Question

Steel Town has three neighborhoods with the following demographics: a. Calculate the dissimilarity index between high-income Black and high-income White households. b. Calculate the dissimilarity index between low-income Black and high-income White households. c. Calculate the dissimilarity index between low- and high-income households. d. Calculate the dissimilarity index between Black and White households. e. Between (a) and (b), which dissimilarity index is higher? What is the intuition behind this difference?

Answer 1

To calculate the dissimilarity index, compare the percentages of different household types in each neighborhood and follow the steps provided. The dissimilarity index between high-income Black and high-income White households is likely higher than the dissimilarity index between low-income Black and high-income White households. This is due to the possibility of residential segregation based on income and racial factors.

Step-by-step explanation:

a. Calculate the dissimilarity index between high-income Black and high-income White households.

To calculate the dissimilarity index, you need to compare the percentage of high-income Black households in each neighborhood with the percentage of high-income White households in each neighborhood.

1. Calculate the percentage of high-income Black households in each neighborhood by dividing the number of high-income Black households by the total number of households in each neighborhood.
2. Calculate the percentage of high-income White households in each neighborhood by dividing the number of high-income White households by the total number of households in each neighborhood.
3. Subtract the percentage of high-income White households from the percentage of high-income Black households in each neighborhood.
4. Take the absolute value of the difference.
5. Add up the absolute differences for all neighborhoods.
6. Divide the sum by 2 to get the dissimilarity index.

b. Calculate the dissimilarity index between low-income Black and high-income White households.

To calculate the dissimilarity index, you need to compare the percentage of low-income Black households in each neighborhood with the percentage of high-income White households in each neighborhood.

1. Calculate the percentage of low-income Black households in each neighborhood by dividing the number of low-income Black households by the total number of households in each neighborhood.
2. Calculate the percentage of high-income White households in each neighborhood by dividing the number of high-income White households by the total number of households in each neighborhood.
3. Subtract the percentage of high-income White households from the percentage of low-income Black households in each neighborhood.
4. Take the absolute value of the difference.
5. Add up the absolute differences for all neighborhoods.
6. Divide the sum by 2 to get the dissimilarity index.

c. Calculate the dissimilarity index between low- and high-income households.

To calculate the dissimilarity index, you need to compare the percentage of low-income households in each neighborhood with the percentage of high-income households in each neighborhood.

1. Calculate the percentage of low-income households in each neighborhood by dividing the number of low-income households by the total number of households in each neighborhood.
2. Calculate the percentage of high-income households in each neighborhood by dividing the number of high-income households by the total number of households in each neighborhood.
3. Subtract the percentage of high-income households from the percentage of low-income households in each neighborhood.
4. Take the absolute value of the difference.
5. Add up the absolute differences for all neighborhoods.
6. Divide the sum by 2 to get the dissimilarity index.

d. Calculate the dissimilarity index between Black and White households.

To calculate the dissimilarity index, you need to compare the percentage of Black households in each neighborhood with the percentage of White households in each neighborhood.

1. Calculate the percentage of Black households in each neighborhood by dividing the number of Black households by the total number of households in each neighborhood.
2. Calculate the percentage of White households in each neighborhood by dividing the number of White households by the total number of households in each neighborhood.
3. Subtract the percentage of White households from the percentage of Black households in each neighborhood.
4. Take the absolute value of the difference.
5. Add up the absolute differences for all neighborhoods.
6. Divide the sum by 2 to get the dissimilarity index.

e. Between (a) and (b), which dissimilarity index is higher? What is the intuition behind this difference?

The dissimilarity index between high-income Black and high-income White households is likely to be higher than the dissimilarity index between low-income Black and high-income White households. This is because high-income households of different races are less likely to live in the same neighborhoods compared to low-income households. High-income households have more choices and can afford to live in neighborhoods that suit their preferences and needs, which can contribute to residential segregation.