Question

3. Studies of the degree of residential segregation between blacks and whites use the segregation index, defined as 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 nonwhites living in each block is the same for all blocks in the city. This index can assume values ranging from 0 to 100, with higher values indicating greater segregation (the national average was 65 in 1990 and 59 in 2000). The table below shows Census 2000 data for a random sample of states. (NOTE: I could give you data for all of the states, but then you would only need descriptive statistics. I used a random sample to give you an opportunity to use inferential statistics.) Is racial segregation the same across regions of the county or is it different? If it is different, where is the difference and how meaningful is the difference? Use an ANOVA, follow-up procedures (if necessary), and effect size to answer these research questions. (Make sure to check the assumptions.) Use a significance level of 0.05. Use SPSS for the analysis.

Northeast South Midwest West

New Jersey: 70 Alabama: 60 North Dakota: 54 New Mexico: 40

Pennsylvania: 75 Tennessee: 69 Michigan: 80 Alaska: 51

Rhode Island: 62 West Virginia: 59 Nebraska: 70 Hawaii: 52

Maine: 42 Virginia: 52 Minnesota: 64 Washington:55

New York: 80 Georgia: 57 Kansas: 60 Wyoming: 54

Vermont: 35 North Carolina: 51 Illinois: 78 Idaho: 42

Massachusetts: 64 Louisiana: 58 Wisconsin: 81 Arizona: 46

Answer 1

ANOVA one way with Post Hoc Test by using SPSS

Step 1: Enter the data in SPSS

*Untitled1 [DataSet0] - IBM SPSS Statistics Data Edito File Edit View Data Transform Analyze ion Index 70 75 62 42 80 35 64 60 69 59 64 60 51 58 Northeast Northeast Northeast Northeast Northeast Northeast Northeast South 10 South 12 13 14. 15 16 17 South Midwest Midwest Midwest Midwest Midwest Midwest Midwest West West 80 70 64 60 78 81 40 51 19 20 21 23

Step: 2 Inspecting the data Post Hoc Tests

Go to Analyse --> General Linear Model --> Univariate ,

A table will open and Dependent variable --> Index and in Fixed Factors --> Region

Now select post hoc in right side and select Region , then slect TUKEY for analysis

Again select options button and select Estimates of Effect size and Homogenity tests. The default value will 5% level of significance

PRESS continue the following shows the output.

Univariate Analysis of Variance Between-Subjects Factors Region Midwest West Levene's Test of Equality of Error Dependent Variable Index Tests the null hypothesis that the error variance of the dependent variable is equal acros groupe a. Design: Interoept Region Tests of Between-Subjects Effects Dependent Variable: Index Type lII Sum Partial Ea Mean Square 4.542 1 100320.571 873.881 4 542 21.420 100320.571 1504 280 521.420 14.708 Corrected Total 4319.429 a. R Squared 382 (Adjusted R Squared- 282) Post Hoc Tests Region Multiple Comparisons Dependent Variable: Index Tukay HSD Difference ( Std. Error S Lower Bound U Midwest Northeast 843 0.43 21.00 843 5.727 5.727 5.727 5727 5.727 6.727 5.727 6.727 5.727 5.727 5.727 .727 24 23 West 006 5.20 38.80 Nartheast Midaest 24.23 7.37 12.57 943 1.00 11.57 -21.00 12.57 11.57 153 3.23 28.37 25.23 8.37 West 209 4.23 27.37 5.20 3.23 4.23 -38.80 28.37 27.37 200 Based on observed means The error term is Mean Square(Error)114.798 The mean differanoe is significant at the.05 leval Homogeneous Subsets Tukey HSD3 48 57 81.14 61.14 69.57 Means for groups in homogeneous subeets are Based on observed means The error term i' Mean Square(Error) 14.709 a. Uses Harmonic Mean Sample Size - 7.000 b. Alpha0

Conclusions based on ANOVA table

In Levene's test the p-value = 0.024 < 0.05 which means we reject the hypothesis of equal variances. The assumption of population variances are equal doesn't meet.

In ANOVA table the p-value for region is 0.012 < 0.05 , which means the value is highly significant. So reject the hypothesis and conclude that the population means are not all equal.

The multiple correlation table shows which means are statistically significant. The * symbol in Multiple correlation table shows Statistically significant difference means.