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

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.

Q1. Problem-Solving Among 5-, 6-, and 7-year-olds 7-year-old6-year-old5-year-old

Step 1: Form Hypotheses H 0 : H 1 :

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

Step 3: Compute F

7-year-old (n 1 = 3)6-year-old (n 2 = 3)5-year-old (n 3 = 3) Y1Y1 Y12Y12 Y2Y2 Y22Y22 Y3Y3 Y32Y  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

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 Y32Y Y = (Y1 + Y2 + Y3) / 3

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 Y32Y MSW =

Step 4: Create ANOVA Source Table SourceSSdfMSF Between Within1262 Total388

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

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.

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

Step 1: Form Hypotheses H 0 : H 1 :

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

Step 3: Compute F

Northeast (n 1 = 4)North Central (n 2 = 4)South (n 3 = 4)West (n 4 = 4) Y1Y1 Y12Y12 Y2Y2 Y22Y22 Y3Y3 Y32Y32 Y4Y4 Y42Y  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= Y 3 = SSW3= Y 4 = SSW4= 42.75

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 Y42Y

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 Y42Y

Step 4: Create ANOVA Source Table SourceSSdfMSF Between Within Total

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