EDPR 7/8542 – Statistical Methods Applied to Education II



A researcher is interested in two methods of note taking strategies and the effect of these methods on the overall GPAs of college freshmen. After obtaining 30 men and 30 women volunteers in freshmen orientation, she randomly assigns 10 men and 10 women to Method 1, 10 men and 10 women to Method 2, and 10 men and 10 women to a control condition. During the first month of the spring semester, individuals in the two note taking method groups receive daily instruction on the particular note taking method to which they were assigned. The control group receives no note taking instruction. Fall and spring GPAs for all participants are recorded.

One factor (independent variable) for this study is gender with two levels, and the second factor is note taking method with three levels. The design for this study is described as a 2 ( 3 ANOVA (the number of levels of gender by the levels of note taking method). The data set has 60 cases and three variables: a factor differentiating men from women, a second factor distinguishing among the three note taking method groups, and a dependent variable, the students’ spring semester GPA minus their fall semester GPA (GPA Improvement).

Given the above scenario and the applicable data, answer the following questions:

1. What would the null hypotheses for the two main effects and the interaction be for this study? Show/write the appropriate symbols or the expression in words.

Gender Main Effect

H0: (1. = (2.

There is no difference between the gender row means.

Note Taking Method Main Effect

H0: (.1 = (.2 = (.3

There is no difference among the note taking method column means.

Gender by Note Taking Method Interaction

H0: all ((jk – (j. – (.k + () = 0

There is no difference in the gender by note taking method (JK) cell means that cannot be explained by the differences among the gender (row) means, the note taking method (column) means, or both. In other words, there is no interaction between the two independent variables (gender and note taking method).

2. What would the alternative hypotheses for the two main effects and the interaction be for this study? Show/write the appropriate symbols or the expression in words.

Gender Main Effect

H1: (1. ( (2.

The gender row means differ (are not equal).

Note Taking Method of Instruction Main Effect

H1: (.i ( (.k for some i, k

At least one pair or combination of means differs (are not equal).

At least one mean differs significantly from the other two means.

Gender by Note Taking Method Interaction

H1: all ((jk – (j. – (.k + () ( 0

There are differences among the cell population means that cannot be attributed to the main effects. In other words, there is an interaction between the two independent variables (gender and note taking method).

3. Determine if the underlying assumptions of the two-way ANOVA are met for these data.

a. Was the assumption of normality met for these data? Indicate how you made this determination (using an alpha level of .01 for the Shapiro-Wilks test).

YES – the assumption of normality is met.

Looking at the standardized skewness compared to a critical value of +3.29, we see that none of the levels in either independent variable were significantly skewed.

Gender: Male [pic] Female [pic]

Note Taking Method: Method 1 [pic]

Method 2: [pic] Control: [pic]

Also, looking at the Sig. (p) value in the Shapiro-Wilks test for each level of either independent variable, we see that none of them were significant.

Gender: Male, p (.487) > α (.01) Female, p (.029) > α (.01)

Note Taking Method: Method 1, p (.081) > α (.01)

Method 2, p (.766) > α (.01) Control, p (.392) > α (.01)

b.. Was the assumption of independence met for these data? Indicate how you made this determination.

YES – the assumption of independent is met.

The volunteers for the study were randomly assigned either Method 1, Method 2, or the Control group, and as such making the groups independent of each other.

c. Was the assumption of homogeneity of variance met for these data? Indicate how you made this determination.

Yes – the assumption of homogeneity of variance is met.

The Levene’s test resulted in an F(5, 54) = .575, p = .719. Comparing the significance value of .719 to the a priori alpha level (( = .05) – we see that p (.719) > ( (.05), therefore the null hypothesis of no difference is retained. By retaining the null hypothesis – this indicates the assumption of homogeneity of variance is met.

[pic]

4. Determine which (if any) effects were significant.

a. Was the J (row) main effect significant? Indicate how you made this determination.

NO, the J (Row) Main Effect is not significant, p (.438) > α (0.05)

F(1, 54) = .612, p = .438

b. Was the K (column) main effect significant? Indicate how you made this determination.

