# Factorial ANOVA Analysis

### Factorial ANOVA Analysis

In this assignment, you will conduct a two-way factorial ANOVA. Use the Caffeine, Exercise, and Heart Rate Dataset given in the resources. Refer to page 544 of your Applied Statistics text for context of this imaginary study. Use the DAA Template in the resources to write up your assignment. Do not consider this template to be the final word on writing your paper or APA style and formatting. Be sure to consult the APA Style and Format link provided in the resources.

You may watch the video, How to Calculate a Two Way ANOVA Using SPSS, from Statisticsfun to help with this assignment.

#### Step 1

Write Section 1 of the DAA. Provide context for the Caffeine, Exercise, and Heart Rate Dataset. Include a definition of the specified variables, including factors, levels of each factor, and the outcome variable. Define the corresponding scales of measurement for each variable. Specify the sample size of the dataset.

#### Step 2

Write Section 2 of the DAA. Analyze the assumptions of the factorial ANOVA. Paste the SPSS histogram output for heart rate and discuss your visual interpretations. Paste SPSS descriptives output showing skewness and kurtosis values for heart rate and interpret them (that is, values of 0 are perfectly normal; values between +1 and -1 are ideal; values Â±2 are acceptable; values beyond Â±2 are a potential violation). Report the results of the Levene test and interpret it. Summarize whether or not the assumptions of the factorial ANOVA are met.

#### Step 3

Write Section 3 of the DAA. Specify a research question related to the factorial ANOVA. Articulate the null hypothesis and alternative hypothesis for Factor A, Factor B, and the A x B interaction. Specify the alpha level.

#### Step 4

Write Section 4 of the DAA.

• Begin by reporting the grand mean on Y, the means of Y for both main effects (A, B), and the means of the interaction ( A*B) to provide context. You may paste SPSS output of these descriptive statistics, but you should also report them in the narrative.
• Paste SPSS output of the A*B cell means plot on Y. Designate Factor A on the horizontal axis and separate lines for Factor B. Provide a visual interpretation of this graph in terms of possible main effects and an interaction.
• Paste the SPSS output for the factorial ANOVA. Report the results for both main effects and the interaction, including F, degrees of freedom, the F value, the p value, a calculation of effect size, and interpretation of the effect size (calculate and report simple eta squared; do not use partial eta squared from SPSS output).
• Report SPSS calculations of observed power and interpret them in terms of Type II error for each factor and the interaction.
• Interpret the results against the null hypotheses articulated in Section 3 for each factor and the interaction.

#### Step 5

Write Section 5 of the DAA. Discuss the conclusions of the factorial ANOVA as it relates to the research question. Conclude with an analysis of the strengths and limitations of one-way ANOVA.

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