Factors in Education Inequality

Maria Keerthi, Aarushi Dubey, Ayesha Nabiha

Introduction (Part 1: Data Collection)

The early youth of a child is a developmental time where students are learning how to perform many tasks and learn skills, both book smart and street smart, that can help them in life. One of those skills that begins to develop in a young age is literacy in basic math and reading, as the majority of math that one deals with in adulthood, such as basic algebra with money, is taught in middle school, and reading comprehension is key to understanding the majority of events that happen in an adults life - understanding forms, learning new information, searching for housing, etc. Therefore, it is important that all children in this developmental stage have equitable opportunities deserving of them that in such a key growth period, they all have the tools and education necessary to learn such important and long lasting skills such as math and reading comprehension.

However, not all students are given such equally fitted opportunities. The US education system has long been known to have varying standards of education, where differences in education quality begin as early as pre-kindergarten, but not a lot of documentation has been procured to confirm on any large variation in education quality. It is imperative that if these differences in education quality exist, and are continuing to exist over time, then they be resolved on an institutional level.

So, our focus of this tutorial is to confirm if education inequality is reflected by national math and reading examination differences, see if a continuation of inequality in education is occurring, and to recognize factors such as gender or state that may play significant roles in such (if they exist), and use such analysis to predict how future years education inequality will be if the current education system/institution is maintained.

Our null hypothesis will be that gender and state do not have any relationship or impact on math or reading literacy in children in developmental stages. Our alternative hypothesis will be that gender and state have some relationship or impact on math or reading literacy in children in developmental stages. We defined math literacy and reading literacy by the mathematics and reading scores given by student on the NAEP Test - the National Assessment of Educational Progress Test which is a standardized national educational assessment that tracks math and reading progress across the states of the US.

The data that we will be examining can be found here: - specifically the states_all_extended.csv found on the site. The dataset contains compiled US Education data, such as the number of students enrolled in 1st through 12th grade for all states, average math scores for gendered groups from state and year combinations, and more. We decided to specifically focus on the data concerning the average math and average english scores that 4th graders gave on the NAEP test, as it is found by research that 4th grade to 5th grade is the key developmental period for children.

Part 2: Data Management/Representation

First we have to import the necessary libraries that we need to load the dataset. We are using pandas, numpy, and matplotlib.pyplot, geopandas, and statsmodels. Pandas is used for the DataFrame object since that is an easy way to store tabular data. Numpy is used for its math functionality and mathplotlib.pyplot is used to plot graphs demonstrating relationships between variables in our data. Geopandas will be used to create heat maps of our data, and statsmodels will be used for hypothesis testing and finding our p-values.

As an FYI, we were using Jupyter Notebook through the Anaconda distribution for our work. In order for geopandas to be installed and imported in, we had to create a new Anaconda environment with a lower Python version to install geopandas onto our machine, and then we were able to successfully import geopandas in this environment. Aid in this process is heavily credited to mick-d here: https://github.com/conda/conda/issues/9367#issuecomment-628231987

In [240]:
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import geopandas as gpd
import statsmodels.api as sm

Because we had to use an Anaconda environment with a lower Python version, we got some warnings on certain Python commands we were using with our previous higher Python version, but we chose to bypass them right now - we will come back later to update the commands to the correct Python version equivalence!

In [241]:
def warn(*args, **kwargs):
    pass
import warnings
warnings.warn = warn

Now we have to load the data. The data is stored in the "states_all_extended.csv" file and so we have to load it into a DataFrame. This can be done using pandas "read_csv" method. We will store this data in a variable called "school_data".

In [242]:
school_data = pd.read_csv("states_all_extended.csv")

# display first few rows
school_data.head()
Out[242]:
PRIMARY_KEY STATE YEAR ENROLL TOTAL_REVENUE FEDERAL_REVENUE STATE_REVENUE LOCAL_REVENUE TOTAL_EXPENDITURE INSTRUCTION_EXPENDITURE ... G08_HI_A_READING G08_HI_A_MATHEMATICS G08_AS_A_READING G08_AS_A_MATHEMATICS G08_AM_A_READING G08_AM_A_MATHEMATICS G08_HP_A_READING G08_HP_A_MATHEMATICS G08_TR_A_READING G08_TR_A_MATHEMATICS
0 1992_ALABAMA ALABAMA 1992 NaN 2678885.0 304177.0 1659028.0 715680.0 2653798.0 1481703.0 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
1 1992_ALASKA ALASKA 1992 NaN 1049591.0 106780.0 720711.0 222100.0 972488.0 498362.0 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
2 1992_ARIZONA ARIZONA 1992 NaN 3258079.0 297888.0 1369815.0 1590376.0 3401580.0 1435908.0 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
3 1992_ARKANSAS ARKANSAS 1992 NaN 1711959.0 178571.0 958785.0 574603.0 1743022.0 964323.0 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
4 1992_CALIFORNIA CALIFORNIA 1992 NaN 26260025.0 2072470.0 16546514.0 7641041.0 27138832.0 14358922.0 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN

5 rows × 266 columns

Looking at the data, we can see that there are a few columns we will not need. For example PRIMARY_KEY isn't a data point we need to consider when testing our hypothesis so we can get rid of it. We can use the DataFrame method drop and specify the columns we want to drop.

In [243]:
school_data = school_data.drop(columns=['PRIMARY_KEY'])

We only want to use data that is from 2009 and beyond because data before 2009, our dataset did not record gender demographics for the NAEP test result averages.

In [244]:
# get previous number of rows
prev_rows = len(school_data.index)
school_data = school_data[school_data['YEAR'] >= 2009]
# get current number of rows
curr_rows = len(school_data.index)

print(str(prev_rows - curr_rows) + " rows were dropped.")

school_data.head()

1193 rows were dropped.
Out[244]:
STATE YEAR ENROLL TOTAL_REVENUE FEDERAL_REVENUE STATE_REVENUE LOCAL_REVENUE TOTAL_EXPENDITURE INSTRUCTION_EXPENDITURE SUPPORT_SERVICES_EXPENDITURE ... G08_HI_A_READING G08_HI_A_MATHEMATICS G08_AS_A_READING G08_AS_A_MATHEMATICS G08_AM_A_READING G08_AM_A_MATHEMATICS G08_HP_A_READING G08_HP_A_MATHEMATICS G08_TR_A_READING G08_TR_A_MATHEMATICS
867 ALABAMA 2009 745668.0 7186390.0 728795.0 4161103.0 2296492.0 7815467.0 3836398.0 2331552.0 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
868 ALASKA 2009 130236.0 2158970.0 312667.0 1357747.0 488556.0 2396412.0 1129756.0 832783.0 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
869 ARIZONA 2009 981303.0 8802515.0 1044140.0 3806064.0 3952311.0 9580393.0 4296503.0 2983729.0 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
870 ARKANSAS 2009 474423.0 4753142.0 534510.0 3530487.0 688145.0 5017352.0 2417974.0 1492691.0 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
871 CALIFORNIA 2009 6234155.0 73958896.0 9745250.0 40084244.0 24129402.0 74766086.0 35617964.0 21693675.0 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN

5 rows × 265 columns

Since the columns names are a little tricky to figure out, we are going to outline how to read them here:

  • G## - This signifies which grade this value is talking about; for example G04 is referring to grade 4.

  • G##_A_A - This refers to all the students in that grade from all races.

  • G##_x_g - This is read as the number of students of race x and gender g in grade ##; for example G06_AS_M is all asian male students in grade 6.

  • G##_x_g_test - This is average test score of race x and gender g in grade ##; for example G06_AS_A_MATH is the average math score of all asian students in grade 6.

A in place of a gender or race signifies all genders or all races.

The different race codes provided by the dataset are defined as AM - American Indian or Alaska Native, AS - Asian, HI - Hispanic/Latino, BL - Black, WH - White, HP - Hawaiian Native/Pacific Islander and TR - two or more races. (We will not be analyzing individual races in our data analysis, but this information is useful to know for future work.)

Part 3: Exploratory data analysis - Data Visualization/Analysis

We will be doing two parts to our exploratory data analysis.

  • 1) First, we will look to see if any noticeable trends exist between states and average mathematics \& reading scores for 4th grade students over the years - which are indicators of early mathematical and reading literacy skills. To do so, we can generate a 'GROWTH' variable that will calculate the difference between the average 4th grade mathematics/reading scores from 2009 and average 4th grade mathematics/reading score from 2015. We would expect that if there is no education inequality amongst states, then all states should be having the same growth change occur between 2009 to 2015 - whether that be a positive, negative, or stagnant/zero change in average scores - the distribution should be the same. To visualize these comparisons, we generated heat plots to compare all 50 states of the US at once with one another, and analyzed state differences within reading and math.

  • 2) Secondly, we will explore our dataset to see if gender plays a role in mathematic and reading literacy. For such an analysis, we also created a 'GROWTH' variable for female/male and reading/mathematics combinations for each state, out of which we plotted in stacked bar plots for comparison of state and gender on the scores.

