Ecological Data Variables

The reference table below will serve as the list of variables for the figures represented in correlation analysis. Please reference this table as needed to identify variables across those figures.

Variable List and Source for Ecological Analysis, 2001-2022
Variable	Description	Measure Level¹	Data Source
d_seg_ne_wb	White/Black Normalized Exposure Index	District	Stanford Education Opportunity
p_bl	Percent Black	School	NCES
p_hisp	Pecent Hispanic/Latin@	School	NCES
p_wh	Percent white	School	NCES
p_frl	Percent free/reduced lunch	School	NCES
p_tch_not_new	Percent FTE's that are not new teachers	School	PELSB
p_exp6_plus	Percent of FTE's with 6 or more years of experience	School	PELSB
p_tch_grad	Percent of FTE's with a graduate degree (MA, PhD)	School	PELSB
avg_exp	Average years of teacher experience	School	PELSB
p_stu_grd	Percent of students that graduate in four years??	School	MDE
p_stu_drpout	Percent of students that drop out after four years??	School	MDE
p_me_m3	Percent of students that meet or exceed 3rd grade MCA math scores	School	MDE
p_me_r3	Percent of students that meet or exceed 3rd grade MCA reading scores	School	MDE
p_me_m7	Percent of students that meet or exceed 7th grade MCA math scores	School	MDE
p_me_r7	Percent of students that meet or exceed 7th grade MCA reading scores	School	MDE
p_me_m11	Percent of students that meet or exceed 11th grade MCA math scores	School	MDE
p_me_r10	Percent of students that meet or exceed 10th grade MCA reading scores	School	MDE
¹ Most variables are at the school level, except for the district-level segregation indices.

Table 1: Variable list for correlation matrices

Distributions of Ecological Variables

The figures below are show the distribution of the variables used in the correlation matrices. Most of the annual distributions are similar and thus we only present the distributions for one year. They are stratified by level of school as not every variable is applicable to all levels (i.e. 3rd grade MCA scores only apply to elementary/primary schools). Only schools across the Twin Cities metro with at least 50 students are represented.

Figure 1: Distribution of Ecological Variables for Twin Cities Metro Schools, 2018. Most of these variables represent proportions, with the exception of the district-level normalized exposure index (d_seg_ne_wb). This index is still represented on a 0-1 scale, with lower numbers indicating less segregation and more numbers indicating more segregation (See the Segregation Indices tab for more information).

Figure 2: Distribution of Average Teacher Experience for Twin Cities Metro Schools, 2018.

Cross-Sectional Correlation Matrices

Elementary Schools

Note

The correlation matrix below shows elementary schools in the Twin Cities metro area with at least 50 students. Some of the PELSB measures are not available in 2003 so they were removed from the analysis for those years.

Figure 3: Correlations for Twin Cities Elementary Schools, 2021.

See Table 1 for the list of variables.

We can also look at Figure 7 to see the trends over time.

Middle Schools

Note

The correlation matrix below shows middle schools in the Twin Cities metro area with at least 50 students. Some of the PELSB measures are not available in 2003 so they were removed from the analysis for those years.

Figure 4: Correlations Across Metro Midle Schools, 2021.

See Table 1 for the list of variables.

We can also look at Figure 8 to see the trends over time.

High Schools

Note

The correlation matrix below shows high schools in the Twin Cities metro area with at least 50 students. Some of the PELSB measures are not available in 2003 so they were removed from the analysis for those years.

Figure 5: Correlations Across Metro High Schools, 2021.

See Table 1 for the list of variables.

We can also look at Figure 9 to see the trends over time.

Correlations Over Time

Note

The figure below is an example of the plots we will use to understand the correlation trends over time. Please refer to this chart and the interpretation as needed.

Figure 6: Correlations Between District-Level Normalized Epxosure Segregation and Ecological Variables, 2001-2021.

See Table 1 for the list of variables.

Interpreting figure above correctly can certainly be a challenge. For the most part, if you see lines with an upward trajectory, that is good. Since most of the variables are coded so that higher percentages are better (with the exception of percent of students that are on free or reduced lunch), we would want to see a correlation getting stronger in a positive direction (away from 0), or weaker from a negative direction (towards 0), between the faceted variable of interest (d_seg_ne_wb in this example) and the outcome variable plotted. This is unfortunately the case for most variables except the one being shown above, where the higher the d_seg_ne_wb raw score, the more segregated districts are.

The expectations of what we would see between segregation indices and various outcomes is biased by what prior literature has shown. Given the fundamental challenges in adequately funding public schools equitably across the TC metro area, which would lead to staff retention difficulties, we would expect to see a negative correlation between White-Black normalized exposure index (d_seg_ne_wb) and average years of teacher experience (avg_exp). As segregation increases, we should see the average years of teacher experience decrease, producing a negative correlation. This is exactly why a temporal analysis is helpful. As we can see, in 2006 the correlation was actually positive (albeit weak), indicating that as segregation increased, we saw a general trend of increased average teacher experience. However, as time goes one, this positive correlation gets weaker and eventually becomes a negative correlation by 2016, gaining in strength through 2021 (lagged effect?).

Elementary Schools

Note

The figure below represents the pearson correlation coefficient between the faceted variable (i.e. the variable at the top of each chart) and the variable for each colored line. Every variable is not available across all years.

Figure 7: Correlations over time for TC Metro Elementary Schools, 2001-2022.

See Table 1 for a list of variables.

Middle Schools

Note

The figure below represents the pearson correlation coefficient between the faceted variable (i.e. the variable at the top of each chart) and the variable for each colored line. Every variable is not available across all years.

Figure 8: Correlations over time for TC Metro Middle Schools, 2001-2022.

See Table 1 for the list of variables.

High Schools

Note

The figure below represents the pearson correlation coefficient between the faceted variable (i.e. the variable at the top of each chart) and the variable for each colored line. Every variable is not available across all years.

Figure 9: Correlations over time for TC Metro High Schools, 2001-2022.

See Table 1 for the list of variables.

In 2022, the typical (measured as a mean) Black child goes to a school that has X% free reduced lunch, and Y years of average teacher experience. In contrast, the typical white child goes to a school that has X% free reduced lunch, and Y years of average teacher experience.

How do you conceptualize “typical”? Did you just take the population weighted mean?

Do more segregated schools have teachers with less experience or education?

MCA/Testing