In this project, we are going to analyze relationships between SAT scores and demographic factors in New York City public schools. The SAT, or Scholastic Aptitude Test, is an exam that U.S. high school students take before applying to college. It has three sections, each of which is worth a maximum of 800 points. High average SAT scores are usually indicative of a good school and of overall school district quality.
New York City has published data on student SAT scores by high school, along with additional demographic datasets.
New York City has a significant immigrant population and is very diverse, so comparing demographic factors such as race, income, and gender with SAT scores is a good way to determine whether the SAT is a fair test. For example, if certain categories of students consistently perform better on the SAT, we would have some evidence that the SAT is unfair.
During our research, we found out that some factors (safety and respect scores, total enrollment, female percentage, White and Asian race percentages, AP test takers percentage, class size) show a positive correlation with SAT scores, while some others (the percentages of english learners, males, Black and Hispanic races, free and reduced lunches, as an indicator of a student's family income) - a negative one. The district with the highest SAT score has the highest safety and respect score. In the survey parents tend to give the highest scores, while students - the lowest.
import pandas as pd
import numpy as np
import re
# Creating a list of all csv files
data_files = [
'ap_2010.csv',
'class_size.csv',
'demographics.csv',
'graduation.csv',
'hs_directory.csv',
'sat_results.csv'
]
# Reading all the datasets from the list and adding them to the dictionary
data = {}
for f in data_files:
d = pd.read_csv('schools/{0}'.format(f))
data[f.replace('.csv', '')] = d
Two other datasets (surveys) are tab delimited and encoded with Windows-1252 encoding, so we'll need to specify it when reading this data. Next, we'll combine the survey datasets into a single dataframe.
# Reading the survey datasets
all_survey = pd.read_csv('schools/survey_all.txt', delimiter='\t', encoding='windows-1252')
d75_survey = pd.read_csv('schools/survey_d75.txt', delimiter='\t', encoding='windows-1252')
# Combining the survey datasets
survey = pd.concat([all_survey, d75_survey], axis=0)
We'll start with renaming the 'dbn'
column (which is a unique ID for each school) of the survey dataframe to 'DBN'
to make the column name consistent with the other datasets. Then, we'll filter the data to leave only relevant columns, which we can figure out from a data dictionary at the original data download location.
# Renaming the column
survey['DBN'] = survey['dbn']
# Creating a list of relevant columns
survey_fields = [
'DBN', # School identification code (district borough number)
'rr_s', # Student Response Rate
'rr_t', # Teacher Response Rate
'rr_p', # Parent Response Rate
#------------NUMBER OF RESPONDENTS------------
'N_s', # students
'N_t', # teachers
'N_p', # parents
#-------------------SCORES--------------------
#--------------STUDENT RESPONSES--------------
'saf_s_11', # Safety and Respect
'com_s_11', # Communication
'eng_s_11', # Engagement
'aca_s_11', # Academic expectations
#--------------TEACHER RESPONSES--------------
'saf_t_11',
'com_t_11',
'eng_t_11',
'aca_t_11',
#---------------PARENT RESPONSES--------------
'saf_p_11',
'com_p_11',
'eng_p_11',
'aca_p_11',
#-----------------TOTAL SCORES----------------
'saf_tot_11',
'com_tot_11',
'eng_tot_11',
'aca_tot_11',
]
# Filtering only relevant columns
survey = survey.loc[:,survey_fields]
# Assigning the dataset to the dictionary
data['survey'] = survey
Now we'll rename the 'dbn'
column to 'DBN'
also for the hs_directory dataset and add the 'DBN'
column to the class_size dataset. In the last case, it's practically a combination of the 'CSD'
and 'SCHOOL CODE'
columns.
# Renaming the column
data['hs_directory']['DBN'] = data['hs_directory']['dbn']
# Creating a function to add a leading 0 where needed
def pad_csd(num):
return str(num).zfill(2)
# Padding zeros
data['class_size']['padded_csd'] = data['class_size']['CSD'].apply(pad_csd)
# Creating the 'DBN' column
data['class_size']['DBN'] = data['class_size']['padded_csd'] + data['class_size']['SCHOOL CODE']
Let's create a column that totals up the SAT scores for the different sections of the exam. Before we do, we have to convert those values to numeric.
