NYC School Performance, Poverty and Class size Analysis

Synopsis:

Considering the importance of education in an increasingly knowledge based economy, I performed an exploratory data analysis of school performance in relation to various attributes that might potentially have an influence, with the following objectives.

• Understand what attributes actually influence school performance.
• Analyse if our current affirmative action plans and college admission policies reflect such influence.

Scope, Variables and Datasets:

Analysis was restricted to NYC puclic schools ( comprising 32 school districts)

Factors considered:

• Attendance rate
• School safety
• Class size
• School district size
• Poverty ratio
• Ethnic background
• Gender ratio
• English language learners ratio

SAT score. covering Math , Reading and Writing was used as an indicator of school performance.

Following datasets were used for the analysis

1. School Attendance File
2. Class size File
3. Demographics File
4. School Safety report
5. 2010 SAT score file
6. 2014 SAT score file

Pre-Processing:

• All source datasets were merged by District-id:School-id to create the master file.
• The dataset was scaled and centered as the features measured are vastly different- for example , poverty ratio is in percentage , class size in tens and SAT scores in hundreds .
• Data set was checked for Near-Zero variance attributes using nearZeroVar function, so they can be dropped from feature set, there were none .
• Data set was checked for highly correlated variables using vif function, so they can be dropped from feature set, there were none .

Feature Selection:

regsubsets was for used feature selection - following 3 features out of the total 8 feature, were picked up by regsubsets as features that have some influence on SAT scores
Class size
Poverty and
Gender Ratio 

To cross validate, feature selection was repeated with steps - the same 3 features were picked up by steps function as well.

##   (Intercept) poverty.ratio          size  female.ratio 
##    -4.4799063    -0.4308900     0.1759099     0.1954207

Influence of Poverty , Class size and gender ratio over school performance:

A linear regression of School Performance with these three variables as the predictors was performed.

## 
## Call:
## lm(formula = total.percent ~ poverty.ratio + size + female.ratio, 
##     data = scaled.district.data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.0172 -0.4736 -0.1017  0.3043  1.8254 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)   
## (Intercept)   -4.47991    1.55994  -2.872  0.00769 **
## poverty.ratio -0.43089    0.14734  -2.925  0.00676 **
## size           0.17591    0.06108   2.880  0.00754 **
## female.ratio   0.19542    0.12841   1.522  0.13925   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6657 on 28 degrees of freedom
## Multiple R-squared:  0.5997, Adjusted R-squared:  0.5568 
## F-statistic: 13.98 on 3 and 28 DF,  p-value: 9.303e-06

Only class-size and poverty features displayed statistically significant influence and hence gender-ratio was dropped from further analysis.

I decided to take a closer look on the impact of these two key attributes on the overall performance.
When a regression plot on school performance was plotted against class size and poverty, the result was a surprise.

While the influence of poverty on SAT scores was in line with the expectation (increased poverty rates result in decreased scores), the impact of class size was totally unexpected.
The trend line shows performance declining with smaller class sizes.

Taking a second look at these plots , the impact of class size over school performance looks like almost a mirror image of poverty plot. I wanted to understand the relation between these two factors. What I found was really interesting.

Clearly, most of the schools in poorer neighborhoods have smaller class sizes than the school districts that are better off.

I decided to look for explanation and came across “Contracts for Excellence Legislation” .

This legislation funded a set of initiatives over a 5 yr period from 2007, including reduction of class size, focused on poor neighborhoods and schools performing below state standards.

Our findings confirm that some action seems to have been taken under the legislation since 2007 as reflected in the 2010 class size data , and that most of the poor neighborhood / low performance schools have comparatively smaller class sizes .

This background presents an interesting question to explore.

Have smaller class sizes really helped to improve the performance of the school districts compared to those with bigger class sizes?
Let us check by comparing the performance of the 2010 class with 2014 class from these schools with smaller class sizes.

Let us take a look at performance change of class size groups by comparing total 2014 scores against 2010 by class size group .

Looking at the overlap in notches in the box plot across size groups , there seems to be no significant improvement in scores for the classes with smaller sizes.

Considering the fact that the city is making significant investments towards reducing class sizes with an objective to improve school performance, it will be interesting to check if there are any changes in scores at a subject level (Math , Reading and Writing) , before rejecting the influence of class size reduction on performance improvement..

Change in Math performance by class size group:

Linear model and plot comparing the change in math score (2014 vs 2010) is shown below. There is no statistically significant improvement in the math performance of schools with smaller classes over this period.

## 
## Call:
## lm(formula = chMath ~ math.size, data = scaled.school.data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.13160 -0.20311 -0.00902  0.20622  0.95957 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept)  0.0093060  0.1108796   0.084    0.933
## math.size   -0.0003822  0.0044963  -0.085    0.932
## 
## Residual standard error: 0.3276 on 347 degrees of freedom
## Multiple R-squared:  2.082e-05,  Adjusted R-squared:  -0.002861 
## F-statistic: 0.007225 on 1 and 347 DF,  p-value: 0.9323

Change in Reading performance by class size group:

Linear model and plot comparing the change in reading score (2014 vs 2010) is shown below. There is no statistically significant improvement in the reading performance of schools with smaller classes over this period.

## 
## Call:
## lm(formula = chReading ~ english.size, data = scaled.school.data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.21348 -0.20204  0.00022  0.22107  1.04587 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept)  -0.112576   0.112919  -0.997    0.319
## english.size  0.004623   0.004572   1.011    0.313
## 
## Residual standard error: 0.3517 on 347 degrees of freedom
## Multiple R-squared:  0.002938,   Adjusted R-squared:  6.421e-05 
## F-statistic: 1.022 on 1 and 347 DF,  p-value: 0.3127

Change in Writing performance by class size group:

Linear model and plot comparing the change in writing score (2014 vs 2010) is shown below. There is no statistically significant improvement in the writing performance of schools with smaller classes over this period.

## 
## Call:
## lm(formula = chWriting ~ english.size, data = scaled.school.data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.04316 -0.19708  0.01551  0.22388  1.05277 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)
## (Intercept)  -0.145804   0.106370  -1.371    0.171
## english.size  0.005988   0.004307   1.390    0.165
## 
## Residual standard error: 0.3313 on 347 degrees of freedom
## Multiple R-squared:  0.005539,   Adjusted R-squared:  0.002673 
## F-statistic: 1.933 on 1 and 347 DF,  p-value: 0.1654

After a detailed analysis of the change in score trends by class size , there is no confirmation that the smaller class sizes have resulted in a statistically significant improvement in student performance over a three year period.

Conclusion:

• Of all the factors analysed, only poverty ration seems to have the most significant impact on school performance - more than any other factor , including ethnic background. Hence , economic background should be an important factor in any affirmative action considerations for college admissions to offset the disadvantage.
• NYC administration has tried to do its bit by reducing the class sizes to help students from impoverished background , but there is no clear evidence to show that smaller classes have helped improve the performance of low performance schools.

References:

Github Source Code