State Data Analysis in Math and Reading Literacy Change

In order to create our heat map, we will need to get the grid coordinates of the United States map with states outlines because our geopandas library, which is the geospatial data mapping Python library we will be using, requires the geometrical coordinates for mapping. We pulled our US states map shapefile and other necessary mapping files from the US Census, which can be found here in this zip file: https://www2.census.gov/geo/tiger/GENZ2018/shp/cb_2018_us_state_500k.zip , and the description on the mapping files can be found here: https://www.census.gov/programs-surveys/geography/technical-documentation/naming-convention/cartographic-boundary-file.html . We manually unzipped the files, and added them to the folder our current notebook was in for our use because then only can geopandas have access to the files, but this can be automated.

Specifically, we used the read_file function from the geopandas library that takes in the name of the shapefile file, which is essentially a set of geometrical coordinates, and uses other CAD and plain text files that come along

In [245]:
usa_states = gpd.read_file("cb_2018_us_state_500k.shp")
usa_states.head()
Out[245]:
STATEFP STATENS AFFGEOID GEOID STUSPS NAME LSAD ALAND AWATER geometry
0 28 01779790 0400000US28 28 MS Mississippi 00 121533519481 3926919758 MULTIPOLYGON (((-88.50297 30.21523, -88.49176 ...
1 37 01027616 0400000US37 37 NC North Carolina 00 125923656064 13466071395 MULTIPOLYGON (((-75.72681 35.93584, -75.71827 ...
2 40 01102857 0400000US40 40 OK Oklahoma 00 177662925723 3374587997 POLYGON ((-103.00257 36.52659, -103.00219 36.6...
3 51 01779803 0400000US51 51 VA Virginia 00 102257717110 8528531774 MULTIPOLYGON (((-75.74241 37.80835, -75.74151 ...
4 54 01779805 0400000US54 54 WV West Virginia 00 62266474513 489028543 POLYGON ((-82.64320 38.16909, -82.64300 38.169...

We will be matching our grid coordinates for each state provided in the usa_states dataframe with state educational information in our school_data dataframe. Let's see what states or territories are provided in both dataframe.

In [246]:
print("We have grid coordinates for: {}".format(list(usa_states["NAME"])))

We have grid coordinates for: ['Mississippi', 'North Carolina', 'Oklahoma', 'Virginia', 'West Virginia', 'Louisiana', 'Michigan', 'Massachusetts', 'Idaho', 'Florida', 'Nebraska', 'Washington', 'New Mexico', 'Puerto Rico', 'South Dakota', 'Texas', 'California', 'Alabama', 'Georgia', 'Pennsylvania', 'Missouri', 'Colorado', 'Utah', 'Tennessee', 'Wyoming', 'New York', 'Kansas', 'Alaska', 'Nevada', 'Illinois', 'Vermont', 'Montana', 'Iowa', 'South Carolina', 'New Hampshire', 'Arizona', 'District of Columbia', 'American Samoa', 'United States Virgin Islands', 'New Jersey', 'Maryland', 'Maine', 'Hawaii', 'Delaware', 'Guam', 'Commonwealth of the Northern Mariana Islands', 'Rhode Island', 'Kentucky', 'Ohio', 'Wisconsin', 'Oregon', 'North Dakota', 'Arkansas', 'Indiana', 'Minnesota', 'Connecticut']
In [247]:
print("We have state math and reading score information for: {}".format(list(school_data["STATE"].unique())))

We have state math and reading score information for: ['ALABAMA', 'ALASKA', 'ARIZONA', 'ARKANSAS', 'CALIFORNIA', 'COLORADO', 'CONNECTICUT', 'DELAWARE', 'DISTRICT_OF_COLUMBIA', 'FLORIDA', 'GEORGIA', 'HAWAII', 'IDAHO', 'ILLINOIS', 'INDIANA', 'IOWA', 'KANSAS', 'KENTUCKY', 'LOUISIANA', 'MAINE', 'MARYLAND', 'MASSACHUSETTS', 'MICHIGAN', 'MINNESOTA', 'MISSISSIPPI', 'MISSOURI', 'MONTANA', 'NEBRASKA', 'NEVADA', 'NEW_HAMPSHIRE', 'NEW_JERSEY', 'NEW_MEXICO', 'NEW_YORK', 'NORTH_CAROLINA', 'NORTH_DAKOTA', 'OHIO', 'OKLAHOMA', 'OREGON', 'PENNSYLVANIA', 'RHODE_ISLAND', 'SOUTH_CAROLINA', 'SOUTH_DAKOTA', 'TENNESSEE', 'TEXAS', 'UTAH', 'VERMONT', 'VIRGINIA', 'WASHINGTON', 'WEST_VIRGINIA', 'WISCONSIN', 'WYOMING', 'DODEA', 'NATIONAL']

Looking at our State values for both the grid coordinate data (usa_states) and the math/reading score data (school_data), we can see that the school_data dataframe does not contain information on the United States Virgin Islands, American Samoa, Puerto Rico, Guam, or the Commonwealth of the Northern Mariana Islands. Therefore, we will need to drop those territories' information from our grid data, and create a final grid data dataframe called 'states_coords.'

In [248]:
# Dropping territories that do not have data in the education data dataset
states_coords = usa_states[usa_states.NAME != "United States Virgin Islands"]
states_coords = states_coords[states_coords.NAME != "American Samoa"]
states_coords = states_coords[states_coords.NAME != "Puerto Rico"]
states_coords = states_coords[states_coords.NAME != "Guam"]
states_coords = states_coords[states_coords.NAME != "Commonwealth of the Northern Mariana Islands"]
states_coords = states_coords.sort_values(by = ['NAME']) # For readability

We can also notice that the formatting of the state names in the two dataframes differs. Since our geopandas libarary will need our mapping and statistical information to be merged together, we need to merge them on a common key value, which can be the state names. Therefore, we updated the formatting of the NAME variable in states_coords with the STATE variable formatting in school_data.

In [249]:
# Matching formatting of NAME variable in states_coords with STATE variable formatting in education data 
for row, curr_state in states_coords.iterrows():
    states_coords.at[row, 'NAME'] = curr_state['NAME'].replace(' ', '_')
    states_coords.at[row, 'NAME'] = states_coords.at[row, 'NAME'].upper()
    
states_coords = states_coords.rename(columns = {"NAME": "STATE"})
states_coords.head()
Out[249]:
STATEFP STATENS AFFGEOID GEOID STUSPS STATE LSAD ALAND AWATER geometry
17 01 01779775 0400000US01 01 AL ALABAMA 00 131174048583 4593327154 MULTIPOLYGON (((-88.05338 30.50699, -88.05109 ...
27 02 01785533 0400000US02 02 AK ALASKA 00 1478839695958 245481577452 MULTIPOLYGON (((179.48246 51.98283, 179.48656 ...
35 04 01779777 0400000US04 04 AZ ARIZONA 00 294198551143 1027337603 POLYGON ((-114.81629 32.50804, -114.81432 32.5...
52 05 00068085 0400000US05 05 AR ARKANSAS 00 134768872727 2962859592 POLYGON ((-94.61783 36.49941, -94.61765 36.499...
16 06 01779778 0400000US06 06 CA CALIFORNIA 00 403503931312 20463871877 MULTIPOLYGON (((-118.60442 33.47855, -118.5987...

Vice versa, we can also see that the grid coordinate dataset does not have any DODEA or NATIONAL values (which are present in the school_data, so we can drop those values from the school_data dataframe.

We can also isolate our 2009 school_data values and 2015 school_data values from the main school_data frame right now, as we will use this information soon. As we only care about the grade 4 average score values, we can drop other extra columns not relevant to us such as revenues on a federal or state level, enrollment amounts, etc.

