An independent measures research study compares three treatment conditions using a sample of n=5 in each treatment. For this study, the three samples have SS1=10, SS2=20, SS3= 15. What value would be obtained for MS within?
To find the mean square within (MS within), we need to calculate the sum of squares within (SS within) and then divide it by the degrees of freedom within (df within).
The sum of squares within can be calculated by summing the individual sum of squares for each treatment condition:
SS within = SS1 + SS2 + SS3
SS within = 10 + 20 + 15
= 45
Since we have three treatment conditions and each condition has n=5, the degrees of freedom within can be calculated as follows:
df within = (n-1) x number of treatment conditions
df within = (5-1) x 3
= 4 x 3
= 12
Finally, we can calculate the mean square within (MS within) by dividing the sum of squares within (SS within) by the degrees of freedom within (df within):
MS within = SS within / df within
MS within = 45 / 12
= 3.75
Therefore, the value obtained for MS within in this study is 3.75.
To calculate the value of MS within (mean square within), we need to calculate the mean square of the variances within each treatment condition.
First, let's find the degrees of freedom (df) within each treatment condition. The degrees of freedom within each treatment condition are equal to the sample size (n) minus 1. In this case, the sample size is 5 for each treatment, so df within each treatment is 5 - 1 = 4.
Next, we can calculate the mean square within by dividing the sum of squares within each treatment by the degrees of freedom within each treatment.
- Mean Square Within (MS within) for Treatment 1: MS1 = SS1 / df1 = 10 / 4 = 2.5
- Mean Square Within (MS within) for Treatment 2: MS2 = SS2 / df2 = 20 / 4 = 5
- Mean Square Within (MS within) for Treatment 3: MS3 = SS3 / df3 = 15 / 4 = 3.75
To obtain the overall value of MS within, we take the average of these mean squares within each treatment:
MS within = (MS1 + MS2 + MS3) / 3 = (2.5 + 5 + 3.75) / 3 = 3.75
So, the value obtained for MS within would be 3.75.