A subset of 188 students from 5 schools drawn from the High School and Beyond (HSB) study, a nationally representative survey of U.S. high school students conducted by the National Center for Education Statistics. The data include student-level variables (math achievement, SES, demographics) and school-level variables (school size and sector). This small subset is frequently used to introduce multilevel/hierarchical concepts where students are nested within schools.
Format
A tibble with 188 rows and 7 columns:
- minority
Minority status. Type: numeric. Binary indicator (0/1) where 1 = racial/ethnic minority, 0 = non-minority (White). 52% minority.
- female
Sex of student. Type: numeric. Binary indicator (0/1) where 1 = female, 0 = male. 63% female.
- ses
Socioeconomic status composite. Type: numeric. Range: (-1.66, 1.51). Mean = -0.06. Standardized composite of family income, parental education, and parental occupation.
- mathach
Mathematics achievement score. Type: numeric. Range: (-2.83, 24.99). Mean = 11.27. This is the primary outcome variable.
- size
School enrollment size. Type: numeric. Range: (455, 1855). Mean = 1,088. 5 unique values corresponding to the 5 schools.
- sector
School sector. Type: numeric. Binary indicator (0/1) where 1 = Catholic school, 0 = public school. 36% Catholic.
- schoolid
School identifier. Type: numeric. Values: 1224, 1288, 1296, 1308, 1317. Five unique school IDs from the HSB sampling frame.
Source
Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical Linear
Models: Applications and Data Analysis Methods (2nd ed.). Sage
Publications. Data originally from the High School and Beyond study,
National Center for Education Statistics.
Original data file: hsb_sub.dta
Details
This dataset is used to illustrate regression concepts where observations are nested within groups (students within schools). Key analyses include: examining the relationship between SES and math achievement, comparing public and Catholic school effects on achievement while controlling for student demographics, and exploring school-level variation in the SES-achievement relationship.
The nesting structure (188 students in 5 schools) provides an introduction to the concepts underlying multilevel modeling, even when standard OLS regression is used. The sector variable allows for ANCOVA-style analyses comparing school types.
Examples
data(hsb_sub)
head(hsb_sub)
#> # A tibble: 6 × 7
#> minority female ses mathach size sector schoolid
#> <int> <int> <dbl> <dbl> <int> <int> <int>
#> 1 0 1 -1.53 5.88 842 0 1224
#> 2 0 1 -0.588 19.7 842 0 1224
#> 3 0 0 -0.528 20.3 842 0 1224
#> 4 0 0 -0.668 8.78 842 0 1224
#> 5 0 0 -0.158 17.9 842 0 1224
#> 6 0 0 0.0220 4.58 842 0 1224
# SES effect on math achievement
lm(mathach ~ ses, data = hsb_sub)
#>
#> Call:
#> lm(formula = mathach ~ ses, data = hsb_sub)
#>
#> Coefficients:
#> (Intercept) ses
#> 11.457 3.307
#>
# ANCOVA: sector effect controlling for SES and demographics
lm(mathach ~ ses + minority + female + sector, data = hsb_sub)
#>
#> Call:
#> lm(formula = mathach ~ ses + minority + female + sector, data = hsb_sub)
#>
#> Coefficients:
#> (Intercept) ses minority female sector
#> 12.545 1.681 -3.196 -1.549 3.981
#>