Assignment 5 – ANOVAs
by
Ewing Coleman Green
ARC 8912 CRN 31743
Statistical Methods
Nova Southeastern University
March 30, 2013
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Assignment 5 – ANOVAs
This assignment is comprised of two sections. The first involves a one-way ANOVA test
on the effects of marital status on life satisfaction, and the second a two-way ANOVA test on the
effect of alcohol on mate selection at night-clubs.
One-way ANOVA test
The independent variable for this test is marital status and the dependent variable is life
satisfaction. The null hypothesis is the life satisfaction means of all marital status groups are
equal. Conversely, the alternate hypothesis is the life satisfaction means of all marital status
groups are not all equal.
Using SPSS version 20 a one-way ANOVA test was conducted on the data using a
confidence level of 95%. The sample sizes for each of the marital status groups are shown in
Table 1 below.
Table 1
Output from a One-Way ANOVA test on life satisfaction versus marital status, showing sample
sizes by marital status
It is appropriate to note that the widowed group only includes 3 participants, thus introducing the
likelihood of increased sampling error for this group (Creswell, p. 146). This also creates
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additional challenge to inferring statistical meaning for the purposes of interpretation and
attempts to generalize meaning.
Additional outputs from the analysis provided the means and standard deviations for each
of the levels of marital status, as shown in Table 2 below.
Table 2
Outputs from a One-Way ANOVA test on life satisfaction versus marital status, showing mean
and standard deviation results
The data show mathematically different means and standard deviations for each of the
five marital groups. For example, the range of means is 4.53-4.94, with the separated group
scoring the lowest life satisfaction and the married group showing the highest. The results of
Levene’s Test of Equality of Error Variances shows p = .068, therefore a null hypothesis of equal
variances across all groups of the dependent variable fails to be rejected.
The SPSS analysis output also gave the F statistic (F = 1.22), degrees of freedom (df = 4,
224), p value (p = .31), and eta squared (η2 = .02). The results are shown See Table 3 below.
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Table 3
Outputs from a One-Way ANOVA test on life satisfaction versus marital status, showing F
statistic, degrees of freedom, p value, and eta squared (η2) results
The resulting p value of .31 indicates the means are not significantly different (p > .05).
In addition, according to Green and Salkind (2008), an effect size index, η2, of .02 represents a
small difference in the life satisfaction means by marital status. Green and Salkind (2008)
reported, “What is a small versus a large η2 is dependent on the area of investigation. However,
η2 of .01, .06, and .14 are, by convention, interpreted as small, medium, and large effect sizes,
respectively” (p. 185).
Since the analysis resulted in non-statistical significance, Post Hoc tests were not
conducted.
Overall, SPSS analysis found that life satisfaction of the participants sampled amongst
the five marital groups are not statistically significantly different. This results in failing to reject
the null hypothesis. Morgan, Reichert, and Harrison (2002) was used to write the following. The
hypothesis in this study predicated that life satisfaction means of all marital status groups are
equal. To evaluate this prediction, a one-way ANOVA test was conducted on the data using a
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confidence level of 95%. Results indicated life satisfaction means by marital group are not
significantly different, F(4, 224) = 1.22, p > .05, eta2 = .02.
Two-way ANOVA test
The independent variables for this test are participant gender with two levels and the
amount of alcohol consumed by participants with three levels. The dependent variable is
attractiveness of the mate whom the participant was chatting up during the evening. The null
hypothesis is alcohol consumption for both males and females does not effect the subjective
perception of physical attractiveness of mates. Conversely, the alternate hypothesis is
alcohol consumption for both males and females does effect the subjective perception of physical
attractiveness of mates.
Using SPSS version 20 a two-way ANOVA test was conducted on the data using a
confidence level of 95%. Table 4 below shows the results for Between-Subjects Factors and
Levene’s Test of Equality of Error Variances.
Table 4
Outputs from a Two-Way ANOVA test on mate selection, showing Between-Subjects Factors and
Levene’s Test of Equality of Error Variances results
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The results of Levene’s Test of Equality of Error Variances shows p = .202, therefore a
null hypothesis of equal variances across all groups of the dependent variable fails to be rejected.
According to Green and Salkind (2008), the extent to which non-significance occurs and sample
sizes vary among groups, “the resulting p-value of the overall F statistic is untrustworthy” (p.
