# One Way MANCOVA

Statistics Solutions provides a data analysis plan template for the one way MANCOVA 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: One Way MANCOVA**

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, is there a statistically significant difference among the dependent variables (dependent variable 1, dependent variable 2) by independent variable (group 1 vs. group 2 vs. ….)?

H_{o}: After controlling for covariate 1, there is no statistically significant difference among the dependent variables (dependent variable 1, dependent variable 2) by group (group 1 vs. group 2 vs. ….).

H_{a}: After controlling for covariate 1, there is a statistically significant difference among the dependent variable (dependent variable 1, dependent variable 2) by group (group 1 vs. group 2 vs. ….).

*Data Analysis*

To examine the research question, a Multivariate Analysis of Covariance (one way MANCOVA) will be conducted to assess whether or not differences exist on the dependent variables (dependent variable 1, dependent variable 2) by independent variable (independent variable vs. independent variable). The independent (or grouping) variable will be group 1 vs. group 2. Covariate 1… will be entered as covariates. The One way MANCOVA will be conducted first to assess the impact of the independent or grouping variables on the dependent variables (variable, variable and variable). Post hoc analysis will consist of ANCOVA’s which will be conducted on the dependent variables to assess specific differences among the variables by independent variable. The assumptions of One way MANOVA—normality and homogeneity of variance/covariance matrices will be assessed.

The Multivariate Analysis of Covariance (MANCOVA) looks at the mean differences among groups on a combination of dependent variables and determines the likelihood that those differences occurred by chance while controlling for the effects of one or more covariates. The MANCOVA creates a linear combination of the dependent variables in order to create a grand mean on a set of dependent variables to have the ability to assess group differences. While multiple ANCOVA’s could be conducted to analyze the same variables, the use of multiple ANCOVAs inflate the Type I error rate; here, the MANCOVA helps control for that inflation. The two assumptions of homogeneity of variance and normality will be assessed. Normality assumes that the scores are normally distributed and can be visually represented by a bell curve; they will be assessed using the one sample Kolmogorov Smirnov test. Homogeneity of variance assumes that both groups have equal variances; they will be assessed using Levene’s test. The multivariate equivalent to homogeneity of variance, homogeneity of covariance matrices, will be tested using Box’s M Test.

**Reference**

Statistics Solutions. (2013). Data analysis plan: One Way MANCOVA [WWW Document]. Retrieved http://www.statisticssolutions.com/academic-solutions/member-resources/member-profile/data-analysis-plan-templates/data-analysis-plan-one-way-mancova-2/