Two Way analysis of variance

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Exampe of two way analysis of variance - write up and APA style tables

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Two way analysis of variance:

Two way analysis of variance Dr. Elsa-Sofia Morote http://www.internationalprofessor.com

This example was taken from Chapter “Two Way Analysis of Variance” –from Green and Sallkind :

This example was taken from Chapter “Two Way Analysis of Variance ” –from Green and Sallkind 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.

Factorial Design:

Factorial Design First factor (independent variable) for this study is gender with two levels, and the S econd factor (independent variable) is note taking method with three levels. Dependent : GPA improvement 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).

2 x 3 Factorial Design:

2 x 3 Factorial Design Note-taking Method Method 1 Method 2 Control Row Totals Gender Men Women Column Totals (Grand Mean)

You can answer three research questions when conducting a Two-Way ANOVA:

You can answer three research questions when conducting a Two-Way ANOVA Method Main Effect: Do the means on changes in GPA differ among Method 1, Method 2, and Control Conditions? Gender main effect: Do the means on change in GPA differ for men and women Students? Method x Gender interaction effect: Do the differences in the means on Change in GPA among the three method conditions vary as a function of Gender?

Checking Assumptions:

Checking Assumptions Assumption 1. The Dependent Variable is Normally Distributed for Each of the Population Was the assumption of normality met for these data? Looking at the standardized skewness compared to a critical value we see that none of the levels in either independent variable were significantly skewed . YES – the assumption of normality is met. Assumption 2. The population variances of dependent variable are the same for All Cells In other words, Was the assumption of homogeneity of variance met for these data? 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. Yes – the assumption of homogeneity of variance is met.

Assumptions:

Assumptions Assumption 3. The Cases Represent Random Samples from the Populations and the scores on the Dependent Variable are independent of each other? Was the assumption of independence met for these data? Indicate how you made this determination. 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. YES – the assumption of independent is met.

See video of how to perform a Two way ANOVA:

See video of how to perform a Two way ANOVA You can download the data and practice following the video http://www.pearsonhighered.com/salkind/ Lesson 26 data file 1 Note taking

Descriptive Statistics:

Descriptive Statistics

Description:

Description A two-factor (2  3) Analysis of Variance was conducted to evaluate GPA improvement as a function of gender and note taking methods. The two independent variables (factors) in this study are gender (Men and Women) and note taking method (Method 1, Method 2, and a Control Group). The dependent variable is the students’ spring semester GPA minus their fall semester GPA (GPA improvement). The means and standard deviations for GPA improvement as a function of gender and note taking methods are presented in Table 1.

Table in APA style:

Table in APA style

Analysis:

Analysis F (1, 54) =.15.856, p<.001 F (2, 54) = 17.809, p < .001. F (2, 54) = 2.921, p = .062 Partial Eta squared: small, medium and large: Conventional cutoffs are .01, .06, .14 respectively

Table explanation:

Table explanation An alpha level of .05 was used for the initial analyses. The test for homogeneity of variance was not significant [ Levene F (5, 54) = .575, p = .719] indicating that this assumption underlying the application of ANOVA was met. The results for the two-way ANOVA indicated a significant main effect for gender, F (1, 54) =.15.856, p<.001 and a significant main effect for note taking method, F (2, 54) = 17.809, p < .001. Additionally , the results show a non-significant interaction between gender and note taking method, F (2, 54) = 2.921, p = .062 ( see Table 2 ),[if significant it would indicated that any differences between the note taking methods were dependent upon which gender the subjects were and that any differences between men and women were dependent upon which note taking method they received] Approximately 23% (  2 = 0.227) of the total variance of the GPA improvement was attributed to gender and 40% (  2 = 0.397) note taking method.

Table in APA style:

Table in APA style

Post-hoc:

Post-hoc

Post Hoc:

Post Hoc Follow-up tests were conducted to evaluate the three note taking methods’ pairwise differences. The alpha level was set at . 017 (. 05/3 ) to control for Type I error over the three pairwise comparisons. The people using note taking Method 2 ( M = .47, SD = .25) had a significantly greater GPA improvement compared to the people using note taking Method 1 ( M = .25, SD = .22), F (1, 54) = 33.507, p < . 017 A review of the group means indicated that men ( M =.38, SD = .27) had a significantly greater GPA improvement than women ( M = .19, SD = . 19)

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