# 14_ANOVA1 - OneWayANOVA Introduction to Analysis of...

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One-Way ANOVA Introduction to Analysis of Variance (ANOVA)

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What is ANOVA? ANOVA is short for ANalysis Of VAriance Used with 3 or more groups to test for MEAN DIFFS. E.g., caffeine study with 3 groups: No caffeine Mild dose Jolt group Level is value, kind or amount of IV Treatment Group is people who get specific treatment or level of IV Treatment Effect is size of difference in means
Rationale for ANOVA (1) We have at least 3 means to test, e.g., H 0 : μ 1 = μ 2 = μ 3 . Could take them 2 at a time, but really want to test all 3 (or more) at once. Instead of using a mean difference, we can use the variance of the group means about the grand mean over all groups. Logic is just the same as for the t-test. Compare the observed variance among means (observed difference in means in the t-test) to what we would expect to get by chance.

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Rationale for ANOVA (2) Suppose we drew 3 samples from the same population. Our results might look like this: 10 0 -10 -20 4 3 2 1 0 Raw Scores (X) 10 0 -10 -20 Three Samples from the Same Population Mean 1 Mean 2 Mean 3 Standard Dev Group 3 Note that the means from the 3 groups are not exactly the same, but they are close, so the variance among means will be small.
Rationale for ANOVA (3) Suppose we sample people from 3 different populations. Our results might look like this: 20 10 0 -10 -20 4 3 2 1 0 Three Samples from 3 Diffferent Populations Raw Scores (X) Mean 1 Mean 2 Mean 3 SD Group 1 Note that the sample means are far away from one another, so the variance among means will be large.

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Rationale for ANOVA (4) Suppose we complete a study and find the following results (either graph). How would we know or decide whether there is a real effect or not? 10 0 -10 -20 4 3 2 1 0 Raw Scores (X) 0 Three Samples from the Same Population Mean 1 Mean 2 Mean 3 Standard Dev Group 3 20 10 0 -10 -20 4 3 2 1 0 Three Samples from 3 Diffferent Populations Raw Scores (X) Mean 1 Mean 2 Mean 3 SD Group 1 To decide, we can compare our observed variance in means to what we would expect to get on the basis of chance given no true difference in means.
Review When would we use a t-test versus 1-way ANOVA?

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