I have a set of sample data for the following scenario already entered into SPSS

Question

I have a set of sample data for the following scenario already entered into SPSS:

You are the director of Institutional Research at a small state university and you have been given the task of gathering information for the dean of the School of Education regarding the performance of their undergraduate students on the Graduate Record Exam (GRE). Data on six variables were collected: gender, overall grade point average (GPA), major GPA, GRE scores in major area, GRE quantitative, GRE verbal, and type of preparation programs. The university is dedicated to maximize student success on the GRE. The university has established five different options for students to prepare for the GREs: option 1 = completely online asynchronous prep course, 2 = completely online synchronous prep course, 3 = complete a hybrid prep course with a combination of online and face to face; 4 = complete a traditional instructor led prep course, and 5 = self-paced paper based prep course.

The dean has simply asked you, “Tell me what works best and for whom?” You decide to establish a pilot study with 50 randomly selected general science education seniors to determine the details of the methodology as well as to provide some initial data and corresponding results to learn if the research plan meets the dean’s needs.

I have the following research question and hypotheses:

Q1. Is major GPA a better predictor of GRE score than preparation program?

H0 : There is no difference in the mean gre scores of the 5 options

H1 : There is a significant difference in the mean gre scores of the 5 options , at least for 2 options

ANOVA

GRE quantitative

Sum of Squares

df

Mean Square

F

Sig.

Between Groups

112412.000

4

28103.000

14.366

.000

Within Groups

88030.000

45

1956.222

Total

200442.000

49

Multiple Comparisons

Dependent Variable:   GRE quantitative

Tukey HSD

(I) Preparation Approach

(J) Preparation Approach

Mean Difference (I-J)

Std. Error

Sig.

95% Confidence Interval

Lower Bound

Upper Bound

1.00

2.00

14.00000

19.77990

.954

-42.2036

70.2036

3.00

71.00000*

19.77990

.007

14.7964

127.2036

4.00

104.00000*

19.77990

.000

47.7964

160.2036

5.00

119.00000*

19.77990

.000

62.7964

175.2036

2.00

1.00

-14.00000

19.77990

.954

-70.2036

42.2036

3.00

57.00000*

19.77990

.045

.7964

113.2036

4.00

90.00000*

19.77990

.000

33.7964

146.2036

5.00

105.00000*

19.77990

.000

48.7964

161.2036

3.00

1.00

-71.00000*

19.77990

.007

-127.2036

-14.7964

2.00

-57.00000*

19.77990

.045

-113.2036

-.7964

4.00

33.00000

19.77990

.463

-23.2036

89.2036

5.00

48.00000

19.77990

.127

-8.2036

104.2036

4.00

1.00

-104.00000*

19.77990

.000

-160.2036

-47.7964

2.00

-90.00000*

19.77990

.000

-146.2036

-33.7964

3.00

-33.00000

19.77990

.463

-89.2036

23.2036

5.00

15.00000

19.77990

.941

-41.2036

71.2036

5.00

1.00

-119.00000*

19.77990

.000

-175.2036

-62.7964

2.00

-105.00000*

19.77990

.000

-161.2036

-48.7964

3.00

-48.00000

19.77990

.127

-104.2036

8.2036

4.00

-15.00000

19.77990

.941

-71.2036

41.2036

*. The mean difference is significant at the 0.05 level.

So I am able to reject the null hypothesis , because major GPA is a more accurate predictor than preparation program for at least one group.

What would be the posthoc analysis for each pair of groups? Which preparation programs are a more accurate predictor than GPA?

ANOVA

GRE quantitative

Sum of Squares

df

Mean Square

F

Sig.

Between Groups

112412.000

4

28103.000

14.366

.000

Within Groups

88030.000

45

1956.222

Total

200442.000

49

Explanation / Answer

Here T test for two means is conducted for each pair

Decision Rule : If p value < 0.05 then program is more accurate than GPA

Results and comparisons

For program (1,2) => p value = 0.954 > 0.05, Fail to reject H0, Not accurate than GPA

For program (1,3) => p value = 0.007 < 0.05, reject H0, Accurate than GPA

For program (1,4) => p value = 0.000 < 0.05, reject H0, Accurate than GPA

For program (1,5) => p value = 0.000 < 0.05, reject H0, Accurate than GPA

For program (2,3) => p value = 0.045 < 0.05, reject H0, Accurate than GPA

For program (2,4) => p value = 0.000 < 0.05, reject H0, Accurate than GPA

For program (2,5) => p value = 0.000 < 0.05, reject H0, Accurate than GPA

And rest of pairs are not accurate than GPA, since p value > 0.05

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