Analysis of Variance Write-up (Graded Assignment)
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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 attitudes about
science among first grade students (1), second grade students (2), third grade students (3).
Code Name Grade Attitude
1 Christian 1 5
2 Noah 1 5
3 Elliana 1 6
4 Alexander 1 6
5 Oliver 1 6
6 Daniel 1 8
7 Dylan 2 5
8 Maryam 2 6
9 Madison 2 6
10 Isaiah 2 7
11 Michael 2 6
12 Elijah 2 5
13 Celia 3 5
14 Joe 3 6
15 Daniel 3 8
16 Larry 3 7
17 Hunter 3 6
18 Mason 3 5
FINDINGS
Overview
The purpose of this study was to see if there was a difference in attitudes about science
among first grade, second grade, and third grade students. The independent variable was grade
level and the dependent variable was attitude about science. 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 in attitudes about science among first grade, second grade, and
third grade students?
Null Hypothesis
H0: There is no significant difference in attitudes about science among first grade, second
grade, and third grade students.
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. 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 18 participants. Scores on the Attitudes About Science Survey can range from 0 to
10. A high score of 10 means that the student had a good attitude towards science whereas a low
score zero means that the student had a poor attitude towards science. Descriptive statistics can
be found in Table 1.
Table 1
Descriptive Statistics
Descriptive Statistics
Grade N Minimum Maximum Mean
Std.
Deviation
First Grade Attitude 6 5 8 6.00 1.095
Valid N (listwise) 6
Second Grade Attitude 6 5 7 5.83 .753
Valid N (listwise) 6
Third Grade Attitude 6 5 8 6.17 1.169
Valid N (listwise) 6
Assumption Testing
Assumption of Normality
The ANOVA requires that the assumption of normality be met. Normality was examined
using Shapiro-Wilks because the sample size was less than 50 participants. The assumption of
normality was met. See Table 2 for Tests of Normality.
Table 2
Tests of Normality
Tests of Normality
Grade
Kolmogorov-SmirnovaShapiro-Wilk
Statistic df Sig. Statistic df Sig.
Attitude First Grade .333 6 .036 .814 6 .078
Second Grade .254 6 .200*.866 6 .212
Third Grade .223 6 .200*.908 6 .421
*. 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 where (p = .674). See Table 3 for Levene’s test of Equality
of Error Variance.
Table 3
Levene’s test of Equality of Error Variance
Levene's Test of Equality of Error Variancesa,b
Levene
Statistic df1 df2 Sig.
Attitude Based on Mean .405 2 15 .674
Based on Median .326 2 15 .727
Based on Median
and with adjusted df
.326 2 13.740 .727
Based on trimmed
mean
.355 2 15 .707
Tests the null hypothesis that the error variance of the dependent variable
is equal across groups.
a. Dependent variable: Attitude
b. Design: Intercept + Grade
Results
An ANOVA was run to see if there was a difference in attitudes about science among
first, second, and third grade students. The independent variable was grade level and the
dependent variable was attitudes about science. The researcher failed to reject the null hypothesis
at the 95% confidence level where F(2, 15) = .16, p = .85. Partial eta square equaled (2part = .
021). The effect size was small. There was not a statistical difference in attitudes about science
among first (M = 6.00, SD = 1.1), second (M = 5.83, SD = .75), and third (M = 6.17, SD =1.17
grade students. Because the researcher failed to reject the null hypothesis, post hoc analysis was
not required. See Table 4 for Tests of Between-Subjects Effects.
Table 4
Tests of Between-Subjects Effects
Tests of Between-Subjects Effects
Dependent Variable: Attitude
Source
Type III Sum
of Squares df
Mean
Square F Sig.
Partial Eta
Squared
Corrected Model .333a2 .167 .160 .854 .021
Intercept 648.000 1 648.000 620.426 .000 .976
Grade .333 2 .167 .160 .854 .021
Error 15.667 15 1.044
Total 664.000 18
Corrected Total 16.000 17
a. R Squared = .021 (Adjusted R Squared = -.110)
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