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Unformatted text preview: ANOVA Comparing the means of more than two groups Analysis of variance (ANOVA) • ! Like a ttest, but can compare more than two groups • ! Asks whether any of two or more means is different from any other. • ! In other words, is the variance among groups greater than 0? Null hypothesis for simple ANOVA • ! H : Variance among groups = 0 OR • ! H : μ 1 = μ 2 = μ 3 = μ 4 = ... μ k X 1 X 2 X 3 Frequency μ 1 = μ 2 = μ 3 X 1 X 2 X 3 Frequency Not all μ 's equal ANOVA's v. ttests An ANOVA with 2 groups is mathematically equivalent to a twotailed 2sample ttest. ! x = ! x n Under the null hypothesis, the sample mean of each group should vary because of sampling error. The standard deviation of sample means, when the true mean is constant, is the standard error: ! x 2 = ! x 2 n Squaring the standard error, the variance among groups due to sampling error should be: ! x 2 = ! x 2 n + Variance group means [ ] If the null hypothesis is not true, the variance among groups should be equal to the real variance among means plus the variance due to ANOVA's v. ttests An ANOVA with 2 groups is mathematically equivalent to a twotailed 2sample ttest. ! x = ! x n Under the null hypothesis, the sample mean of each group should vary because of sampling error. The standard deviation of sample means, when the true mean is constant, is the standard error: ! x 2 = ! x 2 n Squaring the standard error, the variance among groups due to sampling error should be: ! x 2 = ! x 2 n + Variance group means [ ] If the null hypothesis is not true, the variance among groups should be equal to the real variance among means plus the variance due to sampling error. With ANOVA, we test whether the variance among true group means is greater than zero. We do this by asking whether the observed variance among groups is greater than expected by chance: !...
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 Spring '10
 Driscoll
 Statistics, Normal Distribution, Standard Deviation, Variance, Null hypothesis

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