Quantitative Reasoning
Paper 3
An Issue of Inequality
Douglas Massey and Nancy Denton wrote in American Apartheid that: “Residential segregation has become the forgotten factor of American race relations, a minor footnote in the ongoing debate on the urban underclass”[1]. Because we are living in the post-Civil-Rights-era, the issue of residential segregation tends to be sorely overlooked, or relegated to a position in the distant past. In fact, it is still alive, even in a state labeled as progressive, such as Massachusetts.
There is a theory that this residential concentration is a crucial factor in the reproduction of racial and ethnic inequality in the contemporary United States. I do not have the access to the appropriate resources to fully address this theory. However, using Massachusetts 2000 Census Data, I wish to address the inequality of conditions in the racially divided Massachusetts census tracts as a small-scale example of this inequality. The data I used was taken from the one in six sample of the 2000 census at the tract level. The tract is defined as; “small, (1,500-8,000 people) relatively permanent statistical subdivisions of a county or equivalent entity[ies]…”[2]. These divisions, being small and permanent, provide stable units of measurement.
The two conditions I wish to address are the poverty of the census tracts with a high percent black population and the markedly high percentage of census tracts with a high white population and a high percentage of residents holding a graduate degree. By looking at these conditions, I wish to suggest the poverty of the predominantly black census tracts is connected to the lack of predominantly black tracts with a high percentage of residents with graduate degrees. Conversely, this implies that the predominantly white Massachusetts census tracts have a relatively low poverty level and a higher percentage of residents with graduate degrees.
To support my argument, I created two tables using the variables of; percent of the population of Massachusetts census tracts who are black; percent of the population of Massachusetts census tracts who are white; percent of the population of Massachusetts census tracts with a graduate degree; and the percent of Massachusetts census tracts at or below the poverty line according to the 1999 income level. I also constructed three charts (histograms) to aid me in recoding these variables. Furthermore, Chart 2, which illustrates the distribution of the percent of white residents in Massachusetts census tracts, helps support the assumption I wish to make; that is, the Massachusetts census tracts identified as having a low percent black population were almost certainly predominantly white. This assumption helps to illustrate the inequality between the predominantly white census tracts and the ones dominated by minority races (nonwhites).
Given this assumption and the evidence I will present, I feel the disparity between the predominantly white census tracts and those dominated by minorities, the example here being blacks, is evident through the inequalities in the poverty level of the census tracts in relation to the racial makeup, as well as the percent of residents in census tracts who hold a graduate degree, suggesting a disparity in educational opportunities, as well.
The first variable I chose to work with was the percent of the population of
the Massachusetts census tracts who were black according to the 2000 census. I used Chart 1 to help me recode this variable. Chart 1 illustrates the distribution of the percent black population in the Massachusetts census tracts. A strong clustering at the low end of the histogram can be seen, with most tracts having a population of blacks between 0 and 5 percent. The mean is 5.9% and the median, which is not listed, is around 7%. I chose to divide the variable between low and medium at 10%, however, because there was a significant concentration between 0 and 10%. I felt this division best represented the overall concentration of blacks in Massachusetts census tracts; most tracts have a low percentage of blacks, and I felt this break between low and medium at 10% best illustrated this. I used the range of 10-25% for the medium category, as it can be observed there are still significant enough number of tracts in this range to justify it as a category. I used 25% as the breaking value for the high percent black category. In the histogram, the number of tracts with 25% or more blacks is very low and decreases. Furthermore, I felt this represented the spread very well, especially since proportionally, 25% is a very high number of blacks.
I used the variable of the percent of the population of Massachusetts census tracts reporting themselves as white, as well. It provided a contrast to the variable of the percent of black residents in Massachusetts census tracts. Chart 2 aided me in my recoding of the white population. In stark contrast to Chart 1, Chart 2 is skewed negatively, with most of the values falling well above 50%, meaning most census tracts have 50% or more white residents. The mean of 83% further attests to the high concentration of whites. I chose to set the lowest range at 0-70%, reflecting the high proportion of whites in Massachusetts census tracts. I set the medium range at 70-91%, a further reflection of the spread of the white population within Massachusetts tracts. I set the high category for white population at 91% and above, where the number of tracts decreases from the middle range. These different recodings for the races illustrate the whiteness of the Massachusetts census tracts in general; the medium category for the percent white variable is the high category for the percent black, illustrating a disparity between the concentration of these races.
The next variable I chose was the percent of residents in Massachusetts census tracts with a graduate education. Chart 3 illustrates the spread of the percent of the population with graduate degrees within the census tracts. Most of the tracts have between 5 and 10% of the population holding graduate degrees. Based upon this observation, I set the low category at 0-5%. I set the middle category at 5-10%, representing a majority of the tracts. After observing the median of 8.5%, I felt that any tract where 10% of the population or more had a graduate degree was proportionally high, and set 10% as the break for the highest range. Furthermore, setting the break at 10% would include enough tracts to illustrate the relationship between the percent of whites in the census tracts and the percent of residents holding a graduate degree.
