Q2. Perform and Interpret a Two-Way ANOVA. Use the same data set from Q1 for this item.(14 points)

The researchers would also like to know whether or education levels (Educ) significantly influence changes in memory over time (MemChange). However, they suspect that education levels and gender (Gender) may interact. In other words, the researchers want to investigate whether a statistically significant difference in the three education levels is dependent on gender.

Another way to say this is that the researchers want to investigate whether the magnitude of the difference in memory change scores between males and females at education level 1 is statistically significantly different from the magnitude of the difference in memory change scores between males and females at education levels 2 and 3, and so on. There are six groups formed by crossing gender (male, female) and education level (Levels 1, 2, and 3), resulting in the following research questions for the main effects and the interaction.

Main Effect (Gender)

Is there a statistically significant difference between genders in memory score changes?

Main Effect (Education Level)

Is there a statistically significant difference among education levels in memory score changes?

Interaction (Education Level x Gender)

Does a statistically significant difference in changes to memory scores among education levels depend on gender?

Perform a two-way ANOVA with = .05 to answer the questions above.

A. What are the null hypotheses corresponding to our questions in written form?

Main Effect (Gender) H₀ : There is no statistically significant difference between genders in memory score changes.

Main Effect (Education Level) H₀ : There is no a statistically significant difference among education levels in memory score changes

Interaction Effect (Education Level x Gender) H₀ : There is no statistically significant difference in changes to memory scores among education levels depending on gender.

B. What are the two factors (i.e., IVs) and the 1 DV?

Factor 1 = Education Level

Factor 2 = Gender

DV = Memory Change over time

C. Report the 2main effects of the Ftest result in APA format including F, p and partial eta squared².Be sure to paste the relevant SPSS output table here to support your answer.

Between-Subjects Factors
	N
Educ	1	17
2	17
3	16
Gender	1	24
2	26

Tests of Between-Subjects Effects
Dependent Variable: MemChange
Source	Type III Sum of Squares	df	Mean Square	F	Sig.
Corrected Model	422.425a	5	84.485	6.795	<.001>
Intercept	178.185	1	178.185	14.331	<.001>
Educ	204.406	2	102.203	8.220	<.001>
Gender	65.503	1	65.503	5.268	.027
Educ * Gender	143.258	2	71.629	5.761	.006
Error	547.084	44	12.434
Total	1175.716	50
Corrected Total	969.508	49
a. R Squared = .436 (Adjusted R Squared = .372)

Reporting the effects:

Main Effect (gender): F(,) = , p , partial ² =

Main Effect (educ): F(,) = , p , partial ² =

D. What is the decision about the two main effect null hypotheses (reject or fail to reject) based on the initial test result?(1 point)

Between-Subjects Factors
	N
Educ	1	17
2	17
3	16
Gender	1	24
2	26

Tests of Between-Subjects Effects
Dependent Variable: MemChange
Source	Type III Sum of Squares	df	Mean Square	F	Sig.
Corrected Model	422.425a	5	84.485	6.795	<.001>
Intercept	178.185	1	178.185	14.331	<.001>
Educ	204.406	2	102.203	8.220	<.001>
Gender	65.503	1	65.503	5.268	.027
Educ * Gender	143.258	2	71.629	5.761	.006
Error	547.084	44	12.434
Total	1175.716	50
Corrected Total	969.508	49
a. R Squared = .436 (Adjusted R Squared = .372)

E. Part 1: Report the result of the test on the Educ x Gender interaction effect. Report the test result on the interaction effect in APA format including F, p, and partial eta squared².3 decimal places, do not round from your SPSS output.(1 point)

F(, ) = , p , partial ²=

• Part 2: Draw a conclusion regarding if we reject of fail to explain the null hypothesis for the interaction. State the findings and be sure to explain what an "interaction" means.(

F. Repeat the two-way ANOVA analysis, but with the following additional statistics requested before running the analysis. (2 points for pasting output including the chart)

• EM Means: Move Gender*Educ into the "display means for" box. "Compare simple main effects" should be checked and the "confidence interval adjustment" should be "LSD(none)".
• Plots: Enter Educ into the "horizonal axis" box and Gender into the "separate lines" box. Next, click the "add" button, which will add the Educ x Gender variable. Chart type is set to 'Line Chart' already.
• Options: Check the boxes for "descriptive statistics" and "homogeneity tests."

Paste the entire output here including the chart:

G. Examine the line plot in the output. What general observations can you make about the means of the different groups?

H. Is the Levene's Test significant? What does the result (significant or not significant) mean? Explain.

I. What are the results of theEduc*Genderpair-wise comparisons between gender and education levels?Report the result of each of the pair-wise contrasts, including the p value. Then, draw a conclusion based on the findings. Your conclusion should explain the findings and also indicate whether the post hoc test of Educ was necessary. You are looking at the 'pairwise comparisons' output that is separated by gender and reporting 6 values to us(

Female

Level 1 vs. Level 2 result: p

Level 2 vs. Level 3 result: p

Level 1 vs. Level 3 result: p

Male

Level 1 vs. Level 2 result: p

Level 2 vs. Level 3 result: p

Level 1 vs. Level 3 result: p

Conclusion: