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

2. 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

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

4. 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

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

6. 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

7. 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

8. 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

9. 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)

10. 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

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

12. 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

13. 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

14. 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