prime_time_achievement: Indiana Prime Time Third Grade Achievement Evaluation Data

Description

The complete student level data file from the 2000 to 2001 Indiana Department of Education program evaluation of Project Prime Time, reported in Lapsley, Daytner, Kelley, and Maxwell (2002, ERIC ED466679). The evaluation examined the academic performance of N = 10,927 third grade students in n = 573 classrooms (here 586 by the paste(corp, school, class) rule), n = 163 schools, n = 61 school corporations, and 9 Indiana educational service regions as a function of class size, pupil to teacher ratio, and the presence of a Prime Time instructional assistant. The data have been used as a multilevel example through chapters 3, 4, 6, 9, and 10 of Finch, Bolin, and Kelley (2019, Multilevel Modeling Using R, 2nd ed., CRC Press) and are made available here as a benchmark data set for the design, measurement, and analysis of nested data.

Usage

prime_time_achievement

Arguments

Format

A data frame with 10,927 observations on 113 variables. Variables fall into seven blocks: three derived unique cluster identifiers, student level demographics and ability and achievement scores, classroom level variables, school level variables, and school corporation (district) level variables. Original Indiana DOE variable spellings are preserved, including the typos calender (calendar), hispanc1 and hispanc2 (Hispanic), and rmediate (remediate), for code compatibility with Finch, Bolin, and Kelley (2019). The SPSS variable label from the source file is available as attr(prime_time_achievement$VAR, "label") for every variable carried over from the SPSS file; the one derived recode without a source label is classize (see its entry below).

