Analysis of Variance

Complex ANOVAs, ANCOVAs, and MANOVAs 

 

This week we will continue our discussion of ANOVAs to cover more than one independent variable, a covariate, or multiple dependent variables. We will learn how to analyze and interpret the results from a factorial ANOVA (more than one between-subjects or within-subjects independent variable), mixed-design ANOVA (combination of at least one between-subjects and one within-subjects independent variable), ANCOVA (a basic one-way or repeated measures ANOVA with a covariate), and MANOVA (an ANOVA that includes more than one dependent variable). Students will learn how to analyze and interpret the results of these analyses from critiquing research and evaluating results, all in the context of a research study. Also, students will work in the discussion this week to create a research design that would utilize a complex ANOVA, ANCOVA, or MANOVA. 

 

Lane, D. M. (Project Leader) (n.d.). Online statistics education: A multimedia course of study. Rice University. Retrieved from http://onlinestatbook.com/ 

 

Chapter 15: Analysis of Variance 

 

Sukal, M. (2013). Research methods: Applying statistics in research. San Diego, CA: Bridgepoint Education, Inc. 

 

Chapter 8: Factorial and Mixed-Factorial Analysis of Variance 

 

DISCUSSION QUESTION 1: 

 

During this week you will work in the discussion area to identify a research question created in Week 1 that would utilize one of the following: factorial ANOVA, mixed-design ANOVA, ANCOVA, or MANOVA. This discussion will help you work towards your “Week 4 Assignment.” If there are no research questions that fit these types of statistical analyses, you will need to decide on a new question before moving forward with the assignment. 

 

THE QUESTION SHOULD BE OPEN-ENDED AND BE ABOUT WHAT STAGE OF GRIEF OR HEALING IS MORE LIKELY TO PROMOTE FORGIVENESS. OR SOMETHING SIMILAR. 

 

In your initial posting for this assignment, include the following: 

 

Identify an appropriate research question that would require the use of a factorial or mixed-design ANOVA to answer. Pick the question from the list created in Week 1 or identify a new question if there are no appropriate ones from Week 1. 

 

Describe why this question is appropriate for the selected statistical test. 

 

Identify the variables in this study and each of their attributes: discrete or continuous, quantitative or categorical, and scale of measurement (nominal, ordinal, interval, or ratio). 

 

Do the variables fit the qualifications for the selected statistical test? Explain. 

 

List the statistical notation and written explanation for the null and alternative hypotheses. 

 

Describe the types of errors that could occur. 

 

DISCUSSION 2: 

 

Case Study 3 

 

The readings for this week focus on complex ANOVAs, ANCOVAs, and MANOVAs. In this discussion we will apply those concepts to the analysis of a case study. Read the “Stroop Interference” case study presented in Chapter 20 of the Online Statistics Education text. 

 

In the body of your posting, include an overview of the following based on the research questions, “Do males and females differ in the time it takes to correctly conduct the stroop tasks? Are there differences in the time it takes to correctly conduct the various stroop tasks – words, colors, or interference? Finally, does the effect of the stroop task type depend on the gender?” 

Hypotheses: List the statistical notation and written explanations for the null and alternative hypotheses for the study. 

 

Variables: Describe the independent and dependent variables, their levels, operational definitions, and characteristics (e.g., scale of measurement). 

 

Data Analysis: You are given the information below from the ANOVA conducted. Summarize the specific type of statistical test conducted, the results obtained, and conclusions regarding the hypotheses (e.g, can we reject at the .05 or .01 level?). Be sure to describe why this specific ANOVA was selected and if a post-hoc test should be conducted. 

 

Source 

 

df 

 

SS 

 

MS 

 

F 

 

p 

Gender 

 

1 

 

83.3247 

 

83.3247 

 

1.9939 

 

0.1648 

 

Task 

 

2 

 

9525.9733 

 

4762.9867 

 

228.0551 

 

0.0000 

 

Interaction 

 

2 

 

55.8457 

 

27.9228 

 

1.3370 

 

0.2678 

 

Error 

 

45 

1880.5618 

 

41.7903 

 

Critique: Critique the results of the study, paying specific attention to the appropriateness of the analyses conducted, any biases or assumptions that were made, practical significance of the results, and recommendations for improving upon the study (methods or analyses). 

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