Measuring Variations in Private School Enrollment Rates Using ACS Estimates

Measuring Variations in Private School Enrollment Rates Using ACS Estimates Magali Barbieri, Shelley Lapkoff, Jeanne Gobalet Lapkoff & Gobalet Demographic Research, Inc. www.demographers.com May 30, 2014 American Community Survey Users Conference

Private school enrollment rates Affect public school enrollments & enrollment forecasts Vary Over time By race/ethnicity By other (mostly socioeconomic) factors Are not available (at least in California) from administrative records 2

What can we learn about private school enrollment rates from ACS surveys? We studied California K-12 private school enrollment rates, by ethnicity: Using PUMS estimates for Census 2000 PUMAs: ACS 5-year 2007-2011 estimates Several sets of ACS 3-year estimates: 2006-08, 2008-10, 2009-11 Aggregating PUMAs to the county level (or counties to the PUMA level, in less populous areas) 58 California counties became 34 complete counties (each with one or more PUMAs) + 7 multiple-county aggregations (from two to seven counties) 3

What we learned, among other things: Margins of error are large for estimates in areas with small populations: Many counties have insufficient populations for estimates to be useful (statistically significant) Even at the PUMA level (county aggregations), estimates for small race/ethnic groups can have huge error margins Margins of error are large for estimates of enrollment rates for race/ethnic groups that may not comprise a very large share of those sampled 4

Methodology We computed the proportion of K-12 students in private school along with 95% confidence intervals (weighted values standardized to the mean) by race, for California counties/county groupings We computed confidence intervals using the Clopper-Pearson exact confidence interval method (the R package 'PropCIs') In order to constrain the interval to be within plausible margins (between 0 and 1) 5

Results for 5-year ACS estimates 2007-2011 ACS PUMS data PUMAs matched to counties Private K-12 enrollment rates estimated, along with confidence intervals, for: All groups, combined Whites alone Hispanics alone Blacks alone Other groups (not shown)

San Francisco Marin San Mateo Santa Clara Shasta Alameda Contra Costa Orange Santa Barbara Ventura Los Angeles Sonoma DelNorte.et.al Placer Yolo Nevada.et.al Sacramento San Luis Obispo San Diego Monterey.SanBenito Butte Solano Lake.et.al Alpine.et.al Colusa.et.al El Dorado Riverside San Bernardino San Joaquin Kern Sutter.et.al Kings Stanislaus Humboldt Fresno Tulare Madera Imperial Merced 6 All Groups ACS 2007-11 5-year estimates 6 2 2

Map of estimated share of K-12 students enrolled in private school, by county/county group ACS 2007-2011 Estimates of Private K-12 Enrollment Rates

San Francisco San Mateo Marin Los Angeles Santa Clara Santa Barbara Monterey.SanBenito Orange Alameda Ventura Contra Costa Sonoma Riverside Kings San Diego Shasta Sacramento San Joaquin Kern San Bernardino San Luis Obispo DelNorte.et.al Yolo Nevada.et.al Placer Solano Colusa.et.al Tulare Lake.et.al El Dorado Stanislaus Fresno Butte Alpine.et.al Merced Sutter.et.al Humboldt Madera Imperial 6 White alone ACS 2007-11 5-year estimates 6 2 2

San Francisco Shasta San Mateo Butte Placer Alameda Contra Costa Santa Clara Sacramento Yolo Marin Los Angeles Ventura DelNorte.et.al Orange Alpine.et.al Colusa.et.al Sutter.et.al Santa Barbara San Diego Solano Riverside San Bernardino Monterey.SanBenito Nevada.et.al San Joaquin Sonoma Lake.et.al San Luis Obispo Stanislaus Kern Madera Imperial Fresno Tulare Kings Humboldt El Dorado Merced 6 Hispanic ACS 2007-11 5-year estimates 6 2 2