Yes, the K (Column) Main Effect is significant, p (.000) < α (0.05)

F(2, 54) = 17.809, p < .001

c. Was the JK (interaction) significant? Indicate how you made this determination.

Yes, the JK Interaction is significant, p (.000) < α (0.05)

F(2, 54) = 10.543, p < .001

[pic]

5. What proportion of variance in the subjects’ GPA improvement (DV) is attributed to the interaction of gender and note taking method? You will need to calculate this by hand and briefly explain what this value means.

• You DO NOT need to calculate the association for the two main effects.

[pic]

(2 = .1699 or 16.99% (( 17%)

Approximately 17% of the total variance in the dependent variable (DV = GPA improvement) can be attributed to the interaction of the two independent variables (IV1 = gender and IV2 = note taking method).

6. Assuming that the interaction is significant – plot the interaction illustrating the comparison of men and women at each of the note taking method levels. That is, the lines should be gender. Be sure to differentiate the lines in the graph. Briefly explain/discuss the general characteristics of the interaction plot.

[pic]

Since the lines cross at two points – the interaction is considered to be disordinal.

7. Do the Gender Simple Main Effects analysis to test for the statistical significance of men and women differences within each of the note taking method levels. Determine if these effects are significant. Don’t forget to control for Type I error.

The Bonferroni adjustment to control for Type I Error =

[pic] = α( = 0.017

Men (M = .3350) vs. Women (M = .1700) in Note Taking Method 1

Mean Difference =.1650 = Not Significant, p (.047) > α( (0.017)

[pic]

Men (M = .3050) vs. Women (M = .6400) in Note Taking Method 2

Mean Difference = .3350 = Significant, p (.000) < α( (0.017)

[pic]

Men (M = .1650) vs. Women (M = .1050) in Control Group

Mean Difference = .0600 = Not Significant, p (.463) > α( (0.017)

[pic]

8. Calculate the Effect Size (by hand) for each of the significant pairwise differences found from the above analyses.

Using the formula: [pic]

Where MSW =.033, therefore [pic]

Men (M =.3050) vs. Women (M =.6400) in Note Taking Method 2

[pic]

9. Do the Note Taking Method Simple Main Effects analysis to test for the statistical significance of the note taking method differences within each of the gender levels. Determine if these effects are significant. Don’t forget to control for Type I error.

The Bonferroni adjustment to control for Type I Error =

[pic] = α( = 0.025

Note Taking Method in Men

Not Significant, p (.092) > α( (0.025)

[pic]

Note Taking Method in Women

Significant, p (.000) < α( (0.025)

[pic]

10 Conduct pairwise comparisons for each of the significant simple main effects tested above. Don’t forget to control for Type I error.

Since the Note Taking Method Simple Main Effect within Men was not significant ( no post hoc analysis is required.

For Note Taking Method within Women, the Bonferroni adjustment to control for Type I Error = [pic] = α( = 0.008

Note Taking Method 1 (M = .1700) vs. Note Taking Method 2 (M = .6400)

Mean Difference =.4700 = Significant, p (.000) < α( (0.008)

[pic]

Note Taking Method 1 (M = .1700) vs. Control (M = .1050)

Mean Difference =.0650 = Not Significant, p (.427) > α( (0.008)

[pic]

Note Taking Method 2 (M = .6400) vs. Control (M = .1050)

Mean Difference =.5350 = Significant, p (.000) < α( (0.008)

[pic]

11. Calculate the Effect Size (by hand) for each of the significant pairwise differences found from the above analyses.

Using the formula: [pic]

Where MSW =.033, therefore [pic]

Note Taking Method 1 (M =.1700) vs. Note Taking Method 2 (M =.6400)

[pic]

Note Taking Method 2 (M =.6400) vs. Control (M =.1050)

[pic]

12. Write a separate results section for the above findings including tables for the means and standard deviations and the ANOVA summary information. Also include the Figure showing the (HINT) significant interaction.

See Attached…

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