High School

**Studies of Residential Segregation Between Blacks and Whites Using the Segregation Index**

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.

| Region | State | Segregation Index |
|------------|----------------|-------------------|
| Northeast | New Jersey | 70 |
| | Pennsylvania | 75 |
| | Rhode Island | 62 |
| | Maine | 42 |
| | New York | 80 |
| | Vermont | 35 |
| | Massachusetts | 64 |
| South | Alabama | 60 |
| | Tennessee | 69 |
| | West Virginia | 59 |
| | Virginia | 52 |
| | Georgia | 57 |
| | North Carolina | 51 |
| | Louisiana | 58 |
| Midwest | North Dakota | 54 |
| | Michigan | 80 |
| | Nebraska | 70 |
| | Minnesota | 64 |
| | Kansas | 60 |
| | Illinois | 78 |
| | Wisconsin | 81 |
| West | New Mexico | 40 |
| | Alaska | 51 |
| | Hawaii | 52 |
| | Washington | 55 |
| | Wyoming | 54 |
| | Idaho | 42 |
| | Arizona | 46 |

**Research Questions:**
1. Is racial segregation the same across regions of the county or is it different?
2. 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. Use a significance level of 0.05. Use SPSS for the analysis.

**Tasks:**
a. Is the assumption of normality violated or supported (provide evidence)?
- [If violated, can we continue with the ANOVA? Why or why not?]

b. Is the assumption of homogeneity of variance violated or supported (provide evidence)?
- [If violated, can we continue with the ANOVA? Why or why not?]

c. Is the assumption of an absence of outliers violated or supported (provide evidence)?
- [If violated, can we continue with the ANOVA? Why or why not?]

d. Conduct the ANOVA test (regardless of your conclusions from the assumptions tests) and complete the following interpretation.
- The results of the One-way ANOVA analysis indicate that there (is OR is not) a significant difference among the region segregation index means, [tex]$F = \_\_$[/tex], [tex]$p = \_\_$[/tex]. Moreover, [tex]$\_\_$%[/tex] of the variance in segregation index scores can be explained by the independent variable – region.

e. Given the results of the overall (omnibus) ANOVA, should you examine the post hoc Tukey tests?
- a. No, the overall (omnibus) ANOVA was not significant.
- b. Yes, the overall (omnibus) ANOVA was significant.

f. According to the Tukey tests, which pairwise mean comparisons, if any, are statistically significant? (select all that apply)
- a. The Tukey tests are not necessary.
- b. Northeast - South
- c. Northeast - Midwest
- d. Northeast - West
- e. South - Midwest
- f. South - West
- g. Midwest - West

Answer :

Final answer:

The question aims to analyze racial segregation across regions using ANOVA. The assumptions of normality, homogeneity of variance, and absence of outliers need to be checked. The ANOVA test will determine if there is a significant difference among the region segregation index means. Post hoc Tukey tests can be conducted if the overall ANOVA is significant. The results will provide insights into the extent of racial segregation and the meaningfulness of the differences across regions.

Explanation:

To answer the research questions about racial segregation across regions, an ANOVA test is used. Before conducting the ANOVA test, several assumptions need to be checked.

  1. Assumption of normality: To determine if this assumption is violated or supported, we can examine the distribution of the segregation index scores for each region. If the distributions are approximately bell-shaped (normal), the assumption is supported. If not, the assumption is violated.
  2. Assumption of homogeneity of variance: This assumption can be assessed by comparing the variances of the segregation index scores across regions. If the variances are approximately equal, the assumption is supported. If not, the assumption is violated.
  3. Assumption of absence of outliers: Outliers can significantly affect the results of the ANOVA test. To check this assumption, we can examine boxplots or other graphical methods to identify any extreme values.

After checking these assumptions, we can proceed with the ANOVA test. The results of the ANOVA test will indicate whether there is a significant difference among the region segregation index means. If the overall ANOVA is significant, post hoc Tukey tests can be conducted to determine which pairwise mean comparisons are statistically significant.

Based on the results of the ANOVA test, we can also calculate the effect size, which represents the percentage of variance in segregation index scores explained by the independent variable (region).

Learn more about analyzing racial segregation across regions using anova here:

https://brainly.com/question/30885494

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