2 Independent-samples t-tests But what if you have more than two groups?One suggestion: pairwise comparisons (t-tests)
3 Multiple independent-samples t-tests That’s a lot of tests!# groups # tests2 groups = 1 t-test3 groups = 3 t-tests4 groups = 6 t-tests5 groups = 10 t-tests...10 groups = 45 t-tests
4 Inflation of familywise error rate Familywise error rate – the probability of making at least one Type I error (rejecting the Null Hypothesis when the null is true)Every hypothesis test has a probability of making a Type I error (a).For example, if two t-tests are each conducted using a = .05, there is a probability of committing at least one Type I error.
5 Inflation of familywise error rate The formula for familywise error rate:# groups # tests nominal alpha familywise alpha2 groups t-test3 groups t-tests4 groups t-tests5 groups t-tests...10 groups 45 t-tests
6 Analysis of Variance: Purpose Are there differences in the central tendency (mean) of groups?Inferential: Could the observed differences be due to chance?
7 Assumptions of ANOVANormality – scores should be normally distributed within each group.Homogeneity of variance – scores should have the same variance within each group.Independence of observations – observations are randomly selected.
8 Logic of Analysis of Variance Null hypothesis (Ho): Population means from different conditions are equalm1 = m2 = m3 = m4Alternative hypothesis: H1Not all population means equal.
9 Lets visualize total amount of variance in an experiment Total Variance = Mean Square TotalBetween Group Differences(Mean Square Group)Error Variance(Individual Differences + Random Variance)Mean Square ErrorF ratio is a proportion of the MS group/MS Error.The larger the group differences, the bigger the FThe larger the error variance, the smaller the F
10 Logic--cont. Create a measure of variability among group means MSgroupCreate a measure of variability within groupsMSerror
11 Example: Test Scores and Attitudes on Statistics Loves StatisticsHates StatisticsIndifferent94876511123
12 Find the sum of squares between groups Find the sum of squares within groupsTotal sum of squares = sum of between group and within group sums of squares.
13 To find the mean squares: divide each sum of squares by the degrees of freedom (2 different dfs) Degrees of freedom between groups =k-1, where k = # of groupsDegrees of freedom within groups = n-kMSbetween= SSbetween/dfbetweenMSwithin= SSwithin/dfwithinF = MSbetween / MSwithinCompare your F with the F in Table D