In [250]:
# Dropping state values not relevant in education dataset for 2009
data_2009 = school_data[school_data['YEAR'] == 2009]
data_2009 = data_2009[data_2009.STATE != "DODEA"]
data_2009 = data_2009[data_2009.STATE != "NATIONAL"]
data_2009.drop('TOTAL_REVENUE', inplace=True, axis=1)
data_2009.drop('FEDERAL_REVENUE', inplace=True, axis=1)
data_2009.drop('STATE_REVENUE', inplace=True, axis=1)
data_2009.drop('LOCAL_REVENUE', inplace=True, axis=1)
data_2009.drop('ENROLL', inplace=True, axis=1)
data_2009.drop('TOTAL_EXPENDITURE', inplace=True, axis=1)
data_2009.drop('CAPITAL_OUTLAY_EXPENDITURE', inplace=True, axis=1)
data_2009.drop('INSTRUCTION_EXPENDITURE', inplace=True, axis=1)
data_2009.drop('SUPPORT_SERVICES_EXPENDITURE', inplace=True, axis=1)
data_2009.drop('OTHER_EXPENDITURE', inplace=True, axis=1)
data_2009 = data_2009.sort_values(by = ['STATE']) # For readability
data_2009 = data_2009.reset_index()
data_2009.drop('index', inplace=True, axis=1)
data_2009.head()
Out[250]:
STATE YEAR A_A_A G01_A_A G02_A_A G03_A_A G04_A_A G05_A_A G06_A_A G07_A_A ... G08_HI_A_READING G08_HI_A_MATHEMATICS G08_AS_A_READING G08_AS_A_MATHEMATICS G08_AM_A_READING G08_AM_A_MATHEMATICS G08_HP_A_READING G08_HP_A_MATHEMATICS G08_TR_A_READING G08_TR_A_MATHEMATICS
0 ALABAMA 2009 748889.0 57821.0 56628.0 58608.0 59512.0 58656.0 58231.0 58118.0 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
1 ALASKA 2009 131661.0 9926.0 9827.0 10032.0 10046.0 9864.0 9567.0 9657.0 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
2 ARIZONA 2009 1077831.0 85725.0 84033.0 84060.0 83686.0 83193.0 81987.0 82050.0 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
3 ARKANSAS 2009 480559.0 37665.0 36934.0 36903.0 36479.0 36489.0 35958.0 36113.0 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN
4 CALIFORNIA 2009 6263438.0 470783.0 459334.0 459813.0 465866.0 460248.0 461373.0 466893.0 ... NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN

5 rows × 255 columns

And we do the same for the 2015 education dataset.

In [251]:
# Dropping state values not relevant in education dataset for 2015
data_2015 = school_data[school_data['YEAR'] == 2015]
data_2015 = data_2015[data_2015.STATE != "DODEA"]
data_2015 = data_2015[data_2015.STATE != "NATIONAL"]
data_2015.drop('TOTAL_REVENUE', inplace=True, axis=1)
data_2015.drop('FEDERAL_REVENUE', inplace=True, axis=1)
data_2015.drop('STATE_REVENUE', inplace=True, axis=1)
data_2015.drop('LOCAL_REVENUE', inplace=True, axis=1)
data_2015.drop('ENROLL', inplace=True, axis=1)
data_2015.drop('TOTAL_EXPENDITURE', inplace=True, axis=1)
data_2015.drop('CAPITAL_OUTLAY_EXPENDITURE', inplace=True, axis=1)
data_2015.drop('INSTRUCTION_EXPENDITURE', inplace=True, axis=1)
data_2015.drop('SUPPORT_SERVICES_EXPENDITURE', inplace=True, axis=1)
data_2015.drop('OTHER_EXPENDITURE', inplace=True, axis=1)
data_2015 = data_2015.sort_values(by = ['STATE']) # For readability
data_2015 = data_2015.reset_index()
data_2015.head()
Out[251]:
index STATE YEAR A_A_A G01_A_A G02_A_A G03_A_A G04_A_A G05_A_A G06_A_A ... G08_HI_A_READING G08_HI_A_MATHEMATICS G08_AS_A_READING G08_AS_A_MATHEMATICS G08_AM_A_READING G08_AM_A_MATHEMATICS G08_HP_A_READING G08_HP_A_MATHEMATICS G08_TR_A_READING G08_TR_A_MATHEMATICS
0 1173 ALABAMA 2015 743789.0 59023.0 58766.0 57963.0 55808.0 55340.0 54900.0 ... 252.0 260.0 NaN NaN NaN NaN NaN NaN NaN NaN
1 1174 ALASKA 2015 132477.0 10587.0 10512.0 10441.0 10118.0 9793.0 9648.0 ... 263.0 279.0 260.0 282.0 231.0 257.0 242.0 NaN 270.0 285.0
2 1175 ARIZONA 2015 1109040.0 84804.0 87325.0 88194.0 86594.0 85719.0 85202.0 ... 254.0 273.0 NaN NaN 244.0 260.0 NaN NaN NaN NaN
3 1176 ARKANSAS 2015 492132.0 38160.0 38590.0 38410.0 35893.0 35850.0 36020.0 ... 255.0 269.0 NaN NaN NaN NaN NaN NaN NaN NaN
4 1177 CALIFORNIA 2015 6226737.0 444573.0 463881.0 470157.0 485885.0 476427.0 471467.0 ... 249.0 263.0 279.0 304.0 NaN NaN NaN NaN 263.0 289.0

5 rows × 256 columns

Now, we will create a dataframe to hold the calculated differences between grade 4 reading and math scores from 2009 to 2015 (2015 minus 2009) per state that we will soon use for our visualization. To do so, we will traverse through the 2009 and 2015 dataframes concurrently, and pull out each states math and reading scores for all students, and subtract them from one another. This difference in average scores in math and reading will be recorded for each state for map visualization.

In [252]:
# Adding the states to our empty dataframe
g04_15to09_states = pd.DataFrame()
g04_15to09_states[['STATE']] = data_2015[['STATE']]

# Traversing through 2009 and 2015 score dataset and tracking differences
for ind, currstate in data_2009.iterrows():
    read_val2015 = float(data_2015.at[ind, "G04_A_A_READING"])
    read_val2009 = float(data_2009.at[ind, "G04_A_A_READING"])
    read_diff = read_val2015 - read_val2009
    g04_15to09_states.at[ind, "READ_GROWTH"] = read_diff
    
    math_val2015 = float(data_2015.at[ind, "G04_A_A_MATHEMATICS"])
    math_val2009 = float(data_2009.at[ind, "G04_A_A_MATHEMATICS"])
    math_diff = math_val2015 - math_val2009
    g04_15to09_states.at[ind, "MATH_GROWTH"] = math_diff
In [253]:
g04_15to09_states.head()
Out[253]:
STATE READ_GROWTH MATH_GROWTH
0 ALABAMA 1.0 3.0
1 ALASKA 2.0 -1.0
2 ARIZONA 5.0 8.0
3 ARKANSAS 2.0 -3.0
4 CALIFORNIA 3.0 0.0

Now, we will need to merge the dataframe containing the grid coordinates and the dataframe containing the math/reading difference/growth variables together for our future heat map plotting.

In [254]:
map_and_stats = states_coords.merge(g04_15to09_states, on="STATE")
map_and_stats.head()
Out[254]:
STATEFP STATENS AFFGEOID GEOID STUSPS STATE LSAD ALAND AWATER geometry READ_GROWTH MATH_GROWTH
0 01 01779775 0400000US01 01 AL ALABAMA 00 131174048583 4593327154 MULTIPOLYGON (((-88.05338 30.50699, -88.05109 ... 1.0 3.0
1 02 01785533 0400000US02 02 AK ALASKA 00 1478839695958 245481577452 MULTIPOLYGON (((179.48246 51.98283, 179.48656 ... 2.0 -1.0
2 04 01779777 0400000US04 04 AZ ARIZONA 00 294198551143 1027337603 POLYGON ((-114.81629 32.50804, -114.81432 32.5... 5.0 8.0
3 05 00068085 0400000US05 05 AR ARKANSAS 00 134768872727 2962859592 POLYGON ((-94.61783 36.49941, -94.61765 36.499... 2.0 -3.0
4 06 01779778 0400000US06 06 CA CALIFORNIA 00 403503931312 20463871877 MULTIPOLYGON (((-118.60442 33.47855, -118.5987... 3.0 0.0

We can now plot a heat map of the 50 states of the US on their changes in average math and reading scores on the NAEP test from 2009 to 2015. We can first plot a heat map for just the reading score change distribution from 2009 to 2015 for analysis.

In [255]:
fig, ax = plt.subplots(1, figsize=(14, 14))
plt.xticks(rotation=90)
map_and_stats.plot(column = "READ_GROWTH", cmap = "RdYlGn", 
                   linewidth = 0.4, ax = ax, edgecolor = ".4")
ax.set_title('Heat Map of Growth in Reading Literacy for 4th Graders from 2009 to 2016')
bar_info = plt.cm.ScalarMappable(cmap="RdYlGn", norm=plt.Normalize(vmin= -6, vmax=6))
bar_info._A = []

#https://stackoverflow.com/questions/18195758/set-matplotlib-colorbar-size-to-match-graph
cax = fig.add_axes([ax.get_position().x1 + 0.01,ax.get_position().y0,0.05,ax.get_position().height])

cbar = fig.colorbar(bar_info, cax = cax)
ax.set_xlim(-130, -60)
ax.set_ylim(25, 50)
ax.axis("off")
Out[255]:
(-130.0, -60.0, 25.0, 50.0)

Created with help from https://towardsdatascience.com/making-heat-maps-with-literal-maps-how-to-use-python-to-construct-a-chloropleth-6b65e4e33905

(Our map excludes Hawaii and Alaska due to some mapping configuration issues - but just as an FYI, Alaska had a growth of 1.0 and Hawaii had a growth of 2.0).