# Converting the columns to numeric
cols = ['SAT Math Avg. Score',
'SAT Critical Reading Avg. Score',
'SAT Writing Avg. Score']
for c in cols:
data['sat_results'][c] = pd.to_numeric(data['sat_results'][c], errors='coerce')
# Calculating a column with total SAT scores
data['sat_results']['sat_score'] = data['sat_results'][cols[0]] + data['sat_results'][cols[1]] + data['sat_results'][cols[2]]
We'll convert to numeric also some columns of the ap_2010 dataset.
# Converting the columns to numeric
cols = ['AP Test Takers ',
'Total Exams Taken',
'Number of Exams with scores 3 4 or 5']
for col in cols:
data['ap_2010'][col] = pd.to_numeric(data['ap_2010'][col], errors='coerce')
The last step in our data cleaning process will be parsing the latitude and longitude coordinates for each school, using the 'Location 1'
column of the hs_directory dataset.
# Creating functions for parsing the coordinates
def find_lat(loc):
coords = re.findall('\(.+, .+\)', loc)
lat = coords[0].split(',')[0].replace('(', '')
return lat
def find_lon(loc):
coords = re.findall('\(.+, .+\)', loc)
lon = coords[0].split(',')[1].replace(')', '').strip()
return lon
# Parsing the coordinates and converting them to numeric
data['hs_directory']['lat'] = data['hs_directory']['Location 1'].apply(find_lat)
data['hs_directory']['lon'] = data['hs_directory']['Location 1'].apply(find_lon)
data['hs_directory']['lat'] = pd.to_numeric(data['hs_directory']['lat'], errors='coerce')
data['hs_directory']['lon'] = pd.to_numeric(data['hs_directory']['lon'], errors='coerce')
Before combining the datasets, we'll condense some of them so that each value in the 'DBN'
column is unique.
# Condensing the class_size dataset
## Filtering only high schools and 'GEN ED' as the most popular program type
class_size = data['class_size']
class_size = class_size[(class_size['GRADE '] == '09-12')
& (class_size['PROGRAM TYPE'] == 'GEN ED')]
## Calculating average class size per school
class_size = class_size.groupby('DBN').agg(np.mean)
## Resetting index
class_size.reset_index(inplace=True)
## Re-assigning the class_size dataset back to the dictionary
data['class_size'] = class_size
###########################################################################################
# Condensing the demographics dataset
## Filtering the most recent years
data['demographics'] = data['demographics'][data['demographics']['schoolyear'] == 20112012]
###########################################################################################
# Condensing the graduation dataset
## Filtering the most recent full cohort
data['graduation'] = data['graduation'][(data['graduation']['Cohort'] == '2006')
& (data['graduation']['Demographic'] == 'Total Cohort')]
Now, we'll combine all the datasets using the following strategy:
Being the sat_results dataset our main concern, we'll want to preserve as many rows as possible from it while minimizing null values.
While some of the datasets have a lot of missing DBN values, we don't want to lose too many rows (i.e., the data for many high schools) when merging.
Some datasets have DBN values almost identical to those in the sat_results dataset. They also have information we need to keep, and most of our analysis would be impossible if a significant number of rows was missing from those datasets. Therefore, we must avoid missing data in them.
After that, we'll fill missing values.
# Step 1: preserving at maximum the sat_results dataset
combined = data['sat_results']
# Step 2: using left joins
combined = combined.merge(data['ap_2010'], on='DBN', how='left')
combined = combined.merge(data['graduation'], on='DBN', how='left')
# Step 3: using inner joins
to_merge = ['class_size',
'demographics',
'survey',
'hs_directory']
for m in to_merge:
combined = combined.merge(data[m], on='DBN', how='inner')
# Filling missing values
combined = combined.fillna(combined.mean())
combined = combined.fillna(0)
Let's add a column to our combined dataset that specifies the school district.
