Comparison of two-sample test of the mean and one-way ANOVA

# Comparison of - 1 Statistics 101A Professor Esfandiari Comparison of the twosample test of the mean and oneway ANOVA The objective of this handout

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1 Statistics 101A Professor Esfandiari Comparison of the two-sample test of the mean and one-way 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 two-sample 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. (2-tailed) 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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2 The null hypothesis is that gain in the knowledge of the US Constitution is similar for the experimental and control group or law-related 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.

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Comparison of - 1 Statistics 101A Professor Esfandiari Comparison of the twosample test of the mean and oneway ANOVA The objective of this handout

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