Well, this is interesting! If education was being distributed on an equal level across states, then we would expect to see the same amount of growth, whether positive, negative, or none, in the change in reading literacy of 4th graders from 2009 to 2015. As a reminder, we are measuring reading literacy growth by taking the difference of a state's average score for eight graders taking the NAEP reading exam in 2015 from that of the state in 2009. In terms of our heatmap, if we maintain our expectation of equal education occuring, we would expect to see the same color, aka the same growth amount, across all states. However, as we can see by our heatmap above, not all states are experiencing the same growth/change in reading literacy - we have states such as Lousiana and North Carolina which have gone up 3 to 6 points in average reading scores on the NAEP reading exam over 6 year. This is a positive that we would hope to see in our heatmap - that states' reading scores have been improving over the years! However, we can notice that there are other states such as Kansas, and, our state, Maryland, that have gone down by 6 points in a 6 year time span in reading literacy. Looking at the map, we can assess that even other states of the USA are fluctuating in their reading literacy patterns - which is an indicator that reading literacy growth can be dependent on state over time, indicative of there being education inequality by state.

Let's curate a similar heat map for growth in math literacy in 4th graders across the states from 2009 to 2015, and see what the results are there.

In [256]:
fig, ax = plt.subplots(1, figsize=(14, 14))
plt.xticks(rotation=90)
map_and_stats.plot(column = "MATH_GROWTH", cmap = "RdYlBu", 
                   linewidth = 0.4, ax = ax, edgecolor = ".4")
ax.set_title('Heat Map of Growth in Mathematics Literacy for 4th Graders from 2009 to 2016')
bar_info = plt.cm.ScalarMappable(cmap="RdYlBu", norm=plt.Normalize(vmin= -6, vmax=6))
bar_info._A = []

#https://stackoverflow.com/questions/18195758/set-matplotlib-colorbar-size-to-match-graph
cax = fig.add_axes([ax.get_position().x1 + 0.01,ax.get_position().y0,0.05,ax.get_position().height])

cbar = fig.colorbar(bar_info, cax = cax)
ax.set_xlim(-130, -60)
ax.set_ylim(25, 50)
ax.axis("off")
Out[256]:
(-130.0, -60.0, 25.0, 50.0)

Interesting! Regarding math literacy growth, 4th grade students in New York, Vermont, Maryland, New Jersey, and Kansas seem to have gone down by almost 5 to 6 points in their average mathematics score in NAEP mathematics exams from 2009 to 2015, which is a bit disheartening to see. It is noticeable that Maryland and Kansas notably also had a maximum negative growth in reading literacy as well from 2009 to 2015, but New York, Vermont, and New Jersey had, though negative growth, a slightly smaller point decrease - only about 3 to 4 points downward in reading literacy.

In comparing the heat maps for change in math literacy versus change in reading literacy across states from 2009 to 2015, we can also notice that states such as Tenessee, Texas, and Alabama that they had no growth to little positive growth of 0 to 2 points in mathematics literacy over the 6 years, but had negative growth between 2 to 6 points in reading literacy - which might indicate to us that even within educational standards, reading standards of education and math standards of educations may be differing state by state.

Gender and State Data Analysis in Math and Reading Literacy Change

Now, students within a state are not all just one type of person. We can try to look to see how much gendered experiences, with the bounds of "MALE" and "FEMALE", within a state's education are affecting 4th grade students' math and reading literacy growths over the years. In order to compare to see if gendered experiences affect the growths, we can create stacked bar plots to visualize the changes in reading and mathematics growth in comparison for each state.

The code below traverses through the STATE indices of the 2009 education dataset and the 2015 education dataset concurrently, and pulls out the average math or reading score for 4th graders on the NAEP Test for each state and gender (Female or Male) combination possible. After pulling out those values for 2009 and 2015, we subtract the 2009 average from the 2015 average, and we record these differences for each subject (math or reading) and gender (male or female) combination for graphing purposes later on.

In [257]:
states = []
female_math_change = []
male_math_change = []
female_read_change = []
male_read_change = []

for ind, currstate in data_2009.iterrows():
    states.append(map_and_stats["STUSPS"][ind])
    
    # READING CHANGE for FEMALE
    f_read_val2015 = float(data_2015.at[ind, "G04_A_F_READING"])
    f_read_val2009 = float(data_2009.at[ind, "G04_A_F_READING"])
    f_read_diff = f_read_val2015 - f_read_val2009
    female_read_change.append(f_read_diff)
    
    # MATH CHANGE for FEMALE
    f_math_val2015 = float(data_2015.at[ind, "G04_A_F_MATHEMATICS"])
    f_math_val2009 = float(data_2009.at[ind, "G04_A_F_MATHEMATICS"])
    f_math_diff = f_math_val2015 - f_math_val2009
    female_math_change.append(f_math_diff)
    
    # READING CHANGE for MALE
    m_read_val2015 = float(data_2015.at[ind, "G04_A_M_READING"])
    m_read_val2009 = float(data_2009.at[ind, "G04_A_M_READING"])
    m_read_diff = m_read_val2015 - m_read_val2009
    male_read_change.append(m_read_diff)
    
    # MATH CHANGE for MALE
    m_math_val2015 = float(data_2015.at[ind, "G04_A_M_MATHEMATICS"])
    m_math_val2009 = float(data_2009.at[ind, "G04_A_M_MATHEMATICS"])
    m_math_diff = m_math_val2015 - m_math_val2009
    male_math_change.append(m_math_diff)

Great! Now we can plot our growth values. The following code produces a stacked bar plot for the 50 states and the changes between the average mathematics scores from 2009 to 2015 for male and female students per state.

In [258]:
# MATH GROWTH
state_locs = np.arange(len(states)) # the state label locations
bar_width = 0.55  # the width of the bars

fig, ax = plt.subplots(1, figsize=(15, 10))
male_bars = ax.bar(states, male_math_change, bar_width, label = 'MALE', color = 'magenta')
female_bars = ax.bar(states, female_math_change, bar_width, 
                     bottom = male_math_change, label = 'FEMALE', 
                     color = (0.2, 0.7, 0.9, 0.5))

ax.bar_label(male_bars, padding = 4)
ax.bar_label(female_bars, padding = 4)
ax.set_xlabel('State', fontsize = 15)
ax.set_ylabel('Change in Average Math Score', fontsize = 15)
ax.set_title('Mathematics Growth from \'09 to \'15 in NAEP Test by State and Gender', fontsize = 15)
ax.set_xticks(state_locs, states)
ax.legend()

fig.tight_layout()

plt.show()

The following code produces a stacked bar plot for the 50 states and the changes between the average reading scores from 2009 to 2015 for male and female students per state.

In [259]:
# READING
state_locs = np.arange(len(states)) # the state label locations
bar_width = 0.55  # the width of the bars

fig, ax = plt.subplots(1, figsize=(15, 10))
male_bars = ax.bar(states, male_read_change, bar_width, label = 'MALE', color = 'orange')
female_bars = ax.bar(states, female_read_change, bar_width, 
                     bottom = male_read_change, label = 'FEMALE', 
                     color = (0.2, 0.7, 0.9, 0.5))

ax.bar_label(male_bars, padding = 4)
ax.bar_label(female_bars, padding = 4)
ax.set_xlabel('State', fontsize = 15)
ax.set_ylabel('Change in Average Reading Score', fontsize = 15)
ax.set_title('Reading Growth from \'09 to \'15 in NAEP Test by State and Gender', fontsize = 15)
ax.set_xticks(state_locs, states)
ax.legend()

fig.tight_layout()

plt.show()

Let's analyze our math growth plot first. Looking at our change in average math scores per state by gender bar plot, we can notice that female students tended to be on either extremes of math score changes, whereas male students tended to fluctuate less between exteme jumps in score from 2009 to 2015. 38 out of the 50 states/territories had female students having a larger difference - whether negative or positive - in average math scores from 2009 to 2015. This could be explained by the circumstance of two situations often pushed onto 'female' gendered students: 1) those who are gendered as female often have the 'dumb' or 'not smart enough' stereotype pushed onto them, which may become enough reasoning by communities or individuals to push expectations onto such students to do better on these examinations, and 2) those who are gendered as female are also considered to not supposed to worry over education in comparison to other ideal such as homemaking, which can be pushed onto such children at an early age.

Next, let's look at that math plot in comparison our reading growth plot. We can notice that there seem to be only 15 states that had at least one gender (FEMALE or MALE) having a negative point decrease in their state's average reading score on the NAEP test for 4th graders from 2009 to 2015, which is a smaller amount then the 29 states that had at least one gender having a negative point decrease for that state's average math scores from the same population. Specifically, we can see that the differences on the various states between FEMALE and MALE reading scores seems to be a bit smaller in comparison to the breadth of differences for that of math scores, but FEMALE average point jumps in reading still seem to be larger then those for MALE average point jumpts that are positive. We can also notice that DC seems to have the largest positive point increase from 2009 in both MALE and FEMALE groups for both average math and average reading scores, indicating that DC's math and reading standards of teaching may be a good model for other states. Though, it would be interesting to see why FEMALE students had such a higher jump in comparison to MALE students.

