Psych 311 1nd Edition Lecture 21 Outline of Last Lecture I Recall II Mapping onto Generic Test Stat Formula III Coefficient of Determination r 2 IV HT using r Outline of Current Lecture I II III F Test Logic of ANOVA Reference Distribution for ANOVA Current Lecture I F Test ANOVA Analysis of Variance One Way ANOVA used for independent samples design separate samples use when you have one independent variable with two or more levels separate groups conditions Repeated Measures ANOVA sample used twice use when you have one IV with two or more levels measure sample two or more times The 2 levels differentiates F tests from t tests Two Way factorial ANOVA either separate samples and or sample samples we re evaluating 2 IV s each with 2 levels Value you get for F is interpreted the same way no matter which ANOVA test used Type I Error Rate Type II Error Rate 1 1 c c of comparisons the larger c is the more inflation our Type I Error Rate this is a bad thing comes with multiple tests ANOVA allows you to make the comparisons while keeping Type I Error Rate at II Logic of ANOVA Two sources of info 1 Systematic variance the detectable pattern in the data numerator These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute 2 Unsystematic random variance noise in our data the irrelevant stuff denominator Purpose of ANOVA is to detect systematic variance and disregard unsystematic variance ANOVA is comparing the variability between groups against the variability within groups averaged between groups systematic within groups unsystematic difference between groups gives insight to whether our IV had an affect spread of scores determines if there are differences within groups unsystematic is similar to sampling error You average within group variance similar to pooled variance to get single value F between group variance within group variance similar to t observed or obtained diff diff due to SE Most important thing is to detect between group variance is to minimize within group variance minimize SE III Reference Distribution for ANOVA F distribution Positively skewed distribution Extends from 0 00 to with the highest point at 1 00 can NEVER have a negative f value Since you can never have a negative variance since we square the values and ANOVA is the analysis of variances we therefore can never have a negative F value F between group variance within group variance F systematic variance unsystematic variance If between group variance and within group variance measure the same thing then there is no systematic variance IV didn t have an affect F 1 00 in order to reject Ho you need F 1 00 the larger your test stat the more likely you are to reject your Ho
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