Chapter 13 Group Differences All statistics are the average amount of explained variation divided by the average amount of unexplained variation

Variation Explained variation: variation (variance) in the dependent variable attributed to (explained by) the independent variable(s) Explained variance = between variance Unexplained variation: variation that is not attributable to the independent variable(s) Unexplained variance = within variance Unexplained variance is error

Source of Variation Every hypothesis test is the average amount of explained variance divided by the amount of unexplained variance

The F Table The source of variance: some amount of the dependent variable is explained by the independent variable and some amount is not Potential rows for any F Table are: Explained variance Unexplained variance Total amount of variance

F Table Columns Source (of variance) Degrees of freedom Sums of squared deviation Mean square F

Source of Variance Explained variance = between variance The categories (groups) are created by separating the dependent variable scores created by the independent variable groups; the levels of the IV create different groupings of the DV; the levels of the IV explain the differences between the groups

Source of Variance Unexplained variance = within variance Each group is created by the set of scores within a group; a measure of how well the group score represents the group is standard deviation; the amount of variance within a group is referred to as unexplained variance, or error

Source of Variance Total amount of variance: Add the explained to the unexplained variance to get the total amount of variance in the DV available to be explained

Degrees of Freedom (df) Total sample size = N Once a sample has been drawn to study, the size of that sample can no longer vary, lowering the total degrees of freedom by one Total degrees of freedom in an analysis are always the total sample size minus one (N-1)

Sums of Squared Deviation All variance is created through deviations; variance is the sum of the squared deviations of each score to the overall sample mean In ANOVA, the overall sample mean is the grand mean

Sums of Squared Deviation (SS) The Between Groups Sum of Squares The Within Groups Sum of Squares

Mean Square Significance tests are the ratio of the average amount of explained variance to the average amount of unexplained variance Thus, the mean square is calculated by dividing each SS (between or within) by its respective df

F The test statistic for the ANOVA is the F: F is the ratio of the mean square between divided by the mean square within

Percentage of Variance Explained Tells us how much of the dependent variable could be associated with our independent variable SS between is the amount of explained variance SS between/SS total = percentage of explained variance