The exploratory data analysis has given us some idea of what we should expect when developing our predictive models below, which could be that FEMALE gender has more weight in influencing more drastic average math scores for each state, and that there might be less negative growths in the reading growths.

Part 4: Hypothesis Testing/Model Development

Test Score Growth per State Prediction

One of the predictive models we are going to create will be predicting the change in average test scores in Grade 4 based on previous years data for each state. First, we are going to remove all the columns except for state, and the average test scores for math and reading, and drop rows that include regions outside of the 50 states.

In [260]:
# get columns needed
state_avg = school_data[['STATE', 'YEAR', 'G04_A_A_READING', 'G04_A_A_MATHEMATICS']]
state_avg = state_avg[state_avg.STATE != "DODEA"] # dropping rows that are not relevant states
state_avg = state_avg[state_avg.STATE != "NATIONAL"] # dropping rows that are not relevant states
state_avg.head()
Out[260]:
STATE YEAR G04_A_A_READING G04_A_A_MATHEMATICS
867 ALABAMA 2009 216.0 228.0
868 ALASKA 2009 211.0 237.0
869 ARIZONA 2009 210.0 230.0
870 ARKANSAS 2009 216.0 238.0
871 CALIFORNIA 2009 210.0 232.0

Similar to our exploratory data analysis, to create a metric for how the test scores have improved or worsened, we are subtracting the 2009 average reading and math scores from another years average reading and math scores for each state to define how much the average math and reading test scores have changed since 2009. We are storing this metric in a new column, "READING_GROWTH" and "MATH_GROWTH".

In [261]:
# set reading growth to NaN first
state_avg['READING_GROWTH'] = np.NaN

# method to process each row and return the reading average in 2009
def process_reading(row):
    state = row['STATE']
    new = state_avg.loc[state_avg['STATE'] == state]
    new = new.loc[new['YEAR'] == 2009]
    return new['G04_A_A_READING']

# in each row update the reading growth value with the difference between this value and the value in 2009
for i, row in state_avg.iterrows():
    state_avg.at[i, 'READING_GROWTH'] = row['G04_A_A_READING'] - process_reading(row)
    
state_avg['MATHEMATICS_GROWTH'] = np.NaN

# similar function as reading, but for mathematics
def process_reading(row):
    state = row['STATE']
    new = state_avg.loc[state_avg['STATE'] == state]
    new = new.loc[new['YEAR'] == 2009]
    return new['G04_A_A_MATHEMATICS']
 
for i, row in state_avg.iterrows():
    state_avg.at[i, 'MATHEMATICS_GROWTH'] = row['G04_A_A_MATHEMATICS'] - process_reading(row)
    
state_avg.head()
Out[261]:
STATE YEAR G04_A_A_READING G04_A_A_MATHEMATICS READING_GROWTH MATHEMATICS_GROWTH
867 ALABAMA 2009 216.0 228.0 0.0 0.0
868 ALASKA 2009 211.0 237.0 0.0 0.0
869 ARIZONA 2009 210.0 230.0 0.0 0.0
870 ARKANSAS 2009 216.0 238.0 0.0 0.0
871 CALIFORNIA 2009 210.0 232.0 0.0 0.0

Since each state counts as a unique independent variable, we can use the pandas method get_dummies to create a dataframe where each state is represented by either 1 or 0, 1 if the data value is in that state and 0 if the data value is not in that state. Then we will drop the Alabama column because if all the other states are 0 we can assume that the data value must be in Alabama.

In [262]:
# get dummies
state_avg = pd.get_dummies(state_avg, columns=['STATE'])
# drop alabama and reading and mathematics averages since we no longer need them
state_avg = state_avg.drop(columns=['STATE_ALABAMA', 'G04_A_A_READING', 'G04_A_A_MATHEMATICS'])

state_avg.head()
Out[262]:
YEAR READING_GROWTH MATHEMATICS_GROWTH STATE_ALASKA STATE_ARIZONA STATE_ARKANSAS STATE_CALIFORNIA STATE_COLORADO STATE_CONNECTICUT STATE_DELAWARE ... STATE_SOUTH_DAKOTA STATE_TENNESSEE STATE_TEXAS STATE_UTAH STATE_VERMONT STATE_VIRGINIA STATE_WASHINGTON STATE_WEST_VIRGINIA STATE_WISCONSIN STATE_WYOMING
867 2009 0.0 0.0 0 0 0 0 0 0 0 ... 0 0 0 0 0 0 0 0 0 0
868 2009 0.0 0.0 1 0 0 0 0 0 0 ... 0 0 0 0 0 0 0 0 0 0
869 2009 0.0 0.0 0 1 0 0 0 0 0 ... 0 0 0 0 0 0 0 0 0 0
870 2009 0.0 0.0 0 0 1 0 0 0 0 ... 0 0 0 0 0 0 0 0 0 0
871 2009 0.0 0.0 0 0 0 1 0 0 0 ... 0 0 0 0 0 0 0 0 0 0

5 rows × 53 columns

Now we have to split apart the dataset into a train and test dataset so that we can use the test dataset to determine how accurate our predictor is. We are going to predict the years 2017, 2018, and 2019 so we will use those rows as our test data and the rest as our train data. Another note is that not all the years between 2009 to 2019 have recorded average reading and math scores for states in the US. Therefore, when we are splitting our data, we will only keep the values that are actual numeric values, and not NaN values, for both our training and testing sets.

In [263]:
# drop the NaN rows
train_data = state_avg[state_avg['YEAR'] < 2017].dropna()
test_data = state_avg[state_avg['YEAR'] >= 2017].dropna()

We can use Linear SVM from sklearn to make a regression model that will predict the expected increase or decrease in average scores for math and reading. We will make one each for reading and one for mathematics. But first, we have to separate our independent variable (state with year) and dependent (growth) variable.

In [264]:
from sklearn.linear_model import LinearRegression

X_reading = [] # independent values for reading
y_reading = [] # dependent values for reading
X_math = [] # independent values for math
y_math = [] # dependent values for reading

# iterate through each row and add the year and state to the X variables and the growths to the y variables
for i, row in train_data.iterrows():
    add = row[3:].tolist()
    add.insert(0, row['YEAR'])
    X_reading.append(add)
    y_reading.append(row['READING_GROWTH'])
    X_math.append(add)
    y_math.append(row['MATHEMATICS_GROWTH'])

We are going to use the Linear Regression model to fit the X (state with year) and y (growth increase/decrease) variables and create a prediction model. Then, we will add the predicted growths done on our testing dataset to a separate column in the test_data DataFrame so we can easily compare the values.

In [265]:
# create reading regression and math regression
reading_regr = LinearRegression().fit(X_reading, y_reading)
mathematics_regr = LinearRegression().fit(X_math, y_math)

X_test_reading = []
X_test_math = []

# accumulate X values for reading and math
for i, row in test_data.iterrows():
    add = row[3:].tolist()
    add.insert(0, row['YEAR'])
    X_test_reading.append(add)
    X_test_math.append(add)
    
# predict based of X values
test_data['PREDICT_READING'] = reading_regr.predict(X_test_reading)
test_data['PREDICT_MATH'] = mathematics_regr.predict(X_test_math)

test_data.head()
Out[265]:
YEAR READING_GROWTH MATHEMATICS_GROWTH STATE_ALASKA STATE_ARIZONA STATE_ARKANSAS STATE_CALIFORNIA STATE_COLORADO STATE_CONNECTICUT STATE_DELAWARE ... STATE_TEXAS STATE_UTAH STATE_VERMONT STATE_VIRGINIA STATE_WASHINGTON STATE_WEST_VIRGINIA STATE_WISCONSIN STATE_WYOMING PREDICT_READING PREDICT_MATH
1281 2017 0.0 4.0 0 0 0 0 0 0 0 ... 0 0 0 0 0 0 0 0 3.642157 3.666667
1288 2017 -4.0 -7.0 1 0 0 0 0 0 0 ... 0 0 0 0 0 0 0 0 0.892157 0.166667
1295 2017 5.0 4.0 0 1 0 0 0 0 0 ... 0 0 0 0 0 0 0 0 4.142157 6.666667
1302 2017 0.0 -4.0 0 0 1 0 0 0 0 ... 0 0 0 0 0 0 0 0 3.142157 0.666667
1309 2017 5.0 0.0 0 0 0 1 0 0 0 ... 0 0 0 0 0 0 0 0 3.392157 1.916667

5 rows × 55 columns

To analyze if being in a particular state does affect growth of reading and math test scores, we can use statsmodel to see the p value of each coefficient, which will be the states with year, we are passing into the model.

