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Write-Up: ANOVA (Analysis of Variance) w/ Tukey Instructions and Template

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Instructions: For this graded assignment, you will complete the write-up below after completing the corresponding tutorial to this assignment. You will delete figures and tables where appropriate and then insert correct figures and tables. Also delete and then insert correct answers where there is RED text.

To begin, cut and paste the data set below into SPSS (or you can type in the data manually).  Do not copy the header row when you paste into SPSS. Before carrying out the analysis in SPSS, you need to set up your data file correctly using the “Variable View” tab. 

Scenario: The purpose of this study was to see if there was a difference in salaries of professors who teach math (1), science (2), or English (3).


Code
Name Subject Salary
1 Williams 1 84000
2 Smith 1 85000
3 Logan 1 95000
4 Alexander  1 75000
5 Oliver  1 87000
6 Daniels 1 87000
7 Jones 2 98000
8 Jefferson 2 85000
9 Madison 2 88000
10 Kelley 2 89000
11 Michaels  2 87000
12 Acara 2 88000
13 Welch 3 65000
14 Christian  3 56000
15 McBride 3 58000
16 Elm 3 57000
17 Toller 3 66000
18 Mason  3 65000

FINDINGS

Overview

The purpose of this study was to see if there was a difference in salaries of professors who teach math, science, or English. The independent variable was type of professor and the dependent variable was salary. A One-way Analysis of Variance (ANOVA) was used to test the hypothesis.  This Findings Section includes the research question, null hypothesis, data screening, descriptive statistics, assumption testing, and results.

Research Question

            RQ: Is there a difference between salaries of professors who teach math, science, or English?

Null Hypothesis

            H0: There is no significant difference between salaries of professors who teach math, science, or English.

Data Screening

            Data screening was conducted on each group’s dependent variable. The researcher sorted the data on each variable and scanned for inconsistencies. No data errors or inconsistencies were identified. Box and whiskers plots were used to detect outlierson each dependent variable. No outliers were identified. See Figure 1 for box and whisker plots.   

Figure 1. Box and whisker plots.

Descriptive Statistics

            Descriptive statistics were obtained on the dependent variable for each group.  The sample consisted of 00 participants.  The average salary of a college professor in the United States is $65,000.  Descriptive statistics can be found in Table 1.

Table 1

Descriptive Statistics

Assumption Testing

Assumption of Normality

            The ANOVA requires that the assumption of normality be met. Normality was examined using Shapiro-Wilks/Kolmogorov-Smirnov because the sample size was less than 50 participants.  The assumption of normality was met/not met. See Table 2 for Tests of Normality.

Table 2

Tests of Normality

Assumption of Homogeneity of Variance  

            The ANOVA requires that the assumption of homogeneity of variance be met. The assumption of homogeneity of variance was examined using the Levene’s test.  The assumption of homogeneity of variance was met/not met where (p = .000).  See Table 3 for Levene’s test of Equality of Error Variance.

Table 3

Levene’s test of Equality of Error Variance

Results

            An ANOVA was run to see if there was a difference between salaries of professors who teach math, science, or English. The independent variable was type of professor and the dependent variable was salary. The researcher rejected/failed to reject the null hypothesis at the 95% confidence level where F(0, 00) = 00, p = .00.  Partial eta square equaled (h2part = .000).  The effect size was very large/large/medium/small.   There was/was not a statistical difference in salaries among math (M = 00, SD = 00), science (M = 00, SD = 00), and English (M = 00, SD = 00) professors. See Table 4 for Tests of Between-Subjects Effects.

Table 4

Tests of Between-Subjects Effects

            Because the researcher rejected the null, post hoc analysis was required.  A Tukey test was performed to compare all possible pairs of group means among the three salaries.  Based on this test, it was found that English(M = 00, SD = 00) were paid significantly higher/lower than math(M = 00, SD = 00) and science (M = 00, SD = 00) professors.  See Table 5 for pairwise comparisons.

Table 5

Pairwise Comparisons

Write-Up: ANOVA (Analysis of Variance) w/ Tukey Instructions and Template

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