# Factorial ANOVA

Statistics Solutions provides a data analysis plan template for the Factorial ANOVA analysis.  You can use this template to develop the data analysis section of your dissertation or research proposal.

The template includes research questions stated in statistical language, analysis justification and assumptions of the analysis.  Simply edit the blue text to reflect your research information and you will have the data analysis plan for your dissertation or research proposal.

Data Analysis Plan: Factorial ANOVA

Copy and paste the following into a word document to use as your data analysis plan template.

Research Question:

RQ: Is there a statistically significant difference on dependent variable by independent variable 1 and independent variable 2?

H1o: There is no statistically significant difference on dependent variable by independent variable 1 and independent variable 2?

H1a: There is a statistically significant difference on dependent variable by independent variable 1 and independent variable 2?

Data Analysis

To examine the research question, a factorial Analysis of Variance (ANOVA) will be conducted.  Factorial ANOVA’s are used in research when one wants to analyze differences on a continuous dependant variable between two or more independent discrete grouping variables.  In this analysis, dependent variable will be compared by both independent variable 1 and independent variable 2.  Independent variable 1 has two groups (group 1 vs. group 2). Independent variable 2 has two groups (group 3 vs. group 4). The ANOVA uses the F test, which allows researchers to make the overall comparison on whether group means differ.  The F test is the ratio of two independent variance estimates of the same population variance.  Considering an alpha of 0.05, if the calculated F-value is larger than the critical F-value after accounting for degrees of freedom, the null hypothesis (Ho) will be rejected and the alternative hypothesis (Ha) will be accepted.  F-test degrees of freedoms are calculated between groups (K – 1) and within groups (N – K - 1) where K equals number of groups.  The results of the factorial ANOVA will be presented in the form of main effects and the interactions among study variables.  If a significant interaction is revealed, post hoc analyses will be conducted consisting of a series of independent t-tests.

The assumptions of normality and homogeneity of variance will be assessed.  Normality assumes that the scores are normally distributed (symmetrical bell shaped) and will be assessed using the one sample Kolmogorov Smirnov (KS) test.  Homogeneity of variance assumes that both groups have equal error variances and will be assessed using Levene’s test.

Reference