In [266]:
# create statsmodel for reading data
p_reading = sm.OLS(train_data['READING_GROWTH'].tolist(), sm.add_constant(X_reading)).fit()
p_reading.summary()
Out[266]:
OLS Regression Results
Dep. Variable: y R-squared: 0.501
Model: OLS Adj. R-squared: 0.334
Method: Least Squares F-statistic: 2.997
Date: Mon, 16 May 2022 Prob (F-statistic): 1.12e-07
Time: 15:54:25 Log-Likelihood: -381.05
No. Observations: 204 AIC: 866.1
Df Residuals: 152 BIC: 1039.
Df Model: 51
Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975]
const -658.8039 114.346 -5.762 0.000 -884.716 -432.892
x1 0.3284 0.057 5.779 0.000 0.216 0.441
x2 -2.7500 1.283 -2.143 0.034 -5.286 -0.214
x3 0.5000 1.283 0.390 0.697 -2.036 3.036
x4 -0.5000 1.283 -0.390 0.697 -3.036 2.036
x5 -0.2500 1.283 -0.195 0.846 -2.786 2.286
x6 -3.0000 1.283 -2.338 0.021 -5.536 -0.464
x7 -2.2500 1.283 -1.753 0.082 -4.786 0.286
x8 -2.7500 1.283 -2.143 0.034 -5.286 -0.214
x9 1.2500 1.283 0.974 0.332 -1.286 3.786
x10 -1.7500 1.283 -1.364 0.175 -4.286 0.786
x11 0.7500 1.283 0.584 0.560 -1.786 3.286
x12 0.7500 1.283 0.584 0.560 -1.786 3.286
x13 -2.2500 1.283 -1.753 0.082 -4.786 0.286
x14 -1.2500 1.283 -0.974 0.332 -3.786 1.286
x15 -1.0000 1.283 -0.779 0.437 -3.536 1.536
x16 -0.5000 1.283 -0.390 0.697 -3.036 2.036
x17 -3.0000 1.283 -2.338 0.021 -5.536 -0.464
x18 -2.2500 1.283 -1.753 0.082 -4.786 0.286
x19 1.7500 1.283 1.364 0.175 -0.786 4.286
x20 -2.2500 1.283 -1.753 0.082 -4.786 0.286
x21 4.125e-12 1.283 3.21e-12 1.000 -2.536 2.536
x22 -1.5000 1.283 -1.169 0.244 -4.036 1.036
x23 -2.5000 1.283 -1.948 0.053 -5.036 0.036
x24 -1.2500 1.283 -0.974 0.332 -3.786 1.286
x25 -2.2500 1.283 -1.753 0.082 -4.786 0.286
x26 -3.7500 1.283 -2.922 0.004 -6.286 -1.214
x27 -2.5000 1.283 -1.948 0.053 -5.036 0.036
x28 -1.0000 1.283 -0.779 0.437 -3.536 1.536
x29 4.121e-12 1.283 3.21e-12 1.000 -2.536 2.536
x30 -0.2500 1.283 -0.195 0.846 -2.786 2.286
x31 -1.5000 1.283 -1.169 0.244 -4.036 1.036
x32 -2.7500 1.283 -2.143 0.034 -5.286 -0.214
x33 -2.7500 1.283 -2.143 0.034 -5.286 -0.214
x34 1.0000 1.283 0.779 0.437 -1.536 3.536
x35 -2.7500 1.283 -2.143 0.034 -5.286 -0.214
x36 -2.5000 1.283 -1.948 0.053 -5.036 0.036
x37 -1.2500 1.283 -0.974 0.332 -3.786 1.286
x38 -1.7500 1.283 -1.364 0.175 -4.286 0.786
x39 4.125e-12 1.283 3.21e-12 1.000 -2.536 2.536
x40 -1.7500 1.283 -1.364 0.175 -4.286 0.786
x41 -2.2500 1.283 -1.753 0.082 -4.786 0.286
x42 -4.0000 1.283 -3.117 0.002 -6.536 -1.464
x43 -1.2500 1.283 -0.974 0.332 -3.786 1.286
x44 -3.0000 1.283 -2.338 0.021 -5.536 -0.464
x45 1.0000 1.283 0.779 0.437 -1.536 3.536
x46 -2.5000 1.283 -1.948 0.053 -5.036 0.036
x47 -1.2500 1.283 -0.974 0.332 -3.786 1.286
x48 0.2500 1.283 0.195 0.846 -2.286 2.786
x49 -2.0000 1.283 -1.558 0.121 -4.536 0.536
x50 -0.7500 1.283 -0.584 0.560 -3.286 1.786
x51 0.2500 1.283 0.195 0.846 -2.286 2.786
Omnibus: 6.101 Durbin-Watson: 1.995
Prob(Omnibus): 0.047 Jarque-Bera (JB): 8.918
Skew: 0.113 Prob(JB): 0.0116
Kurtosis: 3.999 Cond. No. 1.81e+06


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.81e+06. This might indicate that there are
strong multicollinearity or other numerical problems.

We can do the same for the math data.

In [267]:
# create statsmodel for math data
p_math = sm.OLS(train_data['MATHEMATICS_GROWTH'].tolist(), sm.add_constant(X_math)).fit()
p_math.summary()
Out[267]:
OLS Regression Results
Dep. Variable: y R-squared: 0.511
Model: OLS Adj. R-squared: 0.347
Method: Least Squares F-statistic: 3.114
Date: Mon, 16 May 2022 Prob (F-statistic): 4.02e-08
Time: 15:54:25 Log-Likelihood: -403.42
No. Observations: 204 AIC: 910.8
Df Residuals: 152 BIC: 1083.
Df Model: 51
Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975]
const -366.1167 127.593 -2.869 0.005 -618.201 -114.032
x1 0.1833 0.063 2.891 0.004 0.058 0.309
x2 -3.5000 1.432 -2.444 0.016 -6.329 -0.671
x3 3.0000 1.432 2.095 0.038 0.171 5.829
x4 -3.0000 1.432 -2.095 0.038 -5.829 -0.171
x5 -1.7500 1.432 -1.222 0.224 -4.579 1.079
x6 -1.7500 1.432 -1.222 0.224 -4.579 1.079
x7 -5.2500 1.432 -3.666 0.000 -8.079 -2.421
x8 -1.5000 1.432 -1.047 0.297 -4.329 1.329
x9 3.5000 1.432 2.444 0.016 0.671 6.329
x10 -3.0000 1.432 -2.095 0.038 -5.829 -0.171
x11 -1.2500 1.432 -0.873 0.384 -4.079 1.579
x12 0.2500 1.432 0.175 0.862 -2.579 3.079
x13 -3.5000 1.432 -2.444 0.016 -6.329 -0.671
x14 -2.5000 1.432 -1.746 0.083 -5.329 0.329
x15 0.2500 1.432 0.175 0.862 -2.579 3.079
x16 -2.0000 1.432 -1.397 0.165 -4.829 0.829
x17 -3.2500 1.432 -2.269 0.025 -6.079 -0.421
x18 -1.0000 1.432 -0.698 0.486 -3.829 1.829
x19 -0.5000 1.432 -0.349 0.727 -3.329 2.329
x20 -2.7500 1.432 -1.920 0.057 -5.579 0.079
x21 -3.0000 1.432 -2.095 0.038 -5.829 -0.171
x22 -2.5000 1.432 -1.746 0.083 -5.329 0.329
x23 -2.5000 1.432 -1.746 0.083 -5.329 0.329
x24 -1.5000 1.432 -1.047 0.297 -4.329 1.329
x25 0.7500 1.432 0.524 0.601 -2.079 3.579
x26 -3.7500 1.432 -2.619 0.010 -6.579 -0.921
x27 -3.5000 1.432 -2.444 0.016 -6.329 -0.671
x28 -0.2500 1.432 -0.175 0.862 -3.079 2.579
x29 -2.2500 1.432 -1.571 0.118 -5.079 0.579
x30 -2.5000 1.432 -1.746 0.083 -5.329 0.329
x31 -3.0000 1.432 -2.095 0.038 -5.829 -0.171
x32 -1.0000 1.432 -0.698 0.486 -3.829 1.829
x33 -4.7500 1.432 -3.317 0.001 -7.579 -1.921
x34 -2.2500 1.432 -1.571 0.118 -5.079 0.579
x35 -2.5000 1.432 -1.746 0.083 -5.329 0.329
x36 -2.2500 1.432 -1.571 0.118 -5.079 0.579
x37 -1.5000 1.432 -1.047 0.297 -4.329 1.329
x38 -2.5000 1.432 -1.746 0.083 -5.329 0.329
x39 -2.5000 1.432 -1.746 0.083 -5.329 0.329
x40 -1.7500 1.432 -1.222 0.224 -4.579 1.079
x41 -2.0000 1.432 -1.397 0.165 -4.829 0.829
x42 -3.7500 1.432 -2.619 0.010 -6.579 -0.921
x43 1.7500 1.432 1.222 0.224 -1.079 4.579
x44 -1.0000 1.432 -0.698 0.486 -3.829 1.829
x45 -0.5000 1.432 -0.349 0.727 -3.329 2.329
x46 -4.2500 1.432 -2.968 0.003 -7.079 -1.421
x47 -0.5000 1.432 -0.349 0.727 -3.329 2.329
x48 -0.7500 1.432 -0.524 0.601 -3.579 2.079
x49 -0.7500 1.432 -0.524 0.601 -3.579 2.079
x50 -2.5000 1.432 -1.746 0.083 -5.329 0.329
x51 0.2500 1.432 0.175 0.862 -2.579 3.079
Omnibus: 7.342 Durbin-Watson: 1.715
Prob(Omnibus): 0.025 Jarque-Bera (JB): 8.179
Skew: -0.316 Prob(JB): 0.0167
Kurtosis: 3.750 Cond. No. 1.81e+06


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.81e+06. This might indicate that there are
strong multicollinearity or other numerical problems.