# Creating a function for extracting the district
def get_first_two_chars(dbn):
return dbn[0:2]
# Creating the 'school_dist' column
combined['school_dist'] = combined['DBN'].apply(get_first_two_chars)
Here we'll take a look at how the 'sat_score'
column correlates with the others.
correlations = combined.corr()['sat_score']
print(correlations[:35])
print(correlations[35:])
SAT Critical Reading Avg. Score 0.986820 SAT Math Avg. Score 0.972643 SAT Writing Avg. Score 0.987771 sat_score 1.000000 AP Test Takers 0.523140 Total Exams Taken 0.514333 Number of Exams with scores 3 4 or 5 0.463245 Total Cohort 0.325144 CSD 0.042948 NUMBER OF STUDENTS / SEATS FILLED 0.394626 NUMBER OF SECTIONS 0.362673 AVERAGE CLASS SIZE 0.381014 SIZE OF SMALLEST CLASS 0.249949 SIZE OF LARGEST CLASS 0.314434 SCHOOLWIDE PUPIL-TEACHER RATIO NaN schoolyear NaN fl_percent NaN frl_percent -0.722225 total_enrollment 0.367857 ell_num -0.153778 ell_percent -0.398750 sped_num 0.034933 sped_percent -0.448170 asian_num 0.475445 asian_per 0.570730 black_num 0.027979 black_per -0.284139 hispanic_num 0.025744 hispanic_per -0.396985 white_num 0.449559 white_per 0.620718 male_num 0.325520 male_per -0.112062 female_num 0.388631 female_per 0.112108 Name: sat_score, dtype: float64 rr_s 0.232199 rr_t -0.023386 rr_p 0.047925 N_s 0.423463 N_t 0.291463 N_p 0.421530 saf_s_11 0.337639 com_s_11 0.187370 eng_s_11 0.213822 aca_s_11 0.339435 saf_t_11 0.313810 com_t_11 0.082419 eng_t_11 0.036906 aca_t_11 0.132348 saf_p_11 0.122913 com_p_11 -0.115073 eng_p_11 0.020254 aca_p_11 0.035155 saf_tot_11 0.318753 com_tot_11 0.077310 eng_tot_11 0.100102 aca_tot_11 0.190966 grade_span_max NaN expgrade_span_max NaN zip -0.063977 total_students 0.407827 number_programs 0.117012 priority08 NaN priority09 NaN priority10 NaN lat -0.121029 lon -0.132222 Name: sat_score, dtype: float64
Unsurprisingly, 'SAT Critical Reading Avg. Score'
, 'SAT Math Avg. Score'
, and 'SAT Writing Avg. Score'
are strongly correlated with 'sat_score'
.
We can also make some other observations:
'total_enrollment'
and its proxies ('total_students'
, 'N_s'
, 'N_p'
, 'N_t'
, 'AP Test Takers'
, 'Total Exams Taken'
, and 'NUMBER OF SECTIONS'
) have a strong positive correlation with 'sat_score'
. This seems counterintuitive: we'd expect smaller schools where students receive more attention to have higher scores.'saf_t_11'
and 'saf_s_11'
) correlate with SAT scores.'aca_s_11'
) correlate with SAT scores, but this doesn't hold for ratings from teachers and parents.'ell_percent'
) has a strong negative correlation with SAT scores.Let's now visualize how the survey columns of our combined dataset correlate with SAT scores. Before, we've created a list of those columns called 'survey_fields'.
import matplotlib.pyplot as plt
%matplotlib inline
print(survey_fields)
['DBN', 'rr_s', 'rr_t', 'rr_p', 'N_s', 'N_t', 'N_p', 'saf_s_11', 'com_s_11', 'eng_s_11', 'aca_s_11', 'saf_t_11', 'com_t_11', 'eng_t_11', 'aca_t_11', 'saf_p_11', 'com_p_11', 'eng_p_11', 'aca_p_11', 'saf_tot_11', 'com_tot_11', 'eng_tot_11', 'aca_tot_11']
First, we'll remove DBN since it's a unique identifier, not a useful numerical value for correlation.
# Removing DBN
survey_fields.remove('DBN')
# Plotting the correlations
combined.corr()['sat_score'][survey_fields].plot.barh(figsize=(15, 15),
color='slateblue',
fontsize=23)
plt.title('SAT scores vs. Survey correlations', fontsize=35)
plt.xlabel('SAT scores', size=23)
plt.show()
From this plot, we can confirm once again some of our observations above:
'N_s'
, 'N_p'
, 'N_t'
) have a strong positive correlation with SAT scores.In addition, this plot allows us to discern some new patterns:
Let's investigate in more detail the correlation of how teachers and students perceive safety and respect at school with SAT scores.
