California Test Score Data
Yoho
2022-09-17
1 Introduction
The data are from all 420 K-6 and K-8 districts in California with data available for 1998 and 1999. The data set contains information on test performance, school characteristics and student demographic backgrounds for school districts.
Test scores are on the Stanford 9 standardized test administered to 5th grade students. School characteristics (averaged across the district) include enrollment, number of teachers (measured as “full-time equivalents”, number of computers per classroom, and expenditures per student. Demographic variables for the students are averaged across the district.
A data frame with 420 observations on the following 14 variables.
- district: character. District code.
- school: character. School name.
- county: factor indicating county.
- grades: factor indicating grade span of district.
- students: Total enrollment.
- teachers: Number of teachers.
- calworks: Percent qualifying for CalWorks (income assistance).
- lunch: Percent qualifying for reduced-price lunch.
- computer: Number of computers.
- expenditure: Expenditure per student.
- income: District average income (in USD 1,000).
- english: Percent of English learners.
- read: Average reading score.
- math: Average math score.
2 Data
data(CASchools, package="AER")
dta <- CASchools# have a look
glimpse(dta)Rows: 420
Columns: 14
$ district <chr> "75119", "61499", "61549", "61457", "61523", "62042", "685…
$ school <chr> "Sunol Glen Unified", "Manzanita Elementary", "Thermalito …
$ county <fct> Alameda, Butte, Butte, Butte, Butte, Fresno, San Joaquin, …
$ grades <fct> KK-08, KK-08, KK-08, KK-08, KK-08, KK-08, KK-08, KK-08, KK…
$ students <dbl> 195, 240, 1550, 243, 1335, 137, 195, 888, 379, 2247, 446, …
$ teachers <dbl> 10.90, 11.15, 82.90, 14.00, 71.50, 6.40, 10.00, 42.50, 19.…
$ calworks <dbl> 0.5102, 15.4167, 55.0323, 36.4754, 33.1086, 12.3188, 12.90…
$ lunch <dbl> 2.0408, 47.9167, 76.3226, 77.0492, 78.4270, 86.9565, 94.62…
$ computer <dbl> 67, 101, 169, 85, 171, 25, 28, 66, 35, 0, 86, 56, 25, 0, 3…
$ expenditure <dbl> 6384.91, 5099.38, 5501.95, 7101.83, 5235.99, 5580.15, 5253…
$ income <dbl> 22.69000, 9.82400, 8.97800, 8.97800, 9.08033, 10.41500, 6.…
$ english <dbl> 0.00000, 4.58333, 30.00000, 0.00000, 13.85768, 12.40876, 6…
$ read <dbl> 691.6, 660.5, 636.3, 651.9, 641.8, 605.7, 604.5, 605.5, 60…
$ math <dbl> 690.0, 661.9, 650.9, 643.5, 639.9, 605.4, 609.0, 612.5, 61…We compute the student-teacher ratio and a score which is the average of math and reading scores. The number of schools in each county is calculated and augment to the data frame.
dta <- dta |> mutate(stratio = students/teachers,
score = (math+read)/2) |>
add_count(county)3 Visualization
# OLS regression lines over county with more than 10 schools
ggplot(subset(dta, n > 10), aes(x=stratio, y=score, group=county)) +
geom_point(alpha=0.5) +
stat_smooth(aes(group=1),
method="lm", formula=y ~ x, se=F) +
labs(x="lunch",
y="Score (average of math and reading)") +
facet_grid(. ~ county)
theme_minimal() List of 93
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- attr(*, "validate")= logi TRUE3.1 Problem
Replace stratio with lunch in the above plot.
Graph each county (with more than 10 schools) in one panel of a plot with a single regression line for each.
4 Simple regression
summary(lm(score ~ stratio, data=subset(dta, n > 10)))
Call:
lm(formula = score ~ stratio, data = subset(dta, n > 10))
Residuals:
Min 1Q Median 3Q Max
-44.44 -14.23 0.42 13.92 47.84
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 709.472 13.324 53.2 < 2e-16
stratio -2.830 0.673 -4.2 3.7e-05
Residual standard error: 19.5 on 249 degrees of freedom
Multiple R-squared: 0.0663, Adjusted R-squared: 0.0625
F-statistic: 17.7 on 1 and 249 DF, p-value: 3.66e-054.1 Problem
Regress score over student-teacher ratio for each county. Compare the average estimated slope coefficients with the value of estimates from the overall regression ignoring county clusters.
5 Referenecs
Stock, J.H. & Watson, M.W. (2007). Introduction to Econometrics. 2nd Ed. Boston: Addison Wesley.