The last variable I used was the percent of people in Massachusetts census tracts with 1999 income at or below the poverty level. Chart 4, illustrating the spread of the poverty level within Massachusetts census tracts, helped me decide how to recode the variable. I noticed most of the census tracts fell within the 0-10%, however, there was still a significant spread above 10%, which I felt said something about the poverty level in the tracts. I set the medium range at 10-25%, observing a number of tracts still in this range. To emphasize the height of the poverty level I observed, I set the high range at 25% and above. These breaks, I felt, would emphasize high levels of poverty, which I observed. While the number of tracts does decline after 10%, I observed enough tracts falling within the higher ranges to justify using these high ranges. Furthermore, I felt these breaks would emphasize an association between the percent black in a census tract and the poverty level.
To illustrate the inequality of the living conditions of blacks and whites, I looked at the relationship between the percent black in the census tracts and the poverty level of the census tracts, and the percent white in the census tracts and the percent of residents in the census tracts holding a graduate degree. My findings were hardly surprising after observing the overall spread of the populations in the charts; the disparity between the spread of the percent black and white in Massachusetts census tracts was unequal suggested a strong possibility of inequality in favor of the majority.
I constructed Table 1 using the recoded variables of percent of blacks in Massachusetts census tracts and the poverty level of the census tracts according to the 1999 income level. I observed an overall positive relationship between the percent black population in Massachusetts census tracts and the poverty level of the tracts; as the percent of blacks in the tracts increased, the poverty level did, too. An example of this relationship can be observed in the high poverty level column. Of the 1171 census tracts with a low concentration of blacks (0-10%), only 6.7% had a poverty level of 25% or more. Moving down the column, the percent of tracts falling within the highest category of poverty level increases sharply. Of the 109 census tracts with 10-25% blacks, 32.1% had a poverty level of 25% or higher, a sharp increase from the low percent black category. The percent of census tracts with a poverty level above 25% increased even further in the tracts with 25% or more blacks, to 42.1%. This further increase is quite chilling, as a poverty level above 25% is very high. The pattern in this column suggests the black population lives in census tracts with very high poverty levels. A further look at the chart shows a majority of the tracts are concentrated in the low percent black and low percent poverty level. In fact, of the 1171 census tracts with a population of blacks falling in the 0-10% category, 74.2% fell within the low poverty level category. Considering the overall high percentage of whites in Massachusetts census tracts, as observed in Chart 2, it is highly probable that the people who are not black in this table are white. What these figures suggest is my research hypothesis; that there is a positive relationship between the percent black population in Massachusetts census tracts and the poverty level of the tracts. The null hypothesis for this table is that there is no relationship between the percent of blacks in the Massachusetts census tracts and the poverty level of the tracts; any observed relationship occurred by chance.
To test the null hypothesis’ accuracy, I conducted a chi-square test using SPSS. The chi-square test is a test of probability; it tells how likely it is that an association between two variables in a given table occurred by chance. The chi-square value is calculated by SPSS and appears as the “Pearson Chi-Square” in the box below Table 1. The value of 280.917 is the observed chi-square value for a table with this many degrees of freedom (df), or 4. The degrees of freedom are calculated by the computer here, but can be done so by hand, simply by subtracting one from the number of rows and columns, then multiplying those two quantities together. The third column in the Chi-Square test box is the level of statistical significance. This was set before I conducted the chi-square test, at .05, or 5%. This means that if the probability of the observed chi-square value occurring by chance is less than 5% (or .05), the null hypothesis can be rejected. If the level of statistical significance is higher than .05, then the null hypothesis has to be accepted. To find the expected chi-square value for a table with this many degrees of freedom set at this level of statistical significance, a distribution chart is necessary. The table has the degrees of freedom in the columns and various statistical significance levels across the rows. To find the expected chi-square value, I first located the degrees of freedom (4), and moved across the row until I came to the .05 statistical significance level column. The expected value of 9.488 is much lower than the observed value of 280.917. This suggests a strong association between the variables of percent black population in Massachusetts census tracts and the poverty level of the tracts. The larger the difference is between the observed and expected chi-square values, the stronger the association between the variables. Furthermore, the observed level of statistical significance is .000, meaning the chances of the high observed chi-square value occurring by chance are less than one in ten thousand, in short, very small, indeed. More significantly, it is lower than the set level of .05. On these grounds, the null hypothesis can be rejected. There is an association between the percent black population in Massachusetts census tracts and the poverty level of the tracts. The percent of tracts with a high poverty level have a higher black population, as well. This suggests that blacks are concentrated into areas of poverty, a mark of inequality. This can further be substantiated by saying, conversely, that whites are concentrated into areas of lower poverty; there is a very high likelihood that the population in the tracts with a low percent black population are white, considering the overall predominance of whites in Massachusetts census tracts, as illustrated by Chart 2.
