Lecture 16_one-way ANOVA

Lecture 16_one-way ANOVA - 10/27/2010 One-way ANOVA 1...

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10/27/2010 1 One-way ANOVA 1 Review • One of the last things we learned was the independent samples t-test ... which evaluated the difference between 2 means – Tested the significance of mean differences between two different groups of people, such as treatment and control groups – Could answer questions such as “Are there differences in depression for people who take Prozac vs. those who take no medication?” 2 Review • In the independent samples t-test we compared the means of two groups and tested statistically whether there were different from one another • If the observed difference between the means was greater than the difference we would expect to see between the means due to chance alone, then we said that the means were “significantly different” 3
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10/27/2010 2 Extending the Logic of the t-test 4 • We can also compare mean differences across more than two groups • We are still interested in whether the differences that we observe between the means is greater than what we would expect by chance alone and if the means are significantly different from one another One-way ANOVA • The name of the test that extends the t- test to examine differences in more than two group means is known as a “ One-way Analysis of Variance (ANOVA) – The test evaluates whether three or more samples come from a single population with the same mean – Uses information on chance variation (i.e., the standard error) to determine whether observed differences in the means indicate that they come from different populations 5 Why not just run Multiple t-tests? • Although you could conduct several independent samples t –tests to examine the difference between more than two means, conducting multiple t-tests leads to inflation of the Type I error rate • ANOVA tests for significant differences among several means without increasing the Type I error rate 6
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10/27/2010 3 Comparison-wise vs. Family-wise Error Rates • Comparison-wise error is the probability of falsely rejecting the null hypothesis for one pair-wise comparison test (i.e., the α-level assigned to each hypothesis test) – With t-tests, we only conducted one comparison… “was one mean different from one other mean?” so this was not a problem – We had one pair-wise hypothesis test, so the comparison-wise error rate was the correct α– level for the study 7 Comparison-wise vs. Family-wise Error Rates • When comparing > 1 group however, we examine >1 pair-wise comparison • Given multiple tests, we will have a cumulative error rate that increases rapidly as the number of comparisons increase • Experiment-wise error : the probability of making a Type 1 error in the overall experiment (i.e., across all pairwise comparisons). 8
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Lecture 16_one-way ANOVA - 10/27/2010 One-way ANOVA 1...

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