One-Way Analysis of Variance (ANOVA), II

1. One-Way Analysis of Variance (ANOVA), II 2011, 12, 6

2. Lab 19 Worksheet Q1 • A developmental psychologist is examining problem-solving ability for grade school children. Random samples of 5-year-old, 6-year-old, and 7-year-old children are obtained with n = 3 in each sample, and problem solving is measured for each child. Do the following data indicate significant differences among the three age groups? Test with alpha = .05.

3. Q1. Problem-Solving Among 5-, 6-, and 7-year-olds

4. Step 1: Form Hypotheses • H0 : • H1 :

5. Step 2: Set Decision Criteria •  = 0.05 • dfb = • dfw = • fcrit =

7. Step 3: Compute F

9. Y = (Y1 + Y2 + Y3) / 3 Compute SSB and MSB (numerator) MSB =

10. Compute SSW and MSw (Denominator) MSW =

11. Step 4: Create ANOVA Source Table

12. Step 5. Make Decision • Compare Fobs to Fcrit.

13. Segregation Index Question • Studies of the degree of residential racial segregation often use the segregation index. This is the percentage of nonwhites who would have to change the block on which they live in order to produce a fully nonsegregated city – one in which the percentage of non-white living in each block is the same for all blocks in the city. This index can assume values range from 0 to 100, with high values indicating greater segregation. The table shows the segregation index for a sample of cities n 2000, classified by region.

14. Are the mean segregation indices different across these four regions?

15. Step 1: Form Hypotheses • H0 : • H1 :

16. Step 2: Set Decision Criteria • Alpha = 0.05 • dfb = • dfw = • Fcrit =

18. Step 3: Compute F

20. Y = (Y1 + Y2 + Y3+ Y4 ) / 4 = Compute SSB and MSB (numerator) MSB =

21. Compute SSW and MSw (Denominator) MSW =

22. Step 4: Create ANOVA Source Table

23. Step 5. Make Decision • Compare Fobs to Fcrit.