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Unformatted text preview: ANOVA Part 1 Lecture 10 Psyc 11 Today Oneway ANOVA t tests extended t tests compare a sample to a population mean or compares two groups What if there are more than 2 groups? We can compare each pair BUT, Type 1 error quickly increases T tests extended If I have 2 groups 1 comparison 4 groups 6 comparisons A B A B C C D A B 3 groups 3 comparisons T tests extended Using a significance level of .05, With 1 t test, the chance of making a Type 1 error = 5% With 3 tests, the chance of making this error = .05 + .05 + .05 = 15% How can we control this? ANOVA An alysis o f Va riance = ANOVA An inferential statistics technique that lets us compare means, variances, and interactions among variables. Examines whether two or more population means are equal This is what we are testing! Oneway ANOVA Used when comparing more than two independent groups. If we compare two groups, we should get the same results as using a t test. In oneway ANOVA, there is 1 independent variable and multiple groups (levels, treatments) We compare the means at the same time The F Distribution A theoretical sampling distribution Used for multiple group comparison (ANOVA) Signal vs. Noise = Signal (Size of difference) Noise (variance within each group) t = M 1 M 2 S pooled F = Signal (variance between groups) Noise (variance within groups) The F ratio If the signal and noise are equal, then this ratio will equal 1. The null hypothesis says that F = 1 As the signal gets larger, F increases. We reject the null when this ratio is significantly larger than 1 F = Signal (variance between groups) Noise (variance within groups) The F distribution The F distribution (and associated test) is always a 1 tailed test. Variance ANOVA analyzes the variance between and within groups. Variance = squared standard deviation Two types of variance we are interested in: Variance BETWEEN groups Variance WITHIN groups Total variance combines these A visual look at variability: BETWEEN GROUPS Variance = Variance = 9.82 Variance = 4627.7 Variance between YELLOW and BLUE = little Variance between BLUE AND RED = Large Variance between YELLOW and RED = very large A visual look at variability: WITHIN GROUPS A lot of variance 234 234 234 234 234 234 234 234 234 234 No variance 126 123 120 125 128 123 129 127 123 120 A little variance 132 300 245 243 115 132 230 132 276 199 A visual look at variability: TOTAL 234 126 132 234 234 234 234 234 234 234 234 234 123 120 125 128 123 129 127 123 120 300 245 243 115 132 230 132 276 199 Putting it together We calculate an F that is the ratio of the variance between groups to the variance within groups. We compare this to a critical value, and decide whether or not there is a significant difference between the groups. Assumptions 1. Normality the dependent variable is normally distributed 1. Homogeneity of variance...
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 Spring '10
 Ryne

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