Question

A college dean is interested in the exam performance of students in a biology course. After the final exam, students are randomly selected from three different section of the biology course. What can be conclude with α = 0.05? The data are below.

section 1	section 2	section 3
84 68 81 65 41 75 64 77 40 78 69	90 82 82 77 75 82 81 91 70 90 82	94 81 87 82 72 77 81 87 67 86 77

Conduct Tukey's Post Hoc Test for the following comparisons:
1 vs. 3: difference =  ; significant:  ---Select--- Yes No
2 vs. 3: difference =  ; significant:  ---Select--- Yes No

f) Conduct Scheffe's Post Hoc Test for the following comparisons:
1 vs. 2: test statistic =  ; significant:  ---Select--- Yes No
2 vs. 3: test statistic =  ; significant:  ---Select--- Yes No

Answer 1

A college dean is interested in the exam performance of students in a biology course. After the final exam, students are randomly selected from three different section of the biology course. What can be conclude with α = 0.05? The data are below.

section 1	section 2	section 3
84 68 81 65 41 75 64 77 40 78 69	90 82 82 77 75 82 81 91 70 90 82	94 81 87 82 72 77 81 87 67 86 77

Conduct Tukey's Post Hoc Test for the following comparisons:
1 vs. 3: difference =  ; significant:  ---Select--- Yes
2 vs. 3: difference =  ; significant:  ---Select--- No

f) Conduct Scheffe's Post Hoc Test for the following comparisons:
1 vs. 2: test statistic =  ; significant:  ---Select--- Yes
2 vs. 3: test statistic =  ; significant:  ---Select--- No

SPSS used

Descriptives
score
	N	Mean	Std. Deviation	Std. Error	95% Confidence Interval for Mean		Minimum	Maximum
					Lower Bound	Upper Bound
1	11	67.4545	14.80111	4.46270	57.5110	77.3981	40.00	84.00
2	11	82.0000	6.54217	1.97254	77.6049	86.3951	70.00	91.00
3	11	81.0000	7.58947	2.28831	75.9013	86.0987	67.00	94.00
Total	33	76.8182	12.05056	2.09773	72.5452	81.0911	40.00	94.00

ANOVA
score
	Sum of Squares	df	Mean Square	F	Sig.
Between Groups	1452.182	2	726.091	6.818	.004
Within Groups	3194.727	30	106.491
Total	4646.909	32

Calculated F=6.818, P=0.004 which is < 0.05 level, ANOVA is significant. There is significance among the three group means.

Multiple Comparisons
Dependent Variable:   score
	(I) section	(J) section	Mean Difference (I-J)	Std. Error	Sig.	95% Confidence Interval
						Lower Bound	Upper Bound
Tukey HSD	1	2	-14.54545*	4.40023	.007	-25.3932	-3.6977
		3	-13.54545*	4.40023	.012	-24.3932	-2.6977
	2	1	14.54545*	4.40023	.007	3.6977	25.3932
		3	1.00000	4.40023	.972	-9.8477	11.8477
	3	1	13.54545*	4.40023	.012	2.6977	24.3932
		2	-1.00000	4.40023	.972	-11.8477	9.8477
Scheffe	1	2	-14.54545*	4.40023	.009	-25.8769	-3.2140
		3	-13.54545*	4.40023	.016	-24.8769	-2.2140
	2	1	14.54545*	4.40023	.009	3.2140	25.8769
		3	1.00000	4.40023	.975	-10.3315	12.3315
	3	1	13.54545*	4.40023	.016	2.2140	24.8769
		2	-1.00000	4.40023	.975	-12.3315	10.3315
*. The mean difference is significant at the 0.05 level.

Tukey test

Comparing 1 and 2, P=0.007 which is < 0.05 level. significant

Comparing 2 and 3 , P=0.972 which is >0.05 level. Not significant

scheffe test

Comparing 1 and 2, P=0.009 which is < 0.05 level. significant

Comparing 2 and 3 , P=0.975 which is >0.05 level. Not significant

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