Essay Grade

1
Week Five ANOVA Exemplar Template
Research Question
Does the mean change in number of days of cold symptoms differ among the
three experimental populations: those who take placebo, those who take low doses of
vitamin C, and those who take high doses of vitamin C?
Hypotheses
H0: The mean change in number of days of cold symptoms does not differ among
the three experimental populations: those who take placebo, those who take low doses of
vitamin C, and those who take high doses of vitamin C.
H1: The mean change in number of days of cold symptoms does differ among the
three experimental populations: those who take placebo, those who take low doses of
vitamin C, and those who take high doses of vitamin C?
Results
A one-way ANOVA 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. The independent variable, the vitamin C factor, included three
levels: placebo, low doses of vitamin C, and high doses of vitamin C. The dependent
variable was the change in the number of days of cold symptoms from the first to second
year. The ANOVA was significant at the .05 level, F(2, 27) = 4.84, p = .02. The strength
of the relationship between the vitamin C treatment and the change in the number of days
with cold symptoms, as assessed by η2, was strong, with the vitamin C factor accounting
for 26% of the variance of the dependent variable.
2
Follow-up tests were conducted to evaluate pairwise differences among means.
Because the variances among the three groups ranged from 16.54 to 30.00, we chose not
to assume that the variances were homogenous and conducted post hoc comparisons with
the use of Dunnett’s C test, a test that does not assume equal variances among the three
groups. There was a significant difference in the means betwee the group that received a
low dose of vitamin C and the placebo group, but no significant difference differences
between the two vitamin C groups and between the high dose and placebo groups. The
group that received a low dose of vitamin C showed on average a greater decrease in
number of days with cold symptoms in comparison to the placebo group. The 95%
confidence interval for the pairwise differences, as well as the means and standard
deviations for the thre groups are reported in Table 1. Figure 1 is a box-plot of
experimental conditions. The appendix depicts the SPSS ANOVA output generated from
the analysis.
Table 1
95% Confidence Intervals of Parities Differences in Mean Change in Number of
Days of Cold Symptoms
Variable
M
SD
3.50
4.14
Low Dose (Vitamin C)
-2.10
4.07
[.47, 10.73*]
High Dose (Vitamin C)
-2.00
5.48
[-.56, 11.56*]
Placebo
Placebo
Low Dose
[-6.12, 5.92]
Note: An asterisk indicates that the 95% confidence interval does not contain zero, and therefore the
difference in means is significant at the .05 significance using Dunnett’s C procedure.
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Figure 1. Boxplot depicting time spent talking by stress condition.
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Appendix
Descriptive Statistics
Dependent Variable: Difference in Days with Colds
Vitamin C Treatment
Placebo
Low Vitamin C Dose
High Vitamin C Dose
Total
Mean
Std. Deviation
3.50
4.143
-2.10
4.067
-2.00
5.477
-.20
5.182
N
10
10
10
30
Levene’s Test of Equality of Error
Variancesa
Dependent Variable: Difference in Days with
Colds
F
1.343
df1
df2
2
27
Sig.
.278
Tests the null hypothesis that the error
variance of the dependent variable is equal
across groups.
a. Design: Intercept + group
Tests of Between-Subjects Effects
Dependent Variable: Difference in Days with Colds
Source
Corrected Model
Intercept
group
Error
Total
Corrected Total
Type III Sum of
Squares
205.400a
1.200
205.400
573.400
780.000
778.800
df
Mean Square
2
1
2
27
30
29
a. R Squared = .264 (Adjusted R Squared = .209)
102.700
1.200
102.700
21.237
F
4.836
.057
4.836
Sig.
.016
.814
.016
Partial Eta
Squared
.264
.002
.264
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Multiple Comparisons
Dependent Variable: Difference in Days with Colds
(I) Vitamin C Treatment
Placebo
Tukey HSD
Low Vitamin C Dose
High Vitamin C Dose
Placebo
Dunnett C
Low Vitamin C Dose
High Vitamin C Dose
(J) Vitamin C Treatment
Mean
Difference (I-J)
Std. Error
Sig.
95% Confidence Interval
Lower Bound
.49
.39
-10.71
-5.21
-10.61
-5.01
.47
Upper Bound
10.71
10.61
-.49
5.01
-.39
5.21
10.73
Low Vitamin C Dose
High Vitamin C Dose
Placebo
High Vitamin C Dose
Placebo
Low Vitamin C Dose
Low Vitamin C Dose
5.60*
5.50*
-5.60*
-.10
-5.50*
.10
5.60*
2.061
2.061
2.061
2.061
2.061
2.061
1.836
High Vitamin C Dose
5.50
2.172
-.56
11.56
-5.60*
1.836
-10.73
-.47
-.10
2.157
-6.12
5.92
-5.50
2.172
-11.56
.56
.10
2.157
-5.92
6.12
Placebo
High Vitamin C Dose
Placebo
Low Vitamin C Dose
Based on observed means.
The error term is Mean Square(Error) = 21.237.
*. The mean difference is significant at the
.030
.033
.030
.999
.033
.999

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