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Question
ookmarks Window Help ngcengage.com Analysis of Variance avioral Sciences participated (dfwti 30 N - K) with n 8 in each treatment. A researcher conducts an experiment comparing three treatment conditions with a separate sample of n s in each treatment. An ANOVA is used to evaluate the data, and the results of the ANOVA are presented in the following table. Complete all missing values in the table. Hint: Begin with the values in the df column. 3. Source ss d Ms etween treatments Within treatments Total 62 SourceSS MS Between 20 2 10F 5.00 Within 42 21 2 treatments Total 62 23 8 6 8 9
Explanation / Answer
Step 1:
Degrees of Freedom (df) of Between Treatments = c - 1
where c = Number of Treatments.
Here, Number of Treatments = 3.
Substituting,
df for Between Treatments = c - 1 = 3 - 1 = 2
Step 2:
Degrees of Freedom for Total = N - 1,
where N = Total number of observations = Number of Treatments X Number of elements in each sample
= 3 X 8 = 24
So,
df for Total = 24 - 1 = 23
Step 3:
Degess of Freedom for Within Treatments = df of Total - df for Between Treatments
= 23 - 2 = 21
Step 4:
Sum of Squares for With Treatments = Mean Sum of Squares within Treatments X Degrees of Freedom of Within Treatments
= 2 X 21 = 42
So,
SS for Within Treatment = 42
Step 5:
Sum of Squares Between Treatments = Total Sum of Squares - Sum of Squares Within Treatments
= 62 - 42 = 20
So,
SS for Between Treatments = 20
Step 6:
Mean Square between Treatments = Sum of Squares between Treatments/Degrees of Freedom for between Treatments
= 20/2 = 10
So,
MS for between Treatments = 10
Step 7:
F = MS for Between Treatments/MS for Within Treatments
= 10/2 = 5
Thus, we get the ANOVA Table as follows:
Source SS df MS F
Between treatments 20 2 10 5.00
Within Treatments 42 21 2
Total 62 23
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