**One way Anova**

The data for Exercises 1 through 3 are in the data set named Lesson 24 Exercise File 1 on the Student Data Disk. The data are from the following research problem.

Marvin is interested in whether blonds, brunets, and redheads differ with respect to their extrovertedness. He randomly samples 1 8 men from his local college campus: six blonds, six brunets, and six redheads. He then administers a measure of social extroversion to each individual.

1. Conduct a one-way ANOVA to investigate the relationship between hair color and social extroversion. Be sure to conduct appropriate post hoc tests. On the output, identify the following:

a. F ratio for the group effect – ?

b. Sums of squares for the hair color effect

c. Mean for redheads

d. p value for the hair color effect

2. What is the effect size for the overall effect of hair color on extroversion?

3. Create a boxplot to display the differences among the distributions for the three hair color groups.

**NB: Writing an APA Results Section**

We present some guidelines for writing a Results section for statistical procedures that may require follow-up tests, such as one-way ANOVA and MANOVA in Unit 7, or the Friedman test in Unit 1 0. Consequently, it may be necessary to reread this material after you have read the other lessons in Unit 7 and the lessons in Unit 1 0 . Some researchers initially provide a description of the general overall analytic strategy that includes the omnibus tests and the follow-up tests. This general description is necessary to the degree that the analyses are unconventional or complex.

The steps required to write a Results section are as follows:

1. Describe the statistical testes), the variables, and the purpose of the statistical testes). For example, “A one-way analysis of variance was conducted to evaluate the relationship between vitamin C and the change in the number of days with cold symptoms from the first year to the second year of the study.”

• Describe the factor or factors. If a factor is a within-subjects factor, be sure to label it as such. Otherwise the reader may assume that it is a between-subjects factor. If a multifactorial design has one or more within-subjects factors, describe each factor as a between-subjects or a within-subjects factor.

• Indicate the number of levels of each factor. It may also be informative to the reader to have a description of each level if the levels are different treatments. However, it is not necessary to report the number of levels and what the levels are for factors with obvious levels such as gender.

• Describe what the dependent variable(s) are.

2. Report the results of the overall testes).

• Describe any decisions about which test was chosen based on assumptions. For example, for a one-way within-subjects ANOVA, justify the choice of using a traditional univariate test instead of a multivariate test.

• Report the test value and significance level (for the one-way ANOVA, F(2, 27) = 4.84, p = .02). For p values of .000, report them as p < .01 . For multifactor designs, report the statistic for each of the main and interaction effects. Tell the reader whether the testes) are significant or not.

• Report statistics that allow the reader to make a judgment about the magnitude of the effect for each overall test (e.g., for the one-way ANOVA, 112 = .4S).

• Italicize all non-Greek symbols except subscripts and superscripts.

3. Report the descriptive statistics. Refer the reader to a table or figure that presents the relevant descriptive statistics (e.g., means and standard deviations for ANOVA designs). A table or figure may not be necessary for simpler designs, such as a one-way ANOVA with three groups. For these simple designs, the descriptive statistics may be presented in the text.

4. Describe and summarize the general conclusions of the analysis. For example, ”The results of the one-way ANOVA supported the hypothesis that different types of vitamin C treatment had a differential effect on the reduction of cold symptoms in individuals.” S. Report the results of the follow-up tests.

• Describe the procedures used to conduct the follow-up tests. Explain any decisions you made about choice of tests based on their assumptions.

• Report the method used to control for ‘TYpe I error across the multiple tests.

• Summarize the results of the follow-up procedures. It may be useful to present the results of the significance tests among pairwise comparisons with a table of means and standard deviations. When possible, report confidence intervals for pairwise comparisons.

• Describe and summarize the general conclusions of the follow-up analyses.

Make sure to include in your description the directionality of the test. For example, the mean for one treatment group is higher or lower than the mean for another group.

6. Report the distributions of the dependent variable for levels of the factor(s) in a graph, if space is available. The graph should be inserted in the text where appropriate.

For example, if the graph pertains to assumptions, you would insert it in the section where assumptions are discussed. Likewise, if the graph reflects the means and standard deviations, it should be presented with the discussion of the descriptive statistics.

** **

**Two way Anova**

Exercises 5 through 8 are based on the following research problem. The data set for this problem is named Lesson 26 Exercise File 2 on the Student Data Disk. Vicki was interested in how much time fathers of children with a disability play with their children who are disabled. To address this question, she found 60 fathers in six categories: (a) fathers with a male child with no physical or mental disability, (b) fathers with a female child with no physical or mental disability, (c) fathers with a male physically disabled child, (d) fathers with a female physically disabled child, (e) fathers with a male mentally retarded child, and (f) fathers with a female mentally retarded child. She asked fathers to record how many minutes per day they spent playing with their child for five days. The SPSS data file contains 60 cases and three variables, a factor indicating the disability status of the child, a factor indicating the child’s gender, and a play time score averaged across the five day.

5. Conduct a two-way ANOVA to evaluate differences among the groups, according to gender and disability status of the child., in the amount of time fathers spent playing with their children.

6. Which follow-up procedures should you use? Why? 7. Write a Results section reporting the results of the analysis.

8. Create a boxplot to show the distributions for the six groups.

**NB: **

**Two APA Results Sections**

We present two results sections, one for a significant main effect and non-significant interaction effect and one for a significant interaction effect.

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