id: Student identifier in the source file (not guaranteed unique; see class_id etc. for stable cluster keys).
region: Indiana educational service region, coded 1 to 9. Sampling stratifier (25% of corporations per region).
corp: School corporation (district) numeric identifier. Note: corp 2400 appears in both region 2 (12 schools) and region 3 (1 school) in the source file, so paste(region, corp) is the cleaner cluster key; see corp_id.
school: Numeric school identifier (unique within corporation).
class: Classroom number within school, 1 to 8. Not unique across schools.
corp_id: Derived. paste(region, corp, sep = "_"). 61 distinct values, matching the count of school corporations reported in Lapsley et al. (2002).
school_id: Derived. paste(corp, school, sep = "_"). 163 distinct values.
class_id: Derived. paste(corp, school, class, sep = "_"). 586 distinct values. (The published report counted 573 classrooms; the small discrepancy reflects a different counting convention used in the manuscript.)
gender: 1 = Female, 2 = Male. 45 NA.
age: Student age in months.
race: Indiana DOE 6-category ethno-racial code: 1 = American Indian / Alaskan, 2 = African American, 3 = Asian American, 4 = Hispanic American, 5 = Caucasian American, 6 = Multi-racial.
geread: Gates-MacGinitie reading.
gevocab: Gates-MacGinitie vocabulary.
gereadcm: Gates-MacGinitie reading composite.
gelang: Gates-MacGinitie language.
gelangmc: Gates-MacGinitie language mechanics.
gelangcm: Gates-MacGinitie language composite.
gemath: Gates-MacGinitie mathematics.
gemathcp: Gates-MacGinitie mathematics computation.
gemathcm: Gates-MacGinitie mathematics composite.
getotal: Gates-MacGinitie total.
ncread: NCE reading (ISTEP+).
ncvocab: NCE vocabulary (ISTEP+).
ncreadcm: NCE reading composite (ISTEP+).
nclang: NCE language (ISTEP+).
nclangmc: NCE language mechanics (ISTEP+).
nclangcm: NCE language composite (ISTEP+).
ncmath: NCE mathematics (ISTEP+).
ncmathcp: NCE mathematics computation (ISTEP+).
ncmathcm: NCE mathematics composite (ISTEP+).
nctotal: NCE total composite (ISTEP+), the criterion variable in the Lapsley et al. (2002) HLM analyses.
aaread: AANCE reading.
aavocab: AANCE vocabulary.
aareadcm: AANCE reading composite.
aalang: AANCE language.
aalangmc: AANCE language mechanics.
aalangcm: AANCE language composite.
aamath: AANCE mathematics.
aamathcp: AANCE mathematics computation.
aamathcm: AANCE mathematics composite.
aatotal: AANCE total.
npanverb: NPA nonverbal reasoning.
npamem: NPA working memory.
npaverb: NPA verbal reasoning.
npatotal: NPA total.
csi: Cognitive Skills Index (student level).
multi: Multi-age classroom indicator (1 = Yes, 2 = No).
typmulti: Type of multi-age classroom (1 = 1st-2nd-3rd grades, 2 = 2nd-3rd, 3 = 3rd-4th, 4 = 2nd-3rd- 4th; NA when multi == 2).
clenroll: Official class enrollment.
classize: Project STAR style class size category: 1 = small (roughly 12-17), 2 = regular (roughly 18-22), 3 = regular-larger (roughly 23-26), 4 = large (27 or more). Boundaries follow the STAR classification (Pate-Bain and Achilles, 1986).
ptratio: Classroom pupil to teacher ratio (IDOE formula: enrollment / [1.00 per full time teacher + 0.33 per full time aide + 0.165 per part time aide]).
ptia: Prime Time Instructional Aide status: 1 = aide present, 2 = no aide, 3 = other assistant listed. The focal treatment indicator.
ptstatus: Status of Prime Time aide: 1 = full time in classroom, 2 = part time in classroom; NA when ptia != 1.
locale: NCES locale code (1 = large central city, 2 = mid-size central city, 3 = urban fringe of large city, 4 = urban fringe of mid-size city, 5 = large town, 6 = small town, 7 = rural).
chapter1: School receives Title I (legacy "Chapter 1") money? 1 = Yes, 2 = No.
ses: School SES, the IDOE percentage of students not eligible for subsidized lunch (0 to 100; higher = more affluent). The school level SES variable used in the Lapsley et al. (2002) HLM analyses.
context: IDOE contextual rank for the school.
calender: School calendar type (1 = traditional, 2 = year round). Typo preserved from source.
senroll: Building (school) enrollment.
sattend: Building attendance rate (percent).
white1: School percent White.
black1: School percent Black.
hispanc1: School percent Hispanic (typo preserved).
asian1: School percent Asian.
aindian1: School percent American Indian.
multi1: School percent multi-racial.
total1: School total percent non-white.
noteach: Number of teachers in the building (full time equivalent).
avgage1: School average teacher age.
avgexp1: School average teacher experience (years).
avgsal1: School average teacher salary (dollars).
spert: School students per teacher.
thrdclss: Number of third grade classrooms in the building.
thrdstud: Number of third graders who took ISTEP+ in the building.
passla1: Building percent passing language arts.
passmth1: Building percent passing math.
passbth1: Building percent passing both.
tmnnce1: Building total battery mean NCE.
rmdnce1: Building reading median NCE. Note: the 56 rows from one building (corp 5740, school 6187) carry the source value 7603, an evident data-entry error in the Indiana DOE file (an NCE is on the 1 to 99 scale, and the same building's other median-NCE columns are in range). The value is preserved as shipped rather than silently corrected, since the true value cannot be recovered; drop or set it to NA before analyzing this column.
lamdnce1: Building language arts median NCE.
mmdnce1: Building mathematics median NCE.
tmdnce1: Building total battery median NCE.
avgcsi1: Building average Cognitive Skills Index.
geog: Geographic category of the corporation (1 = urban, 2 = suburban, 3 = town, 4 = rural). Sampling stratifier within region.
totepp: Corporation total expense per pupil (1997--1999, dollars).
cenroll: Corporation enrollment (all grades).
cattend: Corporation attendance rate (percent).
freelnch: Corporation percent eligible for free lunch.
lep: Corporation percent with limited English proficiency.
speced: Corporation percent in special education.
minority: Corporation percent minority.
white2: Corporation total White public enrollment (raw count).
black2: Corporation total Black public enrollment.
hispanc2: Corporation total Hispanic public enrollment (typo preserved).
asian2: Corporation total Asian public enrollment.
aindian2: Corporation total American Indian public enrollment.
multi2: Corporation total multi-racial public enrollment.
total2: Corporation total non-white public enrollment.
thrdadm: Corporation third grade ADM (average daily membership).
thrdtech: Corporation third grade teachers.
avgage2: Corporation average teacher age.
avgexp2: Corporation average teacher experience (years).
avgsal2: Corporation average teacher salary (dollars).
thrdaide: Corporation third grade aides.
passla2: Corporation percent passing language arts.
passmth2: Corporation percent passing math.
passbth2: Corporation percent passing both.
tmnnce2: Corporation total battery mean NCE.
rmdnce2: Corporation reading median NCE.
lamdnce2: Corporation language arts median NCE.
mmdnce2: Corporation mathematics median NCE.
tmdnce2: Corporation total battery median NCE.
rmediate: Corporation remediation funding per pupil (dollars). Typo preserved.