Table 2 further illustrates an inequality between whites and minority groups. It illustrates the relationship between the percent of whites in Massachusetts census tracts and the percent of people within the tracts holding a graduate degree. I chose to observe the percent of people in the census tracts holding a graduate degree because it is well above the average level of education and was more likely to illustrate an observable pattern. The overall pattern I observed was once again positive; the higher the white population in the census tracts, the higher the percent of people in the tracts with a graduate degree. This overall pattern is quite apparent in the highest percentage of people within the census tracts with a graduate education. Of the 247 Massachusetts census tracts with a low (0-70%) percent white population, 18.6% fell into the lowest percent category of people holding graduate degrees; this is a strong contrast to the 61.1% of tracts with a low white population and low percentage of people with a graduate degree. Furthermore, moving down the column of 10% or more people in the tracts holding a graduate degree, the percent of tracts increases as the percent of whites does, as well. There is a huge increase from the low percent white census tracts to the medium one, from 18.6% to 47.5%, and another, smaller one, between the medium and high percent white census tracts, to 49.5%. This means that in almost half of the census tracts with a white population of 91% or more, 10% or more hold a graduate degree. This is significant because this further supports the inequality between whites and minority groups. My research hypothesis for this table is that there is a direct relationship between the percentage of whites in the census tracts and the percent of people in the tracts holding a graduate degree. The null hypothesis for this table is that there is no relationship between the percent of whites in the census tracts and the percent of people in the tracts holding a graduate degree; any observed relationship is the result of chance.
Once again, I used the chi-square test to see whether the null hypothesis was valid. The observed chi-square value for Table 2 is 212.180. The degrees of freedom for the table are 4 and the statistical significance level was set once again at .05. Looking at the Distribution of Chi-Square table, I noticed the expected chi-square value of 9.488 was very low in comparison to my observed value of 212.180, suggesting a strong association between the two variables. This association was further established when I noticed the level of statistical significance for Table 2 was .000, meaning the likelihood of the high observed chi-square value of 212.180 occurring by chance was less than one in ten thousand. As in Table 1, the chi-square test allowed me to reject the null hypothesis on the basis that the likelihood of my high observed chi-square value occurring by chance was extremely small, smaller than the set level of statistical significance. This allowed me to state, with some degree of certainty, that there is an association between the percent white population in the census tracts and the percent of the people in the census tracts with a graduate education. The tracts with a higher percent white population had a higher percent of people holding a graduate degree, while the tracts with a low percent white population had a lower percent of people with graduate degrees.
This suggests that the tracts with a higher percent white population consist of higher educated individuals, which could possibly be the result of more opportunities for white residents of the census tracts as opposed to minorities, blacks included. It also could reflect the difference in the quality of education and expectations of the predominantly white census tracts. With more research, the claim of Douglas Massey and Nancy Denton, that: “…The isolation and intense poverty of the ghetto provides a supportive structural niche for the emergence of an ‘oppositional culture’ that inverts the values of middle-class society…young people in the ghetto experience strong peer pressure not to succeed in school, which severely limits their prospects for social mobility in the larger society,”[3] could further be supported. This claim serves to bring the findings of Tables 1 and 2 together. It is possible that the overall high white concentration of the Massachusetts census tracts, which Chart 2 illustrates, contributes to the poverty of the more highly populated black census tracts observed in Table 1. This concentration of the black population in poverty could lead to a major inequality in education, as observed in Table 2, where the more predominantly white census tracts had a higher percentage of people with graduate degrees. While these tables do provide possible support for Massey and Denton’s claim, more research would have to be conducted, namely among other nonwhite minority groups in Massachusetts census tracts, to see what the pattern is for census tracts with various groups as the dominant one. However, these tables do make the inequality of conditions for black and white residents in Massachusetts census tracts shockingly clear; the more predominantly white a tract, the less poverty and the higher the level of education of the residents. In order to substantiate the claim for reproduction of inequalities, census data from past decades would have to be compared to the 2000 Massachusetts census data used here. However, the data in this study shows the present conditions are quite bleak from the standpoint of racial equality, at least in Massachusetts.
Chart 1: Distribution of Blacks in MA
Census Tracts
Chart 2: Distribution of White Population
in MA Census Tracts
Chart 3: Distribution of Residents in MA
Census Tracts with Graduate Education
Chart 4: Distribution of Poverty Level for
MA Census Tracts
