Question

A university instructor uses different teaching methods on three separate computer science classes. The instructor wants to evaluate the effectiveness of the methods by comparing the grades between the classes. The grades have been transformed and are in the table below. What can the instructor conclude with a = 0.05? Method A Method B Method с 21 19 21 24 25 20 27 19 23 25 25 20 24 28 35 31 29 26 19 17 20 29 20 17 20 21 22 a) What is the appropriate test statistic? ---Select- b) Obtain/compute the appropriate values to make a decision about Ho. critical value = ; test statistics Decision: --Select-- c) Compute the corresponding effect size(s) and indicate magnitude(s). n? = : ---Select--- d) Make an interpretation based on the results. O At least one teaching method differs on the grade. O None of the teaching methods differed on the grade. e) Regardless of the Ho decision in b), conduct Tukey's post hoc test for the following comparisons: 1 vs. 2: difference i significant: -Select... v 2 vs. 3: difference significant: ---Select f) Regardless of the Ho decision in b), conduct Scheffe's post hoc test for the following comparisons: 1 vs. 3: test statistic = ; significant: ---Select- 2 vs. 3: test statistic = ; significant: Select---

Answer 1

One factor ANOVA Mean 22.1 27.0 20.55 2321 n Std. Dev 9 2.80 Method A 9 4.36 Method B 9 4.23 Method C 27 4.54 Total ANOVA table Source SS Treatment 178.74 Error 357.78 Total 536.52 MS 89.370 14.907 F 6.00 df 2 24 26 p-value .0077

a)

F test statistics (one way ANOVA)

b)

Critical value of F is

$F_c=3.403$

The test statistics is F=6.00

since F > F_c so we reject the null hypothesis

c)

m2 = Σbetween Σtotal 178.74 536.52 0.3331

Effect size is medium

d)

At least one teaching ethod differs on the grade

e)

Following is the output of Post H_oc analysis

Post hoc analysis p-values for pairwise t-tests Method C Method A Method B 20.55 22.1 27.0 Method C 20.55 Method A 22.1 -5878 Method B 27.0 .0035 .0129 Tukey simultaneous comparison t-values (d.f. = 24) Method C Method A Method B 20.55 22.1 27.0 Method C 20.55 Method A 22.1 0.55 Method B 27.0 3.24 2.69 critical values for experimentwise error rate: 0.05 2.50 0.01 3.21

1 vs 2 = 2.69 , difference is signficant

2 vs 3 = 3.24 , difference is signficant

f)

1 vs 2 = 2.69 , difference is signficant

2 vs 3 = 3.24 , difference is signficant

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