Guilford County Schools

Transcription

1 Guilford County Schools First report of two: General observations regarding changes in student population and related demographics This report is based on two primary data sources. 1) The 2000 Census with estimated values for all years through 2009 plus projections for 2013 and These estimates were prepared by one of the world s leading demographic data companies: GeoLytics Inc., East Brunswick, NJ. The present author has used this company for other population and business estimates and has concluded that they hold themselves to a high standard of accuracy and service. 2) The second source is the actual enrollments as provided by Guilford County Schools, 2000 through There are 250 census blocks in Guilford County. All analyses reported below are based on census blocks or their aggregation to the county level. The alpha level for tests of significance was held constant at.05 Projected growth The data suggest that the period of rapid student growth which the county has experienced is slowing down and will taper off to near level. This flattening of growth will happen in the next year or two at the elementary level and then, a few years later, as the student population bubble moves through the grades, the same leveling will be experienced first within middle schools and then within high schools. However these observations pertain to the school system as a totality, and not to individual areas (block groups). The difference in areas is the subject of the second of two reports. Declining correlation between household income and student population: the first indicator of the declining wealth of families that have children in the public schools. The trend away from wealthier families having more children in the schools than poorer families was tested by taking sample years, as follows: Sample year 2001: The correlation between household (HH) Income and population age 6 17 is positive and significant. r = +.22 That is to say, there was, in 2001, a noticeable and significant relationship between the number of students per household and household income. Sample year 2004: The correlation between HH Income and population age 6 17 is weakening, but is still positive and significant. The correlation has declined to r = +.18 Sample year 2007: The correlation between HH Income and population age 6 17 is continuing to grow weaker, but is still positive and significant. r = +.13 Sample (current) year: 2009 Correlation between HH Income and population age 6 17 is continuing to grow weaker, and is no longer significant. r = +.11 Said differently, there is a reasonably probability that the relationship could be zero. Sample year: 2014 based on data estimates prepared by GeoLytics. Correlation drops to near zero. 1

2 The trend detailed above is fascinating if for no other reason than that is it such a steady, consistent movement. Ten years ago, the wealthier the average household within a census block, the more 6 17 year olds would be resident in that neighborhood. As time goes by, this become less and less true until eventually this correlation disappears. This trend would suggest that the population aged 6 17 has become poorer (i.e., are from homes with less income). Increasing negative correlation between household income and rate of change in block group population: a second indicator of the declining wealth of families. Sample year 2001: Correlation between HH Income and rate of population change is near zero but negative (inverse) Sample year 2004: Correlation between HH Income and rate of population change is negative (inverse) but is not significant. r =.12 Sample year 2007: Correlation between HH Income and rate of population change is continuing to grow stronger, and continues to be inverse. It is now significant. r =.15 That is to say that as HH income goes up, rate of growth in population goes down. This might be expected based on the first set of observations, but what is important here is that the student population is going up in the school system as a whole. Those increases are distributed in such a way as to be concentrated in the block groups with the lowest income and this change is happening at an accelerating rate.. Sample (current) year: 2009 Correlation between HH Income and rate of population change is consistent with the prior sample. r =.15 Sample year 2014 based on data by GeoLytics: r =.16 In the meantime, the 6 17 population grew by an average of 684 each year over the past eight years. In the same period, the average HH income of about $53,000 declined slightly in terms of constant dollars. If those income figures were adjusted for the time value of money and for inflation, HH income went down substantially since This declining income is aggravated by the fact that it is an average (an arithmetic mean) and that the wealthier census blocks are far wealthier than the mean, by a factor of five. The distribution has become increasing skewed. The only way the mean HH income can stay the same or decline slightly with growing wealth in a few areas is by a substantial increase in the number of low income households. We know from the above analysis that as income goes down, the change in population goes up, and that as income goes up, the tendency to have 6 17 year olds in the household is going down. Thus, it is reasonable to conclude that the 6 17 population is both growing and getting poorer. The charts on the next page illustrate the persistent skew in income distribution: The top bar covers the entire range of household incomes showing one vertical tick for each of 250 block groups. The width of the bar ranges from zero on the left to $280,000 on the right. Neither of these end points are based on data but were set by the statistical analysis program so that all data points could be included 2