# Plotting 'sat_score' vs. 'saf_s_11'
combined.plot.scatter(x='saf_s_11',
y='sat_score',
figsize=(10, 8),
color='slateblue',
fontsize=14,
s=150,
alpha=0.5)
plt.title('SAT vs. Safety and Respect (from students)', fontsize=22)
plt.xlabel('Safety and Respect scores', size=16)
plt.ylabel('SAT scores', size=16)
plt.show()
# Plotting 'sat_score' vs. 'saf_t_11'
combined.plot.scatter(x='saf_t_11',
y='sat_score',
figsize=(10, 8),
color='slateblue',
fontsize=14,
s=150,
alpha=0.5)
plt.title('SAT vs. Safety and Respect (from teachers)', fontsize=22)
plt.xlabel('Safety and Respect scores', size=16)
plt.ylabel('SAT scores', size=16)
plt.show()
We can clearly see that a positive correlation between safety and respect perception by both students and teachers with SAT scores really exists, even if it isn't so strong. Also, all the schools with "anomalously" high values of SAT scores are related exactly to those with rather high safety and respect scores (starting from around 6.7 according to students and from 7 according to teachers). However, the highest safety and respect scores on both plots are not related to the schools with the highest SAT scores.
It would be interesting to take a look at safety and respect scores by borough.
# Sorting safety and respect scores by borough from the student survey
combined.groupby('boro').agg(np.mean)['saf_s_11'].sort_values(ascending=False)
boro Manhattan 6.831370 Queens 6.721875 Bronx 6.606577 Staten Island 6.530000 Brooklyn 6.370755 Name: saf_s_11, dtype: float64
# Sorting safety and respect scores by borough from the teacher survey
combined.groupby('boro').agg(np.mean)['saf_t_11'].sort_values(ascending=False)
boro Queens 7.365625 Manhattan 7.287778 Staten Island 7.210000 Bronx 7.026882 Brooklyn 6.985849 Name: saf_t_11, dtype: float64
We can deduce that in general, according to both students and teachers, the schools in Manhattan and Queens have the highest safety and respect scores, while those in Brooklyn - the lowest.
Let's look at these scores in more detail, mapping them by district. For this purpose, we'll use the 'saf_tot_11'
column.
from mpl_toolkits.basemap import Basemap
# Grouping the dataframe by district
districts = combined.groupby('school_dist').mean()
districts.reset_index(inplace=True)
# Creating a map
plt.figure(figsize=(15, 10))
m = Basemap(
projection='merc',
llcrnrlat=40.496044,
urcrnrlat=40.915256,
llcrnrlon=-74.255735,
urcrnrlon=-73.700272,
resolution='h'
)
m.drawmapboundary(fill_color='#c1f2f8')
m.drawcoastlines(color='#6D5F47', linewidth=0.4)
m.drawrivers(color='#6D5F47', linewidth=0.4)
m.fillcontinents(color='white')
m.drawcounties(color='black',zorder=999)
longitudes = districts['lon'].tolist()
latitudes = districts['lat'].tolist()
# Plotting districts
m.scatter(
longitudes,
latitudes,
s=200,
zorder=2,
latlon=True,
c=districts['saf_tot_11'],
cmap='RdYlGn' # A traffic-light template, with green - the safest,
) # red - the least safe
plt.colorbar()
plt.title('Average Safety & Respect scores by district', fontsize=23)
plt.show()
It seems that our previous conclusions were actually biased: there is only one district with very low safety and respect score, located in Brooklyn (where we see also the district with the highest score), and this value definitely influences the whole distribution of safety and respect scores, making it heavily left-skewed.
Let's do the same analysis for SAT scores.
