Please verify my answers.

Perform and Interpret a Two-Way ANOVA.

The researchers would also like to know whether 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?

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 DV?

IV Factors: Educational Level and Gender

DV: Memory Change (over time)

As a researcher, you are looking for some form of relationship between variables you are trying to see if the independent variable causes change in the other variable, or which we will calldependent variable. In your case, the de dependent variable is MEMORY CHANGE over time.

Perform theinitial 2x3 two-way ANOVA in SPSS.

• Upload the data from the Excel file.
• Check that all variables are configured correctly in "Measure" under the "Variable View."
• The "Values" for the nominal variables should be specified (e.g.,use the codebook to enter labels that correspond to each value).
• Select "General Linear Model" from the analyze menu and then select "Univariate."
• Enter the DV and IVs in the appropriate boxes. Note that the IVs are "Fixed Factors" because we did not randomly assign participants to their groups
• Click on "Options" and check the box for "estimates of effect size"

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

Reject the null hypothesis because the two main effect p values are lower than the alpha value.

D. Report the main effects of theFtest result in APA form includingF, p and ².Be sure to paste the relevant output table here to support your answer.

Main effect of Gender: F(1, 44) = 7.624, p = .008, partial n2 = .148

Main effect of Education Level: F(2, 44) = 7.322, p = .002, partial n2 = .250

Or

Main effect of Gender: F(1, 44) = 7.624, p = .008, n2 = .148 ?

Main effect of Education Level: F(2, 44) = 7.322, p = .002, n2 = .250 ?

E. Report the result of the test on theEduc x Gender interaction effect:

Report the test result on the interaction effect in APA form includingFand p.

F (2, 44) = 6.067, p = . 005, partial 2 = .216

Draw a conclusion from the hypothesis testing result and state the finding supported by the result. Be sure to explain what an "interaction" means.

There is a significant difference for education and gender because p <0.05, thus the null hypothesis is rejected.Interaction is one factor's effect on the dependent variable at each level of the other factor that shows how the effects differ according to the other factor. An interaction may arise when there are more than three variables

and it describes a situation in which the effect of one causal variable on an outcome depends on the state of a second causal variable. *We need to examine one factor's effect on the DV at each level of the other factor so we can see how the effect differs according to the other factor. This is often the most critical result from a two-way ANOVA, which is performed because the researcher hypothesizes some interaction between the factors.

F. Repeat the two-way ANOVA analysis, but with the following additional statistics requested before running the analysis.

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

Paste output.

Univariate Analysis of Variance

G. Examine the output for the descriptives. What observations can you make about the means of the different groups?

All the means are negative except for the(1) Females in (3) Graduate studies

???We can also see that (1) Females with (2) Bachelor's score higher than (2) Males with (2) Bachelor's. Whether these differences observed numerically are statistically significant remains to be seen.

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

The Levene's test is significant (p = .007), because the p values are less than the alpha value.This means the null hypothesis is rejected. The two variances are significantly different. The null hypothesis says that the variances are generally equal, so the conclusion is that they do differ significantly

I. What are the results of theEduc*Genderpair-wise comparisons between education levels? Report the result of each of the pair-wise contrasts, including thep value.Then, draw a conclusion based on the findings. Your conclusion should explain the findings andalso indicate whether the post hoc test ofEduc was necessary.

???

There are statistically significant differences for females on all education levels. The large changes in females were in bachelor's studies and high school or lower comparisons.

J. Run a one-way ANOVA for the factor education levels (Educ) using only theMemChange data for females. Similarly, run a one-way ANOVA for education levels using only theMemChange data for males. Paste your output and then draw a conclusion based on the findings. Your conclusion should explain the findings andalso indicate whether this post hoc test was necessary.

????Homogeneous Subsets

K. Based on all of the analyses you have run for Q3, how would you summarize the findings?

CODEBO0K

Variable Name	Description	Values
Gender	Gender	1 - Female
		2 - Male
Educ	Education	1 - High school or lower
		2 - Bachelor's degree
		3 - Graduate studies
Age	Age at 1st test session	Number of years
EFChange	Change in executive function from 1st test session to 2nd test session	Test Score
MemChange	Change in memory function from 1st test session to second test session	Test Score

DATA SET

SubID	Gender	Educ	Age	EFChange	MemChange
1	1	2	65.8	-0.9	-1.88
2	1	1	66.9	2.07	-7.83
3	1	1	76.9	4.99	-13.71
4	1	1	79.9	-12.82	-8.99
5	1	1	67.5	-2.89	0.15
6	1	1	84.1	-8.44	-13.11
7	1	1	72.6	-0.68	-15.12
8	1	3	75.6	-5.78	0.51
10	1	2	78.0	-4.36	-0.05
13	1	3	67.2	2.13	0.05
14	1	2	70.0	2.5	1.48
18	1	1	70.6	-5	0.59
22	1	2	75.0	0.93	-5.65
24	1	3	69.5	1.19	0.97
29	1	1	65.2	0.87	-3.81
31	1	1	73.0	15.15	-12.88
38	1	2	66.0	2.64	-7.89
39	1	3	71.4	-1.67	5.55
40	1	3	75.8	-1.25	5.82
41	1	3	65.4	-5.16	-3.91
44	1	3	69.3	8.01	-0.89
45	1	2	68.1	1.32	-1.60
47	1	2	67.8	0.44	-9.81
49	1	2	71.9	1.31	-4.14
9	2	1	69.6	-11.92	0.07
11	2	1	66.3	13.25	-1.30
12	2	2	65.1	-4.56	-3.49
15	2	2	77.7	-6.79	-2.00
16	2	2	69.4	1.28	-0.99
17	2	2	65.3	-6.67	-3.67
19	2	3	78.4	-11.24	-0.25
20	2	2	69.6	-9.98	-1.10
21	2	1	65.8	-4.23	-0.98
23	2	3	68.5	-10.52	2.21
25	2	1	67.0	2.13	0.50
26	2	1	69.9	-1.01	-0.28
27	2	3	86.6	-9.38	-0.96
28	2	2	68.7	1	-1.66
30	2	1	76.8	-9.1	-5.72
32	2	3	66.7	-1.44	1.84
33	2	1	65.5	-1.5	2.06
34	2	2	72.8	-2.26	4.97
35	2	3	79.5	-0.53	2.72
36	2	1	72.9	4.56	-1.45
37	2	3	69.7	7.85	-2.10
42	2	3	67.0	-7.72	-3.61
43	2	3	79.2	9.5	-2.39
46	2	2	77.5	-16.96	1.15
48	2	3	75.8	-1.77	-1.44
50	2	2	68.3	-2.68	-0.48