Question

A researcher is interested in investigating the hypotheses that college achievement is affected by:

(1) home-schooling vs. public schooling;

(2) growing up in a dual-parent family vs. a single-parent family;

(3) the interaction of schooling and family type.

She locates 5 people that match the requirements of each cell in the 2 × 2 (schooling × family type) factorial design, as shown below. In the table, for Family Type 1 = dual-parent and 2 = single-parent, and for Schooling, 1 = home-schooling and 2 = public schooling.

a. What is the appropriate statistical test that we should do here?

b. Run the appropriate statistic in SPSS and report the results.

c. Spell out what the results tell the researcher about the main effect of family type on achievement, the main effect of schooling on achievement, and the interaction of family type and schooling on achievement.

Family Type	Schooling	Achievement
1	1	.50
1	1	.30
1	1	.43
1	1	.52
1	1	.41
1	2	.54
1	2	.29
1	2	.31
1	2	.47
1	2	.48
2	1	.12
2	1	.32
2	1	.22
2	1	.19
2	1	.19
2	2	.88
2	2	.69
2	2	.91
2	2	.86
2	2	.82

Answer 1

a. What is the appropriate statistical test that we should do here?

Two-Way ANOVA test

b. Run the appropriate statistic in SPSS and report the results.

c. Spell out what the results tell the researcher about the main effect of family type on achievement, the main effect of schooling on achievement, and the interaction of family type and schooling on achievement.

The hypothesis being tested is:

H0: There is no main effect of family type on achievement

Ha: There is a main effect of family type on achievement

The p-value is 0.032.

Since the p-value (0.032) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a main effect of family type on achievement.

The hypothesis being tested is:

H0: There is no main effect of schooling on achievement

Ha: There is a main effect of schooling on achievement

The p-value is 0.000.

Since the p-value (0.000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a main effect of schooling on achievement.

The hypothesis being tested is:

H0: There is no interaction of family type and schooling on achievement

Ha: There is an interaction of family type and schooling on achievement

The p-value is 0.000.

Since the p-value (0.000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is an interaction of family type and schooling on achievement.

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