# Sorting SAT scores by borough
sat_by_borough = combined.groupby('boro').agg(np.mean)['sat_score'].sort_values(ascending=False)
print(sat_by_borough)
# Creating a map
plt.figure(figsize=(15, 10))
m = Basemap(
projection='merc',
llcrnrlat=40.496044,
urcrnrlat=40.915256,
llcrnrlon=-74.255735,
urcrnrlon=-73.700272,
resolution='h'
)
m.drawmapboundary(fill_color='#c1f2f8')
m.drawcoastlines(color='#6D5F47', linewidth=0.4)
m.drawrivers(color='#6D5F47', linewidth=0.4)
m.fillcontinents(color='white')
m.drawcounties(color='black',zorder=999)
# Plotting districts
m.scatter(
longitudes,
latitudes,
s=200,
zorder=2,
latlon=True,
c=districts['sat_score'],
cmap='rainbow' # A rainbow template, with red - the highest SAT score,
) # violet - the lowest
plt.colorbar()
plt.title('Average SAT scores by district', fontsize=23)
plt.show()
boro Staten Island 1382.500000 Queens 1286.753032 Manhattan 1278.331410 Brooklyn 1181.364461 Bronx 1157.598203 Name: sat_score, dtype: float64
If to look only at the statistics by borough, it looks like the highest SAT scores are related to Staten Island. However, the map shows that this borough is actually represented by only one district, hence it's definitely under-sampled. In Brooklyn and Bronx there are many districts characterized by very low SAT scores. On the other hand, in Brooklyn there is a district with the highest SAT score, and it's the same district that had also the highest safety and respect score on the previous map.
When looking for correlations, we noticed that the total enrollment highly correlates with SAT scores. Let's take a closer look at their relationships.
# Plotting 'sat_score' vs. 'total_enrollment'
combined.plot.scatter(x='total_enrollment',
y='sat_score',
figsize=(10, 8),
color='slateblue',
fontsize=14,
s=150,
alpha=0.5)
plt.title('SAT vs. Total enrollment', fontsize=22)
plt.xlabel('Total enrollment scores', size=16)
plt.ylabel('SAT scores', size=16)
plt.show()
It looks like this correlation really exists, even if not that strong.
We see that the majority of schools have total enrollment less than 1000 students, so it would be interesting to zoom this range.
# Plotting 'sat_score' vs. 'total_enrollment'
combined.plot.scatter(x='total_enrollment',
y='sat_score',
figsize=(10, 8),
color='slateblue',
fontsize=14,
s=150,
alpha=0.5)
plt.title('SAT vs. Total enrollment', fontsize=22)
plt.xlabel('Total enrollment scores', size=16)
plt.ylabel('SAT scores', size=16)
# Zooming the range 0-1000
plt.xlim(0, 1000)
plt.show()
Hence, for the schools with the total enrollment less than 1000 students (that is, for the majority of the schools) the correlation with SAT scores is even more poor than the global trend.
Next, we are going to plot correlations of percentages of different races vs. SAT scores, to determine whether there are any racial differences in SAT performance.
# Creating a list of columns with races
races = ['white_per',
'asian_per',
'black_per',
'hispanic_per']
# Plotting race correlations vs. SAT scores
combined.corr()['sat_score'][races].plot.barh(figsize=(15, 7),
color='slateblue',
fontsize=23)
plt.title('SAT scores vs. Race correlations', fontsize=35)
plt.xlabel('SAT score correlations', size=23)
plt.xlim(-0.4, 0.7)
plt.show()
From these 4 races, White and Asian show strong positive correlation with SAT scores, with the White slightly dominating, while Black and Hispanic - negative correlation, especially strong for the last one.
This strong negative correlation for the Hispanic race looks curious, let's take a closer look at it.
# Plotting 'sat_score' vs. 'hispanic_per'
combined.plot.scatter(x='hispanic_per',
y='sat_score',
figsize=(10, 8),
color='slateblue',
fontsize=14,
s=150,
alpha=0.5)
plt.title('SAT scores vs. Hispanic students percentage', fontsize=22)
plt.xlabel('Hispanic students %', size=16)
plt.ylabel('SAT scores', size=16)
plt.show()
From this plot, we can confirm a strong negative correlation between Hispanic students percentage and SAT scores. For all the schools where this percentage is higher than 25%, the maximum SAT score is never higher than 1500. And as soon as this percentage decreases from 25%, the number of schools with high SAT scores (as well as SAT scores themselves) drastically increases.
