 participants. Note that several values are missing in the table. What is the missing value for SStotal?

Source	SS	df	MS
Between	xx	xx	12	F = 4.00
Within	xx	xx
Bet. Sub.	35	xx
Error	xx	xx	xx
Total	xx	xx

45

47

80

148

Answer 1

Let us start with the degrees of freedom,

Total number of subjects(N_subjects)=12

Number of treatments(K)=2

Total number of data(N) =12*2=24

Using the above data,we will calculate the degrees of freedom

df_between=K-1=2-1=1

df_within=N-K=24-2=22

df_subjects=N_subjects-1=12-1=11

df_error=df_within-df_subjects=22-11=11

df_total=N-1=24-1=23

Given: SS_{betw.subjects}=35

MS_between=12

We have MS_between=12 and df_between=1

we know that MS_between=SS_between/df_betweeen

12=SS_between/1 which gives SS_between=12*1=12

Therefore,SS_between=12

Now,let us do a reverse calculation.that is,we will use the options of answer to calculate the other values.

First let us assume SS_total=148

SS_total is nothing but sum of SS_between and SS_within

We have SS_between=12 and assuming SS_total=148,we will get

148=12+SS_within

SS_within=148-12 =136

SS_error=SS_within-SS_{betw.subjects}=136-35=101

SS_error=101

As we know that SS_error and SS_{betw.subjects} are subset of SS_within.when we sum those two values ,we will get  SS_within

SS_within=101+35=136

Hence,SS_total=148

The completed ANOVA table is given below:

Source	SS	df	MS	F-statistic
Between	12	1	12	F = 4.00
Within	136	22
Bet. Sub.	35	11
Error	101	11	9.18
Total	148	23