A researcher used an analysis of variance to compare three treatment conditions with

a separate sample of n = 8 participants in each treatment. The results of the analysis are shown
in the following summary. Fill in all missing values in the table. (Hint: Start with the df
values.)

Source SS df MS
Between Treatments ____ ____ ____ F = 4
Within Treatments 63 ____ ____
Total ____ ____

So,the DF is 2, 7 and total is 9 am I correct? Don't know how to get the rest?

Here is how to finish your table:

To calculate df between:
k - 1 = 3 - 1 = 2
Note: k = number of levels.

To calculate df within:
N - k = 24 - 3 = 21
Note: N = total number of values in all levels.

df total = df between + df within = 23

To calculate MS between:
SS between/df between = MS between
Therefore: x/2 = 12; x = 24 (SS between)

To calculate MS within:
�SS within/df within = 63/21 = 3

To calculate F-ratio:
MS between/MS within = F-ratio
Therefore: x/3 = 4; x = 12 (MS between)

SS total = SS between + SS within = 87

Double check my calculations.

You are correct that the degrees of freedom (df) for "Between Treatments" is 2 and the total df is 9. To fill in the missing values, we can use the following formulas:

SS (Sum of Squares) = MS (Mean Square) * df

Let's start with "Within Treatments":

SS (Within Treatments) = MS (Within Treatments) * df (Within Treatments)

Since we have the F statistic (F = 4), we can also use the formula:

F = MS (Between Treatments) / MS (Within Treatments)

Now, let's apply these formulas to fill in the missing values:

Source SS df MS
Between Treatments ____ 20 ____ F = 4
Within Treatments 63 6 ____
Total 83 9

To find the MS (Within Treatments), we rearrange the F formula:

MS (Within Treatments) = MS (Between Treatments) / F

MS (Within Treatments) = 20 / 4

MS (Within Treatments) = 5

Now, we can calculate the SS (Between Treatments):

SS (Between Treatments) = MS (Between Treatments) * df (Between Treatments)

SS (Between Treatments) = 5 * 2

SS (Between Treatments) = 10

Finally, we calculate the Total SS:

Total SS = SS (Between Treatments) + SS (Within Treatments)

Total SS = 10 + 63

Total SS = 73

Plugging these values into the table, we get:

Source SS df MS
Between Treatments 10 2 5 F = 4
Within Treatments 63 6 5
Total 73 9

I hope this helps!

Yes, you are correct that the degrees of freedom (df) for between treatments is 2, the df for within treatments is 7, and the total df is 9. To calculate the missing values in the table, we can follow these steps:

1. Calculate the sum of squares (SS) for Between Treatments:
SS Between = MS Between * df Between
In this case, the MS Between is F (which is 4) and the df Between is 2.
So, SS Between = 4 * 2 = 8

2. Calculate the mean square (MS) for Within Treatments:
MS Within = SS Within / df Within
In this case, we are given the SS Within (which is 63) and need to find the df Within.
Since there are n = 8 participants in each treatment and there are 3 treatments, the total number of participants is 8 * 3 = 24.
Therefore, the df Within is (n * k) - k = (8 * 3) - 3 = 21.
Now, we can calculate the MS Within:
MS Within = 63 / 21 = 3

3. Calculate the Total SS:
Total SS = SS Between + SS Within
In this case, we are given the SS Between (which is 8) and need to find the SS Within.
To find SS Within, we can use the formula:
SS Within = MS Within * df Within = 3 * 21 = 63
Now we can calculate the Total SS:
Total SS = 8 + 63 = 71

Now, let's update the table with the calculated values:

Source SS df MS
Between Treatments 8 2 4
Within Treatments 63 21 3
Total 71 9 -

So, the correct values for the table are SS Between = 8, df Between = 2, MS Within = 3, df Within = 7, and Total SS = 71.

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