Looking at the statsmodel summary, we can see analyze which coefficients had a notable effect on the predicted value. We can list which ones by looking at the P>|t| columns and if they have a value less than our assumed bound of 0.05, then we can consider it to be significant.

In [268]:
# accumulate constant names
const_names = train_data.columns[3:].tolist()
const_names.insert(0, 'YEAR')

reading_significant = []

# iterate through p values and if less than 0.05 add const name to reading_significant
for i in range(len(p_reading.pvalues) - 1):
    if p_reading.pvalues[i + 1] < 0.05:
        reading_significant.append(const_names[i])
        
print("Significant reading test constants: " + str(reading_significant))
print()

math_significant = []

# iterate through p values and if less than 0.05 add const name to math_significant
for i in range(len(p_math.pvalues) - 1):
    if p_math.pvalues[i + 1] < 0.05:
        math_significant.append(const_names[i])
        
print("Significant math test constants: " + str(math_significant))

Significant reading test constants: ['YEAR', 'STATE_ALASKA', 'STATE_COLORADO', 'STATE_DELAWARE', 'STATE_KANSAS', 'STATE_MISSOURI', 'STATE_NEW_MEXICO', 'STATE_NEW_YORK', 'STATE_NORTH_DAKOTA', 'STATE_SOUTH_DAKOTA', 'STATE_TEXAS']

Significant math test constants: ['YEAR', 'STATE_ALASKA', 'STATE_ARIZONA', 'STATE_ARKANSAS', 'STATE_CONNECTICUT', 'STATE_DISTRICT_OF_COLUMBIA', 'STATE_FLORIDA', 'STATE_IDAHO', 'STATE_KANSAS', 'STATE_MARYLAND', 'STATE_MISSOURI', 'STATE_MONTANA', 'STATE_NEW_JERSEY', 'STATE_NEW_YORK', 'STATE_SOUTH_DAKOTA', 'STATE_VERMONT']

Based off just the p values we can see that these states have a determinant factor in the growth of a child's reading and math test score.

An application of this model can be to predict if a state is predicted to perform poorly and change legislation and provide more funding to help the students grow more. We can see if a state is predicted to perform poorly if the state has a negative coefficient in the LinearRegression model. If this state also has a high significance then this state should try to improve their education system.

In [269]:
print("States that have a predicted negative growth in reading:")
for i in range(len(reading_regr.coef_)):
    if(i > 1):
        if reading_regr.coef_[i] < 0 and p_reading.pvalues[i + 1] < 0.05:
            print(const_names[i])
        
print()
print("States that have a predicted negative growth in math:")

for i in range(len(mathematics_regr.coef_)):
    if(i > 1):
        if mathematics_regr.coef_[i] < 0 and p_math.pvalues[i + 1] < 0.05:
            print(const_names[i])

States that have a predicted negative growth in reading:
STATE_COLORADO
STATE_DELAWARE
STATE_KANSAS
STATE_MISSOURI
STATE_NEW_MEXICO
STATE_NEW_YORK
STATE_NORTH_DAKOTA
STATE_SOUTH_DAKOTA
STATE_TEXAS

States that have a predicted negative growth in math:
STATE_ARKANSAS
STATE_CONNECTICUT
STATE_FLORIDA
STATE_IDAHO
STATE_KANSAS
STATE_MARYLAND
STATE_MISSOURI
STATE_MONTANA
STATE_NEW_JERSEY
STATE_NEW_YORK
STATE_SOUTH_DAKOTA
STATE_VERMONT

From these lists we can tell that a notable amount of states have both a negative coefficient and a low p value above 0.05 - and therefore are predicted to have significant negative decreases in point averages for 4th grades on the NAEP test in both reading and writing. Noticeably, we can see that 19 states seem to have significant predicted negative growths in both average math and reading scores for 4th graders, some of which include states such as Maine and California, which have been known to be more

Test Score Growth per Gender per State Prediction

Another set of predictive models that we are creating is predicting the change in average test scores in Grade 4 based on previous years data for each state per gender. We will create 4 models, each for predicting MALE Math Changes per State from some year, FEMALE Math Changes per State from some year, MALE Reading Changes per State from some year, and FEMALE Reading Changes per State from some year. Firstly, we are going to remove all the columns except for state, and the average test scores for math and reading per gender per state.

In [270]:
# get gender-based data
gender_avg = school_data[['STATE', 'YEAR', 'G04_A_M_READING', 'G04_A_M_MATHEMATICS', 'G04_A_F_READING', 'G04_A_F_MATHEMATICS']]
gender_avg = gender_avg[gender_avg.STATE != "DODEA"] # dropping rows that are not relevant states
gender_avg = gender_avg[gender_avg.STATE != "NATIONAL"] # dropping rows that are not relevant states

# display the first few results
gender_avg.head()
Out[270]:
STATE YEAR G04_A_M_READING G04_A_M_MATHEMATICS G04_A_F_READING G04_A_F_MATHEMATICS
867 ALABAMA 2009 212.0 228.0 221.0 228.0
868 ALASKA 2009 207.0 238.0 216.0 236.0
869 ARIZONA 2009 207.0 230.0 213.0 230.0
870 ARKANSAS 2009 211.0 239.0 222.0 236.0
871 CALIFORNIA 2009 207.0 233.0 213.0 231.0

To create a metric for how the test scores have improved, we will, similar to earlier, subtract the 2009 average scores from each state's FEMALE and MALE reading and math averages from those of another year's to define how much the average math and reading test scores have changed since 2009. We are storing this metric in these new columns: "READING_GROWTH_M," "READING_GROWTH_F" and "MATHEMATICS_GROWTH_M," and "MATHEMATICS_GROWTH_F".

First, we will create these columns and use numpy to set the values in those column as empty (np.NaN). Typically, you would use this to denote missing values, but we can use this when we don't know the values up front.

In [271]:
# define columns in dataframe and set to empty 
gender_avg['MATHEMATICS_GROWTH_M'] = np.NaN
gender_avg['MATHEMATICS_GROWTH_F'] = np.NaN
gender_avg['READING_GROWTH_M'] = np.NaN
gender_avg['READING_GROWTH_F'] = np.NaN

# display the first few results 
gender_avg.head()
Out[271]:
STATE YEAR G04_A_M_READING G04_A_M_MATHEMATICS G04_A_F_READING G04_A_F_MATHEMATICS MATHEMATICS_GROWTH_M MATHEMATICS_GROWTH_F READING_GROWTH_M READING_GROWTH_F
867 ALABAMA 2009 212.0 228.0 221.0 228.0 NaN NaN NaN NaN
868 ALASKA 2009 207.0 238.0 216.0 236.0 NaN NaN NaN NaN
869 ARIZONA 2009 207.0 230.0 213.0 230.0 NaN NaN NaN NaN
870 ARKANSAS 2009 211.0 239.0 222.0 236.0 NaN NaN NaN NaN
871 CALIFORNIA 2009 207.0 233.0 213.0 231.0 NaN NaN NaN NaN

Next, we are defining a get_growth() function that will calculate the growth from 2009 to whichever specified year based on the subject, gender (FEMALE or MALE), and year. We will use this method to assign a growth value for each state and year combination with gender.