Author

Ken Kelley

Details

Study background. Indiana's Prime Time program, phased in beginning 1984 to 1985 (Indiana statute; House Bill 1166 of 2001 codified the modern funding formula), was one of the earliest state level initiatives in the United States to use a funding formula to reduce class size and pupil to teacher ratio in Kindergarten through third grade. Funds were distributed to school corporations to maintain a corporation average pupil to teacher ratio of 18:1 in K and grade 1 and 20:1 in grades 2 and 3; corporations could meet the target by hiring additional teachers or, more commonly, paraprofessional instructional assistants. Along with Tennessee's Project STAR (Pate-Bain and Achilles, 1986; covered by Education Week, Research: Sizing Up Small Classes, February 2001), Prime Time was a widely cited national model.

In 1999 the Indiana Department of Education funded a three year program evaluation of Prime Time. The third year of the evaluation, conducted by Daniel K. Lapsley and Katrina M. Daytner (Ball State University and Western Illinois University) with technical assistance from Ken Kelley and Scott E. Maxwell (University of Notre Dame), examined the academic performance of randomly selected Indiana third graders on the state mandated ISTEP+ standardized achievement test as a function of class size, pupil to teacher ratio, and the presence of a Prime Time instructional aide, using hierarchical linear modeling. The preliminary report and the AERA 2002 paper that summarizes the analyses are archived as ERIC document ED466679 (Lapsley, Daytner, Kelley, and Maxwell, 2002). An earlier background report from the same evaluation team, prior to the Notre Dame group joining the project, is archived as ERIC document ED455220.

Sampling. School corporations were drawn by stratified cluster sampling with two rules: 25% of corporations from each of the nine Indiana educational service regions, and at least one urban corporation per region, with the remainder proportionally allocated across geographic categories (urban, suburban, town, rural). The achieved sample was 61 corporations (78% of the target), 163 schools, 573 classrooms as counted in the manuscript (586 by the paste(corp, school, class) rule used here), and 10,927 students (49.6% female; 85% Caucasian, 9.2% African American, 3.2% Hispanic). 4,016 students were in classrooms with a Prime Time instructional assistant (ptia == 1), 6,765 in classrooms without (ptia == 2); the file here shows 4,021 and 6,789 plus 117 ptia == 3 (other assistant listed), with the small differences reflecting cleaning rules applied between the manuscript count and the final SPSS file.

Instruments. Third graders sit for the ISTEP+ (Indiana Statewide Testing for Educational Progress) in September of the school term. The ISTEP+ is published by CTB/McGraw-Hill and includes language arts, reading, and mathematics assessments. Normal Curve Equivalent (NCE) composite scores for these domains and for the total are the ncread / nclang / ncmath / nctotal columns and were the criterion variables in the published HLM analyses. NCE scores have a population mean of 50 and a standard deviation of approximately 21.06, with percentiles 1, 50, and 99 mapping to NCE scores of 1, 50, and 99. The ge* family is the parallel Gates-MacGinitie battery; the aa* family is the African American comparison NCE (AANCE); the npa* family is the cognitive abilities battery used as student level covariates in Finch, Bolin, and Kelley (2019).