3 within the bar. The first and last vertical tick within the bar represents the block groups with the lowest (near $9,000) and highest (about $240,000) average household income. The second chart is called a box and whisker plot. The vertical tick at each end represents the block groups with the lowest and highest average household income. The blue box represents the middle 50%; thatt is, it starts on the left at the 25 tht percentile and stops on the right at the 75th percentile. The vertical tick within the box represents the median or 50 th percentile. Year 2001 (top) and Year 2014 (bottom) There are several notable features of the two sets of charts above. There is no apparent shift in median HH income from 2001 to 2014 (but, in fact, it is going down slightly), but compared to 2001 there are more data points in 2014 at the very low end of the scale. Second, the long tail to the right (which indicates skew) is very prominent in both sets of charts. Thus the reported mean (average) HH income of about $53,000 is not representative of the nature of the block groups within the county. This mean is greatly inflated by the very high income of relatively few block groups. When there is positive or rightward skew, the mode (most common income in this case) always falls to the left of the mean, and the median (50 th percentile or the middle income in this case) falls between the mode and the mean. In a normal distribution, or even in any distribution that has a single mode and is symmetrical, the value of the mode, the median and the mean are alike. Thus, thee divergence of these three measures tells us in very practical terms how skewed this distribution is. For 2001: Mean = Median = Mode = For 2014: Mean = Median = Mode = $53,120 $46,220 $41,583 $52,986 $45,281 $40,650 The average HH income across all block groups The HHH income of the block group that standss in the middle The most common HH income. This is the HHH income thatt the most people are experiencing. The average HH income across all block groups The HHH income of the block group that standss in the middle The most common HH income. This is the HHH income thatt the most people will experience. As noted earlier, the school age population is agingg out. This trend is illustrated in figures 1 and 2, which show a flatteningg graph of elementary age students and a slowing growth of students system wide. 3

4 Figure 1 Census/Enrollment Projections, K 5 4

5 Figure 2 Census/Enrollment Projections, K 12 Technical note on how the projections were made: Using an advanced statistical analysis program, we searched a large number of mathematical models looking for the formula that best fits the Guilford County data, both with respect to census estimates and actual school enrollments. We were committed to finding the single best model; we rejected the concept of using a different model for each of the four analyses (census elementary, actual elementary, census system wide and actual system wide). By best fit we mean the curve of that mathematical formula that generates the smallest sum of squared residuals as evidenced by the curvilinear regression coefficient ξ, which for the sake of simplicity we call r. We were fortunate to find such a model: one that yielded r values of.993,.982,.997 and.997 respectively. These are remarkably high correlations and provide considerablee confidence in the fit, although they do nothing to correct for any errors in the underlying data. The selected model is known as the Multiple Multiplicative Factor Model (MMF). It is described by Benjamin Marlin and Richard Zemel in an abstractt of their paper entitled The Multiple Multiplicative Factor Model.... Marlin and Zemel are faculty members at thee University of Toronto. They write: We present a discrete latent variable model called the MMF model [which]has natural generative semantics for data where multiple factors may influence each element of a data vector. A data vector is represented in the 5

6 latent space as a vector of factors that have discrete, non negative expression levels. The distribution over values for a data element is a product of each factor's prediction for that element, taking into account the degree to which the factor is expressed. The latent, discrete factor vectors, and multiplicative generative semantics of the MMF model make it distinct from other generative latent variable models such as factor analysis, latent Dirichlet allocation, and the mixture of multinomials model. We present empirical results from the collaborative filtering domain showing that a binary/multinomial MMF model outperforms a wide range of other rating prediction methods on two data sets. Our statistical programs (Statgraphics Centurion, Version XV, StatPoint Inc., Herndon, VA and CurveExpert 1.38, by Daniel Hymes, Microsoft Corp.) indicate that the MMF model used the following formula (curve) to fit the Guilford County historic census and enrollment data: y = (ab + cx d ) / ( b + x d ) where, for our data set: a = b = c = d = 2.58 This is a six page report sent to ORED/ITRE on November 30, A second report, to be submitted prior to December 13, 2009 will include a recommended allocation of gain percentage based on elementary school boundaries for the Guilford County Schools. Raymond G. Taylor Commercial Services Corp, a Maine Corporation [Edited for presentation by OREd, 1/11/11.] 6