Sonoma El Dorado Monterey.SanBenito Tulare Shasta Santa Barbara San Luis Obispo San Mateo Santa Clara San Francisco Marin Contra Costa Los Angeles Orange Alameda Humboldt Solano San Diego Riverside San Bernardino Ventura Alpine.et.al San Joaquin Sacramento Merced Placer Kern Imperial Sutter.et.al Madera Fresno Stanislaus Butte Yolo Kings Colusa.et.al DelNorte.et.al Lake.et.al Nevada.et.al 10 9 8 Black alone and Counties ACS 2007-11 5-year estimates 10 9 8 7 7 6 6 2 2

Map of estimated share of NH Black K-12 students enrolled in private school, by county/county group ACS 2007-2011 Counties with very high estimated Black rates ( and )

Map of estimated share of NH Black K-12 students enrolled in private school, by county/county group ACS 2007-2011 Counties with very high estimated Black rates and small Black child population shares

Results for 3-year ACS estimates 2006-2008, 2008-2010 & 2009-2011 ACS estimates PUMS data; PUMAs matched to counties The Census Bureau recommends comparing non-overlapping periods because of duplication of years of data (which complicates various kinds of computations). However, we learned that there may be value in using overlapping periods in order to identify estimates that may be problematic. When we compare estimates from overlapping time periods, differences can be the result of : A true change in the rate Estimation error

Alameda Butte Contra Costa El Dorado Fresno Humboldt Imperial Kern Kings Los Angeles Madera Marin Merced Orange Placer Riverside Sacramento San Bernardino San Diego San Francisco San Joaquin San Luis Obispo San Mateo Santa Barbara Santa Clara Shasta Solano Sonoma Stanislaus Tulare Ventura Yolo Alpine.et.al Colusa.et.al DelNorte.et.al Lake.et.al Monterey.SanBenito.et.al Nevada.et.al Sutter.et.al Alameda Butte Contra Costa El Dorado Fresno Humboldt Imperial Kern Kings Los Angeles Madera Marin Merced Orange Placer Riverside Sacramento San Bernardino San Diego San Francisco San Joaquin San Luis Obispo San Mateo Santa Barbara Santa Clara Shasta Solano Sonoma Stanislaus Tulare Ventura Yolo Alpine.et.al Colusa.et.al DelNorte.et.al Lake.et.al Monterey.SanBenito.et.al Nevada.et.al Sutter.et.al Alameda Butte Contra Costa El Dorado Fresno Humboldt Imperial Kern Kings Los Angeles Madera Marin Merced Orange Placer Riverside Sacramento San Bernardino San Diego San Francisco San Joaquin San Luis Obispo San Mateo Santa Barbara Santa Clara Shasta Solano Sonoma Stanislaus Tulare Ventura Yolo Alpine.et.al Colusa.et.al DelNorte.et.al Lake.et.al Monterey.SanBenito.et.al Nevada.et.al Sutter.et.al The confidence intervals for Black private rates for 2009-11 and 2008-10 didn t particularly signal problems with the estimates, but comparing the 2009-11 estimates with 2006-08 and 2008-10 raised a red flag. 10 10 10 ACS 2009-11 10 9 8 7 6 ACS 2008-10 9 8 7 6 9 8 9 8 7 7 2 2 6 6 2 2 10 9 1 10 8 7 ACS 2006-08 9 8 6 7 6 2 2 Error margins for the 2006-08 estimates are huge 17

Challenges and Questions We found some highly unlikely 5-year ACS estimates of private school enrollment rates, including 40% ( County) and 44% ( County) for Blacks. Margins of error are large for small sub-groups in many counties, even ones with rather large total populations We probably can t believe these estimates. The 3-year ACS estimates are even more unlikely for areas with small sub-group populations We shouldn t use them to measure trends, except perhaps for all groups combined or for geographies with much larger populations Would tests of statistical significance help us know what to believe?

Measuring Variations in Private School Enrollment Rates Using ACS Estimates Jeanne Gobalet Lapkoff & Gobalet Demographic Research, Inc. gobalet@demographers.com