Let's find the schools with more than 95% of Hispanic people.
hispanic_greater_95 = combined[combined['hispanic_per'] > 95][['school_name', 'sat_score']]
hispanic_greater_95
school_name | sat_score | |
---|---|---|
44 | Manhattan Bridges High School | 1058.0 |
82 | Washington Heights Expeditionary Learning School | 1174.0 |
89 | Gregorio Luperon High School for Science and M... | 1014.0 |
125 | Academy for Language and Technology | 951.0 |
141 | International School for Liberal Arts | 934.0 |
176 | Pan American International High School at Monroe | 970.0 |
253 | Multicultural High School | 887.0 |
286 | Pan American International High School | 951.0 |
Researching these schools on Google, we discovered that all of them are specialized on teaching immigrants recently arrived from Spanish-speaking countries, who may not be well-prepared for high school. Among these people, there are many unaccompanied minors and students with limited or interrupted formal education in their countries, having trouble reading in Spanish as well as English. Many of these students are older than traditional high school students and must leave school to support their families. From this context, it's not surprising that these schools demonstrate low SAT results.
Now let's turn our attention to the schools with less than 10% of Hispanic students and an average SAT score greater than 1800.
hispanic_less_10_SAT_greater_1800 = combined[(combined['hispanic_per'] < 10)
& (combined['sat_score'] > 1800)][['school_name', 'sat_score']]
hispanic_less_10_SAT_greater_1800
school_name | sat_score | |
---|---|---|
37 | Stuyvesant High School | 2096.0 |
151 | Bronx High School of Science | 1969.0 |
187 | Brooklyn Technical High School | 1833.0 |
327 | Queens High School for the Sciences at York Co... | 1868.0 |
356 | Staten Island Technical High School | 1953.0 |
Google research showed that all of them are prestigious magnet high schools (which in the U.S. education system means public schools with specialized courses or curricula), specialized in technology and science, having very strict admission tests and accepting only city residents. It looks now quite explainable that, first, there are few immigrants and, second, that average SAT scores are very high there.
Let's investigate gender differences in SAT scores.
# Creating a list of columns with genders
genders = ['male_per', 'female_per']
# Plotting genders correlations vs. SAT score correlations
combined.corr()['sat_score'][genders].plot.barh(figsize=(15, 4),
fontsize=23,
color='slateblue')
plt.title('SAT scores vs. Gender correlations', fontsize=35)
plt.xlabel('SAT score correlations', size=23)
plt.show()
We see that the percentage of females shows a slight positive correlation with SAT scores, and those of males, correspondingly, a slight negative one. It can mean that women do better on the SAT than men. To get more insights, we'll plot the female percentage values and SAT scores.
# Plotting 'sat_score' vs. 'female_per'
combined.plot.scatter(x='female_per',
y='sat_score',
figsize=(10, 8),
color='slateblue',
fontsize=14,
s=150,
alpha=0.5)
plt.title('SAT vs. Female percentage', fontsize=22)
plt.xlabel('Female %', size=16)
plt.ylabel('SAT scores', size=16)
# Adding a 50% line
plt.axvline(50, color='black', linestyle='--')
plt.show()
Naturally, if we plot the percentage of males, the graph would be mirrored with respect to the 50% separation line.
We can make the following observations here:
It would be curious to have a look at the schools from the last 2 clusters.
female_less_50_SAT_greater_1700 = combined[(combined['female_per'] < 50)
& (combined['sat_score'] > 1700)][['school_name', 'sat_score', 'female_per']]
female_less_50_SAT_greater_1700
school_name | sat_score | female_per | |
---|---|---|---|
37 | Stuyvesant High School | 2096.0 | 40.7 |
79 | High School for Mathematics, Science and Engin... | 1847.0 | 34.2 |
151 | Bronx High School of Science | 1969.0 | 42.2 |
155 | High School of American Studies at Lehman College | 1920.0 | 46.2 |
187 | Brooklyn Technical High School | 1833.0 | 41.7 |
198 | Brooklyn Latin School, The | 1740.0 | 45.1 |
327 | Queens High School for the Sciences at York Co... | 1868.0 | 43.5 |
356 | Staten Island Technical High School | 1953.0 | 43.0 |
Here we recognize the same elite high schools, specialized in technology and science, which we've already seen before. It's logical that average SAT scores in these schools are so high. In addition, it seems reasonable that the gender gap for these schools, despite being present (taking also into account that science and techology generally attract more men than women), is not that significant, with the minimum percentage of women around 35%. Most probably, this can be conditioned by gender policy applied in such schools.
