Search for South Florida public schools using this data table:
Among public schools with at least 50 third-graders, there was a significant negative correlation between the percent of students who passed the state reading test and the percent of students receiving free and reduced lunch by school.
For every 1% increase in economically disadvantaged students, a school’s ELA achievement score drops by about 0.5 points. That means if the percent of students receiving free and reduced lunch at a school increased by 10%, we would expect the number of third-graders passing their reading test to drop by 5%.
About 38% of the variance in 3rd-grade ELA achievement scores across the 521 schools included can be explained solely by the percentage of economically disadvantaged students. (Code output below.)
##
## Call:
## lm(formula = grade_3_english_language_arts_achievement_26 ~ pct_free_reduced,
## data = third_graders)
##
## Residuals:
## Min 1Q Median 3Q Max
## -41.885 -8.811 0.102 8.617 39.598
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 88.11084 1.48281 59.42 <2e-16 ***
## pct_free_reduced -0.49735 0.02772 -17.94 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 13.1 on 519 degrees of freedom
## (2 observations deleted due to missingness)
## Multiple R-squared: 0.3829, Adjusted R-squared: 0.3817
## F-statistic: 322 on 1 and 519 DF, p-value: < 2.2e-16
## `geom_smooth()` using formula = 'y ~ x'
The percent of level 3 readers was higher, on average, among charter schools than non-charter schools. Among the 240 charter schools with at least 100 students, about 70% of students of all grades passed their reading tests, while for non-charter schools, the figure was 63%.
Charter schools saw, on average, between 4.9% and 9.1% more students pass the state reading test than non-charters in the four South Florida counties (Dade, Monroe, Palm Beach, Broward). (Code shown below.)
##
## Welch Two Sample t-test
##
## data: soflo_grades24_26_charter$english_language_arts_achievement_26 and soflo_grades24_26_no_charter$english_language_arts_achievement_26
## t = 6.4785, df = 400.2, p-value = 2.724e-10
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 4.887843 9.146622
## sample estimates:
## mean of x mean of y
## 70.21667 63.19943
Among districts with at least 10 schools, no South Florida schools ranked in the top 10 for percent of third-graders who passed the reading test. Miami-Dade ranked No. 11, Monroe ranked No. 13, Broward ranked No. 21 and Palm Beach ranked No. 30 out of 45.
The percent of minority students at each school was also correlated with test scores, though not as strongly as economics. For every 1% increase in its minority student population size, a school’s ELA achievement score drops by about 0.38 points.
About 15% of the variance in South Florida 3rd-grade ELA achievement scores can be explained solely by the percentage of minority students. (Code shown below.)
third_graders$percent_of_minority_students_24=parse_number(third_graders$percent_of_minority_students_24)
model_minority <- lm(grade_3_english_language_arts_achievement_26 ~ percent_of_minority_students_24, data = third_graders)
summary(model_minority)
##
## Call:
## lm(formula = grade_3_english_language_arts_achievement_26 ~ percent_of_minority_students_24,
## data = third_graders)
##
## Residuals:
## Min 1Q Median 3Q Max
## -38.598 -10.696 0.156 10.654 37.914
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 96.31376 3.40924 28.251 <2e-16 ***
## percent_of_minority_students_24 -0.38135 0.03888 -9.808 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 15.31 on 521 degrees of freedom
## Multiple R-squared: 0.1559, Adjusted R-squared: 0.1542
## F-statistic: 96.19 on 1 and 521 DF, p-value: < 2.2e-16