7 Guilford County Schools Second report of two: Procedure used to inform Allocation of Gain using demographic data This report is based on three primary data sources. 1) The 2001 to 2007 estimated values for all years based on the 2000 census, plus sampling and public data gathered each year since that census. 2) 2008 estimates based on the same methodology plus projections for the year ) 2009 estimates based on the same methodology plus projections for the year These estimates were prepared by one of the world s leading demographic data companies: GeoLytics Inc., East Brunswick, NJ. This company provides demographic data to the Urban Institute, the Brookings Institute and a large number of universities and research facilities, including the University of North Carolina at Chapel Hill. Procedure followed. The first step, curvilinear regression: Using a curvilinear regression analysis, as cited in our first report, we combed through various demographic indicators to find any that had a high independent correlation with the estimated school age population. All other population count variables (such as total population, population by age, by race, by gender) were eliminated to reduce the likelihood of co linearity. The two variables that emerged were rate of population change and household income. The relationship and the trends in relationship between these variables and school age population is striking and was explained and graphed in the first report. The second step, building a data set that could be used for making a five year projection: Planning segments, as provided by the OR/Ed laboratory on behalf of the Guilford County Schools, were combined to form 2009 elementary school boundaries. These boundaries were then labeled and printed to acetate in large format. The three sources of data provided by GeoLytics were then combined and stripped to isolate school age population and household income for each year 2001 through Thus the final table included 250 block group segments. For each segment a projection for 2010 through 2014 was made using the mathematical model discussed in the first report. The starting value (2009) for each of these 250 rows was subtracted from the ending value (2014). These differences were then divided into seven ranges as follows: loss of more than 39 students per block group over a five year period, a loss of 13 to 35, a loss of 6 to 12, a loss of 5 to a gain of 3, a gain of 4 to 17, a gain of 18 to 38, and a gain of over 38. The lack of symmetry in these ranges is due to the lack of symmetry in the overall distribution, which was discussed briefly in the first report as it related to income and school age population. The third step. Re-configuring the block group projections to elementary school boundaries: This was a tedious and error prone process; thus it was done twice and reviewed twice. The block group gains and losses were color coded and printed in large format on opaque bond in seven colors that represented the seven ranges. The acetate boundaries for the elementary schools were then laid over the colored block group map. For each elementary school, a judgment was made as to what proportion of each block group color was captured within that school s boundary. Many were obvious (only one to three colors were captured) while others had to be measured and reasoned (some had as many as six out of seven colors). A large table was built with columns for school name, plus each of the 1

8 seven colors, plus additional columns for statistical computations. In the body of this table appears the proportion of each color for each school boundary with a check sum for Total = by school. The fourth step. Computing the Allocation of Gain based on demographics For each school and each block group color, the proportion was weighted by the mid value of the color range. This resulted in the expected number of students that each school might gain or lose over a fiveyear period based on demographic data alone. These gains and losses were then changed into a proportion of the total. [See Table 1.] Observations: 1) The correlation between school age population and income was not used directly in making the projections. Rather it was used as a check on both the projections and the observed correlation. In almost all cases, areas that were strongly in the upper income range (for example, in the North West) showed losses in school age population, and those in the lowest income range showed the largest gain. But this was not uniformly true. Further, in some of the small downtown boundaries, where several block groups converged with differing colors, there was no practical way to check the population change to income hypothesis. 2) Secondly, to the best of my knowledge, this is the first time that a census based demographic approach to informing the Allocation of Gain decisions within an IPSAC project has been attempted. Certainly it will provide another layer of information, but its usefulness will depend on how well it converges with other information (such as land use interviews and projections made solely on past enrollments. 3) Although the present author believes that the demographic data purchased for this study is more reliable and accurate than many other available sources, it is, after all, estimated from a census that is nearing the end of its shelf life as an instrument of projection. The next census is to be taken in 2010 and the release of that information will appear in A reality check on the annual estimates will then be possible. The good news is that the company that provided the data made estimates for the years from 1980 census data, and repeated the same process the following decade. In the meantime, they have earned an excellent reputation, so there is good reason to trust their work for Raymond G. Taylor Commercial Services Corp, a Maine Corporation December 3, 2009 [Edited for presentation by OREd, 1/11/11.] 2

9 Table 1 Census Based AOG, Elem Resolution 3