n=15 and there are 3 groups
These data are analyzed by an ANOVA, and the resutls are reported in the following summary table. fill in all missing values in the table.
* All that is given in the table is the MS(mean square) within treatments=20 and F=4 (f-ratio)
I have to find the SS Between and Within treatments.
The df for between and within treatments, this what I got:
df total=44 (n=15, (15)(3)=45, N=45, dftotal=N-1, 45-1=44)
df between= k-1= 3-1= 2
df within= N-k=45-3= 42
-My question is how do I find the MS within treatments
-SS for within and between treatments,
when only the F (4) is given, the MS of between treatments is given (20), and the df's that I calculated above?
Please help! Thank You
OK, let's look at what you have and what you need in table form:
............ SS ...... df ..... MS ..... F
Between..... ? ....... 2 ...... 20 ..... 4
Within...... ? ....... 42 ..... ?
Total ...... ? ....... 44
To find SS between, take df between times MS between.
To find SS within, take df within times MS within.
SS total is SS between plus SS within.
To find MS within, take MS between and divide by F-ratio.
That should complete the table.
I hope this will help.
Thank you so much!
To find the missing values in the summary table, we can use the formula:
SS Between + SS Within = SS Total
Given that df total = 44 and MS within treatments = 20, we can calculate SS within treatments:
SS Within = MS Within * df Within
Substituting the values:
SS Within = 20 * 42 = 840
Next, we can find SS Between using the formula:
SS Between = SS Total - SS Within
Given that SS Total is missing, we need to find it. We know that:
SS Total = MS Within * df Within + MS Between * df Between
We already have the values for MS Within (20) and df Within (42), and we also have the value of df Between (2) that you calculated. Now we just need to find MS Between.
To find MS Between, we can use the formula:
MS Between = SS Between / df Between
Substituting the values we have:
4 = SS Between / 2
SS Between = 4 * 2 = 8
Now we can find SS Total using the formula:
SS Total = MS Within * df Within + MS Between * df Between
Substituting the values:
SS Total = (20 * 42) + (8 * 2) = 840 + 16 = 856
Finally, we can fill in the missing values in the summary table:
SS Between = 8
SS Within = 840
SS Total = 856