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Unformatted text preview: Discussion section 227 10/26/10 ANOVA (Analysis of Variance) Overview ANOVA is a procedure we use to test the null hypothesis when we want to evaluate the mean differences between two or more groups. The main advantage of ANOVA is that we can make multiple comparisons between groups while keeping the alpha level constant. Hypotheses H : 1 = 2 = 3 H 1 : At least one population mean is different The F statistic The ratio for the F statistic is similar to the tstatistic but uses variance differences instead of mean differences Variance is computed by dividing SS (sum of squares) by df (degrees of freedom) = () ( ) This can also be stated in another way: = + If the null hypothesis is true, the there will be no treatment effect and the ratio would be F=1 Formulas Sums of Squares = ( ) GM is the grand mean = ( ) For each group = ( ) Degrees of freedom = 1 K is the number of groups (means) = 1 = + N is the total number of people in the study = ( 1) = = Notice that because the total variance is sectioned into variance between and within groups, the two portions must then add back to the total: SS between +SS within = ss total df between +df within = df total Mean Squares (variances) = = F ratio = All this information can be summarized in a source table: Source SS df MS F Between ( ) 2 K  1 Within df or NK Total ( ) 2 N 1 The F distribution The distribution is positively skewed with values piling up around 1. No value can be negative since the F ratio is comprised of variance (always positive). Example 1 12 overweight male volunteers were randomly assigned to three different treatment programs designed...
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This note was uploaded on 02/21/2012 for the course PYSC 227 taught by Professor Fairchild during the Fall '10 term at South Carolina.
 Fall '10
 Fairchild

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