184). Green and Salkind (2008) suggest that under these conditions “it is preferable to use
statistics that do not assume equality of population variances, such as the Browne-Forsythe or the
Welch statistics” which are available in SPSS (p. 184).
The means and standard deviations of the dependent variable, mate attractiveness, are
included in Table 5 below.
Table 5
Output from a Two-Way ANOVA test on mate selection, showing Descriptive Statistics results
In addition, Table 6 below shows the Tests of Between-Subject Effects results.
Table 6
Output from a Two-Way ANOVA test on mate selection, showing Tests of Between-Subjects
Effects results
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Data from the Tests of Between-Subjects Effects above was used to complete the following:
Source
df
Mean Square
F
Sig.
Gender
1
168.75
2.03
.161
Alcohol
2
1666.15
20.07
.000
Gender*alcohol
2
989.06
11.91
.000
Using the data from Tables 4 through 6 above, inferences can be made regarding the
statistical significance and hypothesis testing in this study. The resulting overall p value of .000
suggests that alcohol consumption significantly effects perceived mate attractiveness; therefore
the overall null hypothesis is rejected. In addition, according to Green and Salkind (2008), an
effect size index, η2, of .611 represents a large difference in perceived mate attractiveness means
due to alcohol consumption. In addition, there is a statistically significant interaction between
gender and alcohol consumption, p = .000.
Given the statistical significance of results, Post Hoc Tests analysis was conducted.
Results are shown in Table 7 below.
Table 7
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Outputs from a Two-Way ANOVA test on mate selection, showing Post Hoc Tests results
Results indicate statistical significance between both the None to 4 Pints subject groups, p <
.0001, and the 2 to 4 Pints subject groups, p < .0001.
In addition, in order to investigate gender differences, the file was split by gender. This
allowed inferences to be made about the influence of alcohol consumption on perceived mate
attractiveness by gender. Table 8 below shows the SPSS outputs by gender.
Table 8
Outputs from a Two-Way ANOVA test on mate selection, showing Tests of Between-Subjects
Factors, Descriptive Statistics, Levene’s Test of Equality of Error Variances, Tests of BetweenSubjects Effects, and Estimated Marginal Means results by gender
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Upon analyzing the data by gender, the Tests of Between Subject Effects revealed that
male participants had p value of .000 and effect size index, η2, of .661, while females had p value
of .292, and effect size index, η2, of .110. This suggests that male perception of mate
attractiveness in this study was significantly affected by alcohol consumption while females’
perception was not. Therefore, the null hypothesis that alcohol consumption does not effect the
subjective perception of physical attractiveness of mates for males is rejected, while the null
hypothesis that alcohol consumption does not effect the subjective perception of physical
attractiveness of mates for females fails to be rejected.
Morgan, Reichert, and Harrison (2002) was used to write the following. The hypothesis
in this study predicated that alcohol consumption for both males and females does not effect the
subjective perception of physical attractiveness of mates. To evaluate this prediction, a 2
(gender) x 3 (level of alcohol consumption) ANOVA test was conducted on the data using a
confidence level of 95%. Results indicated significant main effects for alcohol consumption, F(5,
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42) = 20.07, p < .0001, η2 = .611. Post Hoc analysis revealed significant differences between
both the None to 4 Pints subject groups, p < .0001, and the 2 to 4 Pints subject groups, p < .0001.
Additional analysis indicated significant results for alcohol consumption on male perception of
mate attractiveness, F(2,21) = 20.52, p < .0001, η2 = .661, and not significant results for alcohol
consumption on female perception of mate attractiveness, F(2,21) = 1.30, p > .05, η2 = .110.
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References
Creswell, J. W. (2012). Educational research: Planning, conducting, and evaluating
quantitative and qualitative research (4th ed.). Upper Saddle River, NJ: Pearson.
Green, S. B., & Salkind, N. J. (2008). Using SPSS for Windows and Macintosh: Analyzing and
understanding data (5th ed.). Upper Saddle River, NJ: Pearson.
Morgan, S. E., Reichert, T., & Harrison, T. R. (2002). From numbers to words: Reporting
statistical results for the social sciences. Boston, MA: Allyn and Bacon.