Write-up: ANOVA with Tukey
Overview
The purpose of this study was to see if there was a significant difference in job
satisfaction among teachers, nurses, or psychologists. The independent variable was the type of
job and the dependent variable was job satisfaction as measured by the Job Satisfaction Scale. 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 significant difference between job satisfaction among teachers, nurses, or
psychologists?
Null Hypothesis
H0: There is no significant difference in job satisfaction among teachers, nurses, or
psychologists.
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 outliers on each dependent variable. One
extreme outlier was identified and removed from the nurses group. See Figure 1 for box and
whisker plots.
Write-up: ANOVA with Tukey
Descriptive Statistics
Descriptive statistics were obtained on the dependent variable for each group. The sample
consisted of 18 participants. Scores on the Job Satisfaction Scale could possibly range from 10 to
100. A high score of 100 is a high job satisfaction score on the Job Satisfaction Scale, whereas a
low score of 10 means that the teacher had low job satisfaction. Descriptive statistics can be
found in Table 1.
Descriptive Statistics
Job N Minimum Maximum Mean
Std.
Deviation
1st Satisfaction 6 80 91 85.33 4.457
Valid N
(listwise)
6
2nd Satisfaction 6 85 98 89.17 4.535
Valid N
(listwise)
6
3rd Satisfaction 6 56 66 60.33 4.227
Valid N
(listwise)
6
Assumption Testing
Write-up: ANOVA with Tukey
Assumption of Normality
The ANOVA requires that the assumption of normality be met. Normality was examined
using Shapiro-Wilks. The assumption of normality was met. See Table 2 for Tests of
Normality.
Table 2: Tests of Normality
Tests of Normality
Job
Kolmogorov-SmirnovaShapiro-Wilk
Statistic df Sig. Statistic df Sig.
Satisfaction 1st .226 6 .200*.891 6 .322
2nd .348 6 .022* .774 6 .34
3rd .210 6 .200*.877 6 .256
*. This is a lower bound of the true significance.
a. Lilliefors Significance Correction
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 (p = .903). See Table 3 for Levene’s test of
Equality of Error Variance.
Table 3
Levene's Test of Equality of Error Variancesa,b
Levene
Statistic df1 df2 Sig.
Satisfaction Based on Mean .103 2 15 .903
Based on Median .141 2 15 .870
Based on Median and with
adjusted df
.141 2 13.327 .870
Based on trimmed mean .149 2 15 .863
Tests the null hypothesis that the error variance of the dependent variable is equal across groups.
a. Dependent variable: Satisfaction
b. Design: Intercept + Job.
Write-up: ANOVA with Tukey
Results
An ANOVA was run to see if there was a difference in job satisfaction among teachers,
nurses, or psychologists. The independent variable was the type of job, and the dependent
variable was job satisfaction. The researcher rejected the null hypothesis at the
95% confidence level where F (2, 15) = 75.7, p = .001. Partial eta square equaled (2part
= .910.) The effect size was extremely large. There was a statistical difference in job satisfaction
among teachers (M=60.33, SD= 4.227) See Table 4 for Tests of Between- Subject Effects.
Tests of Between-Subjects Effects
Dependent Variable: Statisfaction
Source
Type III Sum
of Squares df
Mean
Square F Sig.
Partial Eta
Squared
Corrected
Model
2942.111a2 1471.056 75.698 <.001 .910
Intercept 110293.389 1 110293.389 5675.475 <.001 .997
Job 2942.111 2 1471.056 75.698 <.001 .910
Error 291.500 15 19.433
Total 113527.000 18
Corrected
Total
3233.611 17
a. R Squared = .910 (Adjusted R Squared = .898)
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 professions.
Based on this test, it was found that psychologist (M =60. 33, SD = .4.227) had significantly
lower job satisfaction than teachers (M= 85.33, SD= 4.457) and nurses (M=89.17, SD=4.535).
See Table 5 for Multiple Comparisons.
Write-up: ANOVA with Tukey
Multiple Comparisons
Dependent Variable: atisfaction
Tukey HSD
(I) Job (J) Job
Mean
Difference (I-J) Std. Error Sig.
95% Confidence Interval
Lower
Bound
Upper
Bound
1st 2nd -3.83 2.545 .316 -10.44 2.78
3rd 25.00*2.545 <.001 18.39 31.61
2nd 1st 3.83 2.545 .316 -2.78 10.44
3rd 28.83*2.545 <.001 22.22 35.44
3rd 1st -25.00*2.545 <.001 -31.61 -18.39
2nd -28.83*2.545 <.001 -35.44 -22.22
Based on observed means.
The error term is Mean Square(Error) = 19.433.
*. The mean difference is significant at the .05 level.
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