Let's now find out the schools from the second cluster of high SAT scores. We are especially interested in the uppermost five schools of this cloud, with the amount of women greater than 60% and average SAT scores greater than 1700.
female_greater_60_SAT_greater_1700 = combined[(combined['female_per'] > 60)
& (combined['sat_score'] > 1700)][['school_name', 'sat_score', 'female_per']]
female_greater_60_SAT_greater_1700
school_name | sat_score | female_per | |
---|---|---|---|
5 | Bard High School Early College | 1856.0 | 68.7 |
26 | Eleanor Roosevelt High School | 1758.0 | 67.5 |
60 | Beacon High School | 1744.0 | 61.0 |
61 | Fiorello H. LaGuardia High School of Music & A... | 1707.0 | 73.6 |
302 | Townsend Harris High School | 1910.0 | 71.1 |
Google reserch showed that those are schools with high educational standards, intense curricula, and strict admission requirements. They are mostly specialized in languages, history, social sciences, literature, arts, and music. The highest percentage of women is related to Fiorello H. LaGuardia High School of Music & Art and Performing Arts, which is, as its name suggests, specialized predominantly in different kinds of arts.
Now we'll take a look at the relationship between English learners percentage and SAT scores, since earlier we've noticed a strong negative correlation between them.
# Plotting 'sat_score' vs. 'ell_percent'
combined.plot.scatter(x='ell_percent',
y='sat_score',
figsize=(10, 8),
color='slateblue',
fontsize=14,
s=150,
alpha=0.5)
plt.title('SAT scores vs. English learners percentage', fontsize=22)
plt.xlabel('English learners %', size=16)
plt.ylabel('SAT scores', size=16)
plt.show()
We can notice several things here:
combined[(combined['ell_percent'] > 35) & (combined['sat_score'] > 1400)]['school_name']
46 High School for Dual Language and Asian Studies Name: school_name, dtype: object
This resulted to be a dual language English-Mandarin Chinese academically demanding school.
In the U.S., high school students can take Advanced Placement (AP) exam in a particular subject to earn college credit in that subject.
It makes sense that the number of students at a school who took AP exams would be highly correlated with the school's SAT scores. Let's explore this relationship. Because 'total_enrollment'
is highly correlated with 'sat_score'
, we don't want to bias our results. Instead, we'll look at the percentage of students in each school who took at least one AP exam.
# Calculate the percentage of students in each school who took an AP exam
combined['ap_per'] = combined['AP Test Takers '] * 100/ combined['total_enrollment']
# Plotting 'sat_score' vs. 'ap_per'
combined.plot.scatter(x='ap_per',
y='sat_score',
figsize=(10, 8),
color='slateblue',
fontsize=14,
s=150,
alpha=0.5)
plt.title('SAT vs. AP test taker percentage', fontsize=22)
plt.xlabel('AP test takers %', size=16)
plt.ylabel('SAT scores', size=16)
plt.show()
On this plot, we can distinguish two clusters:
However, there seems to be an issue with the second cluster: many of the values of AP test takers percentage, especially those high, correspond to almost the same value of SAT score, which looks a kind of an average value. One possible explanation here is that this is a consequence of filling missing values, which we did at the beginning of the project after combining datasets. To check this assumption, let's re-run those steps for a test dataset (combined_test) without filling missing values and then re-create the plot above.
