18_anova1

18_anova1 - Review One-way ANOVA, I 9.07 4/15/2004 Multiple...

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One-way ANOVA, I 9.07 4/15/2004 Review between two conditions of an independent variable than two sample means What’s coming up conditions of a single independent variable generalize this new technique to apply to Earlier in this class, we talked about two- sample z- and t-tests for the difference – Does a trial drug work better than a placebo? – Drug vs. placebo are the two conditions of the independent variable, “treatment” Multiple comparisons We often need a tool for comparing more In the next two lectures, we’ll talk about a new parametric statistical procedure to analyze experiments with two or more Then, in the two lectures after that, we’ll more than one independent variable 1
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conditions, or levels We’ll talk An example subjects ANalysis Of Variance = ANOVA A very popular inferential statistical procedure It can be applied to many different experimental designs Independent or related samples An independent variable with any number of Any number of independent variables Arguably it is sometimes over-used. more about this later. Suppose we want to see whether how well people perform a task depends upon how difficult they believe the task will be We give 15 easy math problems to 3 groups of 5 Before we give them the test, we tell group 1 that the problems are easy, group 2 that the problems are of medium difficulty, and group 3 that the problems will be difficult Measure # of correctly solved problems within an allotted time. How do we analyze our results? –H 0 : µ = µ , H 0 : µ = µ , H 0 : µ = µ α single t-test is 0.05 so our experiment-wise error rate is (1-0.95 3 ) = 0.14 which cranks up p even more equal to α We could do 3 t-tests: easy medium medium difficult difficult easy But this is non-ideal With =0.05, the probability of a Type I error in a Here, we can make a Type I error in any of the 3 tests, This is much larger than our desired error rate Furthermore, the 3 tests aren’t really independent, We perform ANOVA because it keeps the experiment-wise error rate 2
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ANOVA •A one-way . ) . ANOVA is the general-purpose tool for determining whether there are any differences between means If there are only two conditions of the independent variable, doing ANOVA is the same as running a (two-tailed) two-sample t-test. Same conclusions Same Type I and Type II error rates Terminology Recall from our earlier lecture on experimental design: ANOVA is performed when there is only one independent variable When an independent variable is studied by having each subject only exposed to one condition, it is a between-subjects factor , and we will use a between-subjects ANOVA When it is studied using related samples (e.g. each subject sees each condition , we have a within- subjects factor , and run a within-subjects ANOVA One-way, between-subjects ANOVA effect. means
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This note was uploaded on 11/11/2011 for the course BIO 9.07 taught by Professor Ruthrosenholtz during the Spring '04 term at MIT.

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18_anova1 - Review One-way ANOVA, I 9.07 4/15/2004 Multiple...

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