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Statistics 101A
Professor Esfandiari
Comparison of the twosample test of the mean and oneway ANOVA
The objective of this handout is to:
1)
Show you how you can calculate the F value for ANOVA with unequal sample
size
2)
Show you that when you are dealing with two samples (F = t^2)
3)
Compare the two‐sample test of the mean and one‐way ANOVA
4)
Show you what SS total means mathematically and conceptually
5)
Elaborate that SS total = SS between + SS within but
Variance total # variance between + variance within
Using the CCE data we want to find out if the experimental group gained more
knowledge of the US Constitution than the control group. The independent variable
is group (experimental vs. control) and the outcome variable is gain in the
knowledge of the US Constitution. To solve this problem, we could either use the
two‐sample test of the mean or one‐way ANOVA and in the following I will show you
both. Remember that two‐sample test of the mean can be used only for the
comparison of the mean in two populations, while one‐way ANOVA is used for the
comparison of the mean in two or more populations.
Results of the twosample test of the mean
Group Statistics
group
N
Mean
Std. Deviation
Std. Error Mean
control
503
9.2644
13.48482
.60126
gain in the knowledge of the US constitution
experimental
961
15.7190
17.50453
.56466
95% Confidence Interval of the Difference
F
Sig.
t
df
Sig. (2tailed)
Mean Difference
Std. Error Difference
Lower and upper
Equal variances
assumed
.000
7.223
1462
.000
6.45463
.89357
8.20744, 4.70
in in the
owledge of
US
nstitution
Equal variances
not assumed
7.825
1263.889
.000
6.45463
.82484
8.07283, 4.83
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The null hypothesis is that gain in the knowledge of the US Constitution is similar for the
experimental and control group or lawrelated education has no effect on the knowledge
of the United States Constitution.
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This note was uploaded on 05/02/2011 for the course STAT 101A taught by Professor Mahtashesfandiari during the Winter '11 term at UCLA.
 Winter '11
 MahtashEsfandiari
 Statistics

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