Nested data structure. The natural hierarchy is student within classroom within school within corporation within region. The derived identifiers corp_id, school_id, and class_id are pre-computed and safe to use as grouping variables; the bare corp and class columns are not unique by themselves. Class sizes range from 3 to 28 students (median 19); schools have 1 to 8 third grade classrooms (median 3) and 11 to 166 students (median 65); corporations have 15 to 756 students (median 117). Variance decomposition for the published outcome nctotal based on the three level random intercept null model lmer(nctotal ~ 1 + (1 | corp_id/school_id)) gives: between-corporation variance 16.29, between-school within corporation variance 22.72, and within school residual variance 240.43, so that ICC$_{\mathrm{corp}}$ $\approx$ 0.058, ICC$_{\mathrm{school|corp}}$ $\approx$ 0.081, and the combined cluster ICC$_{\mathrm{cluster}}$ $\approx$ 0.140. These nontrivial intraclass correlations are the methodological reason multilevel modeling is preferred to ordinary least squares regression for these data.

Level 1, 2, 3 model framework. For an outcome $Y_{ijk}$ on student $i$ in classroom $j$ in school $k$, with student level predictor $X^{(1)}_{ijk}$, classroom level predictor $X^{(2)}_{jk}$, and school level predictor $X^{(3)}_k$, the published Lapsley et al. (2002) family of HLM models has the equations $$Y_{ijk} = \pi_{0jk} + \pi_{1jk} X^{(1)}_{ijk} + e_{ijk} \quad \text{(Level 1)},$$ $$\pi_{0jk} = \beta_{00k} + \beta_{01k} X^{(2)}_{jk} + r_{0jk}, \quad \pi_{1jk} = \beta_{10k} + r_{1jk} \quad \text{(Level 2)},$$ $$\beta_{00k} = \gamma_{000} + \gamma_{001} X^{(3)}_k + u_{00k}, \quad \beta_{01k} = \gamma_{010}, \quad \beta_{10k} = \gamma_{100} \quad \text{(Level 3)},$$ with $e_{ijk} \sim N(0, \sigma^2)$, $r_{jk} \sim N(0, \mathbf{T}_\pi)$, and $u_{00k} \sim N(0, \tau_{00})$. Substituting upward, the reduced form is $$Y_{ijk} = \gamma_{000} + \gamma_{100} X^{(1)}_{ijk} + \gamma_{010} X^{(2)}_{jk} + \gamma_{001} X^{(3)}_k + u_{00k} + r_{0jk} + r_{1jk} X^{(1)}_{ijk} + e_{ijk},$$ which in lme4 translates to lmer(Y ~ X1 + X2 + X3 + (1 + X1 | corp_id/school_id)). The examples give concrete fits as commented code, which the help page therefore does not run; uncomment them to fit them.

Suggested benchmark uses. The data set is intentionally rich enough to support a wide range of demonstrations and benchmarks, including:

Two-, three-, and four-level random intercept and random slope models with lme4, nlme, or glmmTMB.
Cross-level interaction modeling (e.g., race $\times$ class size, ptia $\times$ SES).
ICC, design effect, and cluster level sample size calculations.
Comparisons of unweighted vs. design weighted estimators for stratified cluster samples.
Bayesian multilevel modeling and prior sensitivity (brms, MCMCglmm, rstanarm).
Missing data demonstrations (the ge*, nc*, and aa* columns have non-trivial missingness; see vapply(prime_time_achievement, function(x) sum(is.na(x)), integer(1))).
Multilevel reliability, intraclass correlation, and measurement invariance demonstrations across schools, corporations, and the categorical predictors.

Privacy and identifiability. The student level rows contain no names, addresses, or other personally identifiable information. Demographic variables are age in months, gender, and a six category race code; all other fields are test scores or aggregated school / corporation statistics. The numeric corp, school, and class identifiers are the same administrative numbers used in the original Indiana Department of Education public files for the 2000 to 2001 school year; they could in principle be cross referenced to that public information to identify specific schools or corporations. No individual student can be identified from any combination of variables in this file.

Missing data convention. The Indiana DOE source used 999 as the student level missing data code and 888 as the "not applicable" code for typmulti and ptstatus. The build script converts both to NA (the SPSS missingness ranges already do most of the recoding on import). The retained SPSS variable label is available via attr(prime_time_achievement$X, "label") on every variable carried over from the SPSS file (all columns except the derived recode classize).

References

Primary citation. Lapsley, D. K., Daytner, K. M., Kelley, K., and Maxwell, S. E. (2002). Teacher aides, class size and academic achievement: A preliminary evaluation of Indiana's Prime Time. ERIC document ED466679. https://eric.ed.gov/?id=ED466679.

