Question

1. An experimenter gave the same set of 12 math problems to three groups of people: telling one group the problems are easy, one group the problems are medium, and one group that the problems are hard. The performance of the math problem solving of the three groups are summarized in the table.

Easy	Medium	Difficult
8	5	3
9	6	4
10	6	5
11	7
	8

Mean : 9.5                                 6.4                                            4

The computation of SSs are summarized in the following table.

	SS	DF	MS	F
Between	53.467	??	??	??
Within	12.2	??	??
Total	65.67

1. Fill out the blanks in the above summary table.
2. State your conclusion on the hypothesis testing based on the above analysis.
3. You tried to replicate the study and got the following results.

Easy	Medium	Difficult
5	4	4
6	5	5
7	5	6
8	6
	7

        Mean 6.5                                     5.4                                           5.0

You printed SPSS output, and somehow SSs, DFs, and MSs are not printed well; only the SStotal value is visible. Fill out all the blank using your knowledge on one-way ANOVA.

	SS	DF	MS	F
Between	??	??	??	??
Within	??	??	??
Total	16.667

4. You replicated the same study yet one more time and got the following results.

Easy	Medium	Difficult
6	5	5
7	5	5
6	6	5
7	5
	6

          Mean         6.5                             5.4                                              5.0

                     

You printed SPSS output, and somehow SSs, DFs, and MSs are not printed well; only the SStotal value is visible. Fill out all the blank using your knowledge on one-way ANOVA.

	SS	DF	MS	F
Between	??	??	??	??
Within	??	??	??
Total	6.667

Answer 1

We shall use the following table to make calculations and fill the blanks in the tables given in the question.

(A) The computation of SSs are summarized in the following table.Mean Square Between Groups:

MS_B = SS_B / (k − 1)

	SS	DF	MS	F
BETWEEN	53.467	(3-1)=2	(53.467/2)=26.7335	(26.73/1.356)=19.7208
WITHIN	12.2	(12-3)=9	(12.2/9)=1.3556
TOTAL	65.67

(B) State your conclusion on the hypothesis testing based on the above analysis.

Analysis of Variance Results

F-statistic value = 19.72088

P-value = 0.00051

Set up hypotheses and determine level of significance

H₀: μ₁ = μ₂ = μ₃  

H₁: Means are not all equal (At least one of the mean values does not equal the others) α=0.05

(C) Fill out all the blank using your knowledge on one-way ANOVA.

	SS	DF	MS	F
BETWEEN	4.4667	(3-1)=2	(4.4667/2)=2.2333	(2.2333/1.3556)=1.6475
WITHIN	12.2003	(12-3)=9	(12.2003/9)=1.3556
TOTAL	16.667

Analysis of Variance Results

F-statistic value = 1.6475

P-value = 0.24565

(A) You replicated the same study yet one more time and got the following results.You printed SPSS output, and somehow SSs, DFs, and MSs are not printed well; only the SStotal value is visible. Fill out all the blank using your knowledge on one-way ANOVA.

	SS	DF	MS	F
BETWEEN	4.4667	(3-1)=2	(4.4667/2)=2.2333	(2.2333/0.2445=9.1361
WITHIN	2.2001	(12-3)=9	(2.2001/9)=0.2445
TOTAL	6.667

Analysis of Variance Results

F-statistic value = 9.13606

P-value = 0.00681