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 7-year-old6-year-old5-year-old 560 441 622

4. Step 1: Form Hypotheses H 0 : H 1 :

5. Step 2: Set Decision Criteria  = 0.05 df b = df w = f crit =

7. Step 3: Compute F

8. 7-year-old (n 1 = 3)6-year-old (n 2 = 3)5-year-old (n 3 = 3) Y1Y1 Y12Y12 Y2Y2 Y22Y22 Y3Y3 Y32Y32 52563600 4164 11 6362424  Y 1 =15  Y 1 2 =77  Y 2 =12  Y 2 2 = 56  Y 3 =3  Y 3 2 =5 Y 1 = 5SSW 1 = 2 Y 2 = 4SSW 2 = 8 Y 3 = 1SSW 3 = 2

9. Compute SSB and MSB (numerator) MSB = 7-year-old (n 1 = 3)6-year-old (n 2 = 3)5-year-old (n 3 = 3) Y1Y1 Y12Y12 Y2Y2 Y22Y22 Y3Y3 Y32Y32 560 441 622 Y = (Y1 + Y2 + Y3) / 3

10. Compute SSW and MSw (Denominator) 7-year-old (n 1 = 3)6-year-old (n 2 = 3)5-year-old (n 3 = 3) Y1Y1 Y12Y12 Y2Y2 Y22Y22 Y3Y3 Y32Y32 560 441 622 MSW =

11. Step 4: Create ANOVA Source Table SourceSSdfMSF Between262136.5 Within1262 Total388

12. Step 5. Make Decision Compare F obs to F crit.

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? NortheastNorth CentralSouthWest Buffalo, 77Minneapolis, 58New Orleans, 68San Francisco, 60 Newark, 80Detroit, 85Tampa, 63Dallas, 59 Philadelphia, 72Chicago, 80Miami, 69Los Angeles, 66 Pittsburgh, 67Milwaukee, 82Atlanta, 65Houston, 66

15. Step 1: Form Hypotheses H 0 : H 1 :

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

18. Step 3: Compute F

19. Northeast (n 1 = 4)North Central (n 2 = 4)South (n 3 = 4)West (n 4 = 4) Y1Y1 Y12Y12 Y2Y2 Y22Y22 Y3Y3 Y32Y32 Y4Y4 Y42Y42 775929583364684624603600 806400857225633969593481 725184806400694761664356 674489826724654225664356  Y 1 =296  Y 1 2 =22002  Y 2 = 305  Y 2 2 =23713  Y 3 =265  Y 3 2 =17579  Y 4 =251  Y 4 2 =15793 Y 1 =74 SSW1 = 98 Y 2 =76.25 SSW2= 456.75 Y 3 =66.2 5 SSW3= 22.75 Y 4 = 62.75 SSW4= 42.75

20. Compute SSB and MSB (numerator) MSB = Y = (Y1 + Y2 + Y3+ Y4 ) / 4 = Northeast (n 1 = 4)North Central (n 2 = 4)South (n 3 = 4)West (n 4 = 4) Y1Y1 Y12Y12 Y2Y2 Y22Y22 Y3Y3 Y32Y32 Y4Y4 Y42Y42 77586860 80856359 72806966 67826566

21. Compute SSW and MSw (Denominator) MSW = Northeast (n 1 = 4)North Central (n 2 = 4)South (n 3 = 4)West (n 4 = 4) Y1Y1 Y12Y12 Y2Y2 Y22Y22 Y3Y3 Y32Y32 Y4Y4 Y42Y42 77586860 80856359 72806966 67826566

22. Step 4: Create ANOVA Source Table SourceSSdfMSF Between486.193162.063.14 Within620.251251.69 Total1106.4415

23. Step 5. Make Decision Compare F obs to F crit.