SOLUTION: Fill in the missing values for this ANOVA summary table: S.S. d.f. M.S. F Between 1723.267 7 Within TOTAL 2999.267 51 I am so stuck and have gotten this one wrong sever

Question 1205060: Fill in the missing values for this ANOVA summary table:
S.S. d.f. M.S. F
Between 1723.267 7
Within
TOTAL 2999.267 51
I am so stuck and have gotten this one wrong several times, please help!

Answer by math_tutor2020(3816) (Show Source): You can put this solution on YOUR website!

Refer to this page
https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Inferential_Statistics_and_Probability_-_A_Holistic_Approach_(Geraghty)/13%3A_One_Factor_Analysis_of_Variance_(ANOVA)/13.05%3A_Understanding_the_ANOVA_Table

At the top of that page is the ANOVA template.
Instead of "factor" we'll use "between".
Instead of "error" we'll use "within".

Here's the table your teacher has given you

	SS	df	MS	F
Between	1723.267	7
Within
Total	2999.267	51

We know the SS (sum of squares) values for rows 1 and 3.
The missing SS value is the difference of the two given SS values.

SS within = (SS total) - (SS between)
SS within = 2999.267 - 1723.267
SS within = 1276

Let's update the table

	SS	df	MS	F
Between	1723.267	7
Within	1276
Total	2999.267	51

Refer back to the link I mentioned.
Focus on the "degrees of freedom (df)" column.
The df expressions are:
between = k-1
within = n-k
total = n-1

Notice that
df total = (df between) + (df within) = (k-1)+(n-k) = n-1

The df value for "between" is 7
k-1 = 7
k = 7+1
k = 8
The df value for "total" is 51
n-1 = 51
n = 51+1
n = 52
Therefore
df within = n-k = 52-8 = 44

Or we could say
df within = (df total) - (df between)
df within = 51 - 7
df within = 44
which is a faster shortcut.

Let's update the table

	SS	df	MS	F
Between	1723.267	7
Within	1276	44
Total	2999.267	51

According to that link I posted,
MS between = (SS between)/(df between)
MS between = (1723.267)/(7)
MS between = 246.181
and,
MS within = (SS within)/(df within)
MS within = (1276)/(44)
MS within = 29
There doesn't exist "MS total".
We'll leave that cell blank.
"MS" stands for "Mean Square".

Let's update the table

	SS	df	MS	F
Between	1723.267	7	246.181
Within	1276	44	29
Total	2999.267	51

We have one last gap to fill in.
To get the F statistic, we divide the MS between over the MS within

F = (MS between)/(MS within)
F = (246.181)/(29)
F = 8.489

Here is the fully completed ANOVA table.

	SS	df	MS	F
Between	1723.267	7	246.181	8.489
Within	1276	44	29
Total	2999.267	51

The two cells under the F statistic are left blank.

Some ANOVA tables will include the F critical value and/or the p-value. However, I'll stop here since it appears your teacher wants just up to the F statistic.

Side note: This applies to single factor ANOVA only.

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