# Factorial ANCOVA

Statistics Solutions provides a data analysis plan template for the factorial ANCOVA 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 ANCOVA**

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

*Research Question:*

RQ: After controlling for covariate 1, are there differences on dependent variable by independent variable 1 and independent variable 2?

H_{o}: After controlling for covariate 1, there are no differences on dependent variable by independent variable 1 and independent variable 2?

H_{a}: After controlling for covariate 1, there are differences on dependent variable by independent variable 1 and independent variable 2?

*Data Analysis*

To investigate the research question, a Factorial Analysis of Covariance (factorial ANCOVA) will be conducted to assess differences between independent variables on a single dependent variable after controlling for the effects of one or more covariates. In this analysis, dependent variable will be compared by 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 control variables are covariate 1…. The covariates are chosen specifically because of their known effects on the dependent variable. The purpose is to partial-out the effects of those variables on the dependent variable to determine if the effects are strictly due to the covariate or if the differences are independent of the effects of that covariate.

The *F*-test of significance will be used to assess the main and interaction effects. *F* is the between-groups variance (mean square) divided by the within-groups variance (mean square). When the *F* value is greater than 1, more variation occurs between groups than within groups. When this occurs, the computed *p*-value is small and a significant relationship exists. If significance is found, comparison of the original and adjusted group means can provide information about the role of the covariates. Because predictable variances known to be associated with the dependent variable are removed from the error term, ANCOVA increases the power of the *F* test for the main effect or interaction. Essentially, it removes the undesirable variance in the dependent variable. 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**

Statistics Solutions. (2013). Data analysis plan: Factorial ANCOVA [WWW Document]. Retrieved from http://www.statisticssolutions.com/academic-solutions/member-resources/member-profile/data-analysis-plan-templates/data-analysis-plan-factorial-ancova/