# Re-running the code cell [9] for combined_test, without filling missing values
combined_test = data['sat_results']
combined_test = combined_test.merge(data['ap_2010'], on='DBN', how='left')
combined_test = combined_test.merge(data['graduation'], on='DBN', how='left')
to_merge_test = ['class_size', 'demographics', 'survey', 'hs_directory']
for m in to_merge_test:
combined_test = combined_test.merge(data[m], on='DBN', how='inner')
# Re-running the code cell [31] for combined_test
combined_test['ap_per'] = combined_test['AP Test Takers '] * 100/ combined_test['total_enrollment']
combined_test.plot.scatter(x='ap_per',
y='sat_score',
figsize=(10, 8),
color='slateblue',
fontsize=14,
s=150,
alpha=0.5)
plt.title('SAT vs. AP test taker percentage', fontsize=22)
plt.xlabel('AP test takers %', size=16)
plt.ylabel('SAT scores', size=16)
plt.show()
We've just confirmed that indeed there is a strong positive correlation between AP test takers percentage and SAT scores, right as we expected from the beginning. The anomalous cluster that we saw on the first plot was just a consequence of filling missing values, which, evidently, was not a good approach in this case.
Let's now expore the relationship between average class sizes and SAT scores. Presumably, the smaller the class is, the more attention is given to each student, so the average SAT score should be higher.
# Plotting 'sat_score' vs. 'AVERAGE CLASS SIZE'
combined.plot.scatter(x='AVERAGE CLASS SIZE',
y='sat_score',
figsize=(10, 8),
color='slateblue',
fontsize=14,
s=150,
alpha=0.5)
plt.title('SAT vs. Average class size', fontsize=22)
plt.xlabel('Average class size', size=16)
plt.ylabel('SAT scores', size=16)
plt.show()
Surprisingly, we observe a strong positive correlation here. There is also a cluster of schools with very high SAT scores, but even among them we clearly see the same trend.
To finish with the correlations of SAT scores with the other demographic factors, let's investigate their relationship with 'frl_percent'
- free and reduced lunch percentage. It can seem not so straightforward, but this factor serves as an indicator of the income level of a student's family, since free or reduced lunches are, most probably, offered only to the students from low-income families. Earlier we noted that this factor showed a possibility of a strong negative correlation with SAT scores. Let's see it it's confirmed by a scatter plot.
# Plotting 'sat_score' vs. 'frl_percent'
combined.plot.scatter(x='frl_percent',
y='sat_score',
figsize=(10, 8),
color='slateblue',
fontsize=14,
s=150,
alpha=0.5)
plt.title('SAT vs. Free and reduced lunch', fontsize=22)
plt.xlabel('Free and reduced lunch %', size=16)
plt.ylabel('SAT scores', size=16)
plt.show()
We observe an evident strong negative correlation. It means that the students from subsidized categories (i.e., from poor and low-income families) do worse on the SAT than the students from relatively wealthy families.
Now, we'll put apart SAT scores and investigate another aspect of our dataset: the estimations of different types of scores given by parents, teachers, and students. These score types are:
# Creating a list of lists of columns
cols = [
['saf_p_11', 'saf_t_11', 'saf_s_11'],
['com_p_11', 'com_t_11', 'com_s_11'],
['eng_p_11', 'eng_t_11', 'eng_s_11'],
['aca_p_11', 'aca_t_11', 'aca_s_11']
]
# Creating a list of plot titles
titles = [
'Survey comparison: Safety & Respect scores',
'Survey comparison: Communication scores',
'Survey comparison: Engagement scores',
'Survey comparison: Academic expectations scores'
]
# Creating boxplots for each score type + survey
for i in range(len(cols)):
fig = plt.subplots(figsize=(10, 7))
plt.boxplot(combined[cols[i]].values,labels=['Parents', 'Teachers', 'Students'])
plt.title(titles[i], fontsize=23)
pattern = titles[i].split(': ')[1] # Parsing a score type in a plot title
plt.ylabel(pattern, size=16)
plt.tick_params(labelsize=16)
plt.ylim(2, 10)
plt.show()
The tendency here is evident: of the 3 groups of survey respondents, parents tend to give the highest score estimations, teachers - somewhere in the middle, students - the lowest. The largest range of scores for each score type is the one from teacher survey, including also the minimum value of 1.9 for communication score. The biggest difference between median scores is observed for safety and respect score (parent vs. student surveys).
In this project, we cleaned, combined, visualized and analyzed data from different datasets, containing information about SAT scores and demographics in NYC public high schools. In particular, we explored relationships between SAT scores and various demographic factors, in order to detect possible biases in the SAT. Additionally, we explored survey responses from parents, teachers and students of the schools, on how they estimated other factors, possibly influencing learning results. Below are the main findings of our research.