Use as a multilevel modeling running example. Finch, W. H., Bolin, J. E., and Kelley, K. (2019). Multilevel modeling using R (2nd ed.). CRC Press. The 2nd edition (Finch, Bolin, and Kelley, 2019) is the edition that uses these data; later editions are not authored by Kelley and should not be cited for that use.

Background report from the same evaluation team. Lapsley, D. K., and Daytner, K. M. (2001). Indiana's class size reduction initiative: Teacher perspectives on training, implementation, and pedagogy. ERIC document ED455220. https://files.eric.ed.gov/fulltext/ED455220.pdf.

Indiana statutory context. Indiana General Assembly, House Bill 1166 (2001). https://archive.iga.in.gov/2001/bills/IN/IN1166.1.html.

Project STAR background and Education Week coverage. Pate-Bain, H., and Achilles, C. M. (1986). Interesting developments on class size. Phi Delta Kappan, 67, 662--665. See also Education Week, Research: Sizing up small classes (February 7, 2001), https://www.edweek.org/leadership/research-sizing-up-small-classes/2001/02.

Project STAR teacher aide null result that motivated the Prime Time evaluation. Finn, J. D., Gerber, S. B., Farber, S. L., and Achilles, C. M. (2000). Teacher aides: An alternative to small classes? In M. C. Wang and J. D. Finn (Eds.), How small classes help teachers do their best (pp. 131--174). Temple University Center for Research in Human Development and Education.

Examples

Run this code

data(prime_time_achievement)
dim(prime_time_achievement)

# Variable labels from the SPSS source are preserved on every column:
attr(prime_time_achievement$nctotal, "label")
attr(prime_time_achievement$ptia,    "label")

# Cluster counts, reconciled with Lapsley et al., 2002:
length(unique(prime_time_achievement$corp_id))    # 61
length(unique(prime_time_achievement$school_id))  # 163
length(unique(prime_time_achievement$class_id))   # 586

# Reconciling with the manuscript:
table(prime_time_achievement$gender, useNA = "ifany")
table(prime_time_achievement$race,   useNA = "ifany")
table(prime_time_achievement$ptia)
table(prime_time_achievement$classize)

# ----- Selecting subsets of interest -----

# Caucasian and African American only, the matched race
# supplementary analyses in Lapsley et al., 2002:
pt_wb <- subset(prime_time_achievement, race %in% c(2L, 5L))

# Drop the few "other assistant listed" cases for a clean
# aide / no-aide contrast:
pt_clean <- subset(prime_time_achievement, ptia %in% c(1L, 2L))

# Only rural corporations, coded 4 on geog, which is what the source
# SPSS file's FILTER_$ variable encoded:
pt_rural <- subset(prime_time_achievement, geog == 4L)

# Complete cases on the nctotal-on-race-and-class-size analysis:
analysis_vars <- c("nctotal", "race", "classize", "ses",
                   "corp_id", "school_id", "class_id")
pt_complete <- prime_time_achievement[
  complete.cases(prime_time_achievement[, analysis_vars]),
  analysis_vars
]

# ----- Multilevel fits -----

# Three-level null random intercept model on the full student level
# file. The variance components in the random effects block of the
# summary are the corporation, school within corporation, and residual
# variances behind the intraclass correlations reported in the Details
# section.
m_null <- lme4::lmer(nctotal ~ 1 + (1 | corp_id/school_id),
                     data = prime_time_achievement)
summary(m_null)

# Main effects of race, a student level variable, of ptia and
# classize, classroom level variables, and of ses, a school level
# variable. Compare to Lapsley et al., 2002, which fit closely related
# HLM specifications.
m_main <- lme4::lmer(
  nctotal ~ factor(race) + factor(ptia) + classize + ses +
    (1 | corp_id/school_id),
  data = prime_time_achievement)
summary(m_main)

# Cross-level interaction of ptia with ses. The published finding was
# that the aide benefit was concentrated in higher SES schools, which
# is what the interaction coefficient carries.
m_inter <- lme4::lmer(
  nctotal ~ factor(race) + factor(ptia) * ses + classize +
    (1 | corp_id/school_id),
  data = prime_time_achievement)
summary(m_inter)

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