In [272]:
# method to get growth
def get_growth(row, subject, gender):
    # create a list, new, that contains the average score data from 2009
    state = row['STATE']
    new = gender_avg.loc[gender_avg['STATE'] == state]
    new = new.loc[new['YEAR'] == 2009]
    
    # get the data based on subject and gender and subtract it with 2009 data average score
    if subject == 'MATH':
        if gender == 'M':
            return row['G04_A_M_MATHEMATICS'] - new['G04_A_M_MATHEMATICS']
        else:
            return row['G04_A_F_MATHEMATICS'] - new['G04_A_F_MATHEMATICS']
    else:
        if gender == 'M':
            return row['G04_A_M_READING'] - new['G04_A_M_READING']
        else:
            return row['G04_A_F_READING'] - new['G04_A_F_READING']

# iterate through each row in our dataframe and get the growth based off of subject and gender       
for i, row in gender_avg.iterrows():
    gender_avg.at[i, 'READING_GROWTH_M'] = get_growth(row, 'READ', 'M')
    gender_avg.at[i, 'READING_GROWTH_F'] = get_growth(row, 'READ', 'F')
    gender_avg.at[i, 'MATHEMATICS_GROWTH_M'] = get_growth(row, 'MATH', 'M')
    gender_avg.at[i, 'MATHEMATICS_GROWTH_F'] = get_growth(row, 'MATH', 'F')
    
gender_avg.head()
Out[272]:
STATE YEAR G04_A_M_READING G04_A_M_MATHEMATICS G04_A_F_READING G04_A_F_MATHEMATICS MATHEMATICS_GROWTH_M MATHEMATICS_GROWTH_F READING_GROWTH_M READING_GROWTH_F
867 ALABAMA 2009 212.0 228.0 221.0 228.0 0.0 0.0 0.0 0.0
868 ALASKA 2009 207.0 238.0 216.0 236.0 0.0 0.0 0.0 0.0
869 ARIZONA 2009 207.0 230.0 213.0 230.0 0.0 0.0 0.0 0.0
870 ARKANSAS 2009 211.0 239.0 222.0 236.0 0.0 0.0 0.0 0.0
871 CALIFORNIA 2009 207.0 233.0 213.0 231.0 0.0 0.0 0.0 0.0

We will be creating seperate models for STATE+FEMALE Math Growth, STATE+MALE Math Growth, STATE+FEMALE Reading Growth, and STATE+MALE Reading Growth. Because of this, gender will not be an independent variable, but rather only state will be since each model assumes which gender it is training on. Since each state counts as a unique independent variable, we can use the pandas method get_dummies on a row for each state value to create a dataframe where each state is represented by either 1 or 0, 1 if the data value represents that state, and 0 if the data value does not represent that state. Then we will then drop the Alabama column from our dataset because if all the other state values are 0 then we can assume that the data value must be an Alabama value.

In [273]:
# get dummies
gender_avg = pd.get_dummies(gender_avg, columns=['STATE'])

# drop alabama and reading and mathematics averages since we no longer need them
gender_avg = gender_avg.drop(columns=['STATE_ALABAMA', 'G04_A_M_READING', 'G04_A_F_READING', 'G04_A_M_MATHEMATICS', 'G04_A_F_MATHEMATICS'])

# display the first few results
gender_avg.head()
Out[273]:
YEAR MATHEMATICS_GROWTH_M MATHEMATICS_GROWTH_F READING_GROWTH_M READING_GROWTH_F STATE_ALASKA STATE_ARIZONA STATE_ARKANSAS STATE_CALIFORNIA STATE_COLORADO ... STATE_SOUTH_DAKOTA STATE_TENNESSEE STATE_TEXAS STATE_UTAH STATE_VERMONT STATE_VIRGINIA STATE_WASHINGTON STATE_WEST_VIRGINIA STATE_WISCONSIN STATE_WYOMING
867 2009 0.0 0.0 0.0 0.0 0 0 0 0 0 ... 0 0 0 0 0 0 0 0 0 0
868 2009 0.0 0.0 0.0 0.0 1 0 0 0 0 ... 0 0 0 0 0 0 0 0 0 0
869 2009 0.0 0.0 0.0 0.0 0 1 0 0 0 ... 0 0 0 0 0 0 0 0 0 0
870 2009 0.0 0.0 0.0 0.0 0 0 1 0 0 ... 0 0 0 0 0 0 0 0 0 0
871 2009 0.0 0.0 0.0 0.0 0 0 0 1 0 ... 0 0 0 0 0 0 0 0 0 0

5 rows × 55 columns

When creating predictive models, it is standard norm to split apart our dataset into a train and test set. Typically, the test set contains data the model has never seen before so we can get a more accurate picture on how it performs on real world data. Typically, datasets are split into 60% train and 40% test (more info here: how to split a dataset ).

Because our model is being trained to predict growth from 2009 to later years, we will split apart our dataset with a different convention. We will, similar to before, predict on the years 2017, 2018, and 2019, and so we will use those rows as our test data and the rest as our train data. We will also drop any year's data that have NaN values for average reading and math scores for FEMALE and MALE averages.

In [274]:
train_data = gender_avg[gender_avg['YEAR'] < 2017].dropna()
test_data = gender_avg[gender_avg['YEAR'] >= 2017].dropna()

For our regression model, we will use Linear Regression from sklearn (link for more information: sklearn library). We will make one model per subject, per gender for a total of four models.

First, we will define our X (state with year) and y values (growth for assumed gender) by iterating through each row and adding the year and state to the X variable and the growths to the y variables.

In [275]:
from sklearn.linear_model import LinearRegression

# create X and y lists by respective subject and gender
X_reading_M = []
X_reading_F = []
y_reading_M = []
y_reading_F = []
X_math_M = []
X_math_F = []
y_math_M = []
y_math_F = []

# iterate through each row and update X and y
for i, row in train_data.iterrows():
    # X is state and year
    X = row[3:].tolist()
    X.insert(0, row['YEAR'])

    # for each y (growth for assumed gender), append its respective value 
    X_reading_M.append(X)
    y_reading_M.append(row['READING_GROWTH_M'])
    
    X_reading_F.append(X)
    y_reading_F.append(row['READING_GROWTH_F'])
    
    X_math_M.append(X)
    y_math_M.append(row['MATHEMATICS_GROWTH_M'])
    
    X_math_F.append(X)
    y_math_F.append(row['MATHEMATICS_GROWTH_F'])

Using the Linear Regression model, we will fit the X and y variables we defined above in order to create a prediction model. Then, we will test on our models using the test dataset we defined above.

In [276]:
# create models based on subject and assumed gender and then fit the data
reading_M = LinearRegression().fit(X_reading_M, y_reading_M)
reading_F = LinearRegression().fit(X_reading_F, y_reading_F)

mathematics_M = LinearRegression().fit(X_math_M, y_math_M)
mathematics_F = LinearRegression().fit(X_math_F, y_math_F)

# create X values for state and subject
X_test_reading_M = []
X_test_reading_F = []
X_test_math_M = []
X_test_math_F = []

# accumulate X values for reading and math
for i, row in test_data.iterrows():
    X = row[3:].tolist()
    X.insert(0, row['YEAR'])
    X_test_reading_M.append(X)
    X_test_reading_F.append(X)
    X_test_math_M.append(X)
    X_test_math_F.append(X)
    
# predict based of X values
test_data['PREDICT_READING_M'] = reading_M.predict(X_test_reading_M)
test_data['PREDICT_READING_F'] = reading_F.predict(X_test_reading_F)
test_data['PREDICT_MATH_M'] = mathematics_M.predict(X_test_math_M)
test_data['PREDICT_MATH_F'] = mathematics_F.predict(X_test_math_F)

test_data.head()
Out[276]:
YEAR MATHEMATICS_GROWTH_M MATHEMATICS_GROWTH_F READING_GROWTH_M READING_GROWTH_F STATE_ALASKA STATE_ARIZONA STATE_ARKANSAS STATE_CALIFORNIA STATE_COLORADO ... STATE_VERMONT STATE_VIRGINIA STATE_WASHINGTON STATE_WEST_VIRGINIA STATE_WISCONSIN STATE_WYOMING PREDICT_READING_M PREDICT_READING_F PREDICT_MATH_M PREDICT_MATH_F
1281 2017 4.0 4.0 1.0 -1.0 0 0 0 0 0 ... 0 0 0 0 0 0 1.0 -1.0 1.349624 1.955009
1288 2017 -8.0 -6.0 -4.0 -5.0 1 0 0 0 0 ... 0 0 0 0 0 0 -4.0 -5.0 -2.933476 -2.043989
1295 2017 6.0 3.0 6.0 5.0 0 1 0 0 0 ... 0 0 0 0 0 0 6.0 5.0 7.960281 6.425050
1302 2017 -4.0 -3.0 1.0 -1.0 0 0 1 0 0 ... 0 0 0 0 0 0 1.0 -1.0 -2.173749 0.917987
1309 2017 0.0 0.0 4.0 7.0 0 0 0 1 0 ... 0 0 0 0 0 0 4.0 7.0 3.015859 3.018895

5 rows × 59 columns

To analyze if being in a particular state does affect growth of reading and math test scores for our genders of MALE and FEMALE, we can use statsmodel to see the p-value of each coefficient that we are using in our fitted model.

In [277]:
import statsmodels.api as sm

# create statsmodel for reading data male
p_reading_M = sm.OLS(train_data['READING_GROWTH_M'].tolist(), sm.add_constant(X_reading_M)).fit()
p_reading_M.summary()
Out[277]:
OLS Regression Results
Dep. Variable: y R-squared: 1.000
Model: OLS Adj. R-squared: 1.000
Method: Least Squares F-statistic: 2.040e+27
Date: Mon, 16 May 2022 Prob (F-statistic): 0.00
Time: 15:54:27 Log-Likelihood: 5840.7
No. Observations: 204 AIC: -1.157e+04
Df Residuals: 150 BIC: -1.139e+04
Df Model: 53
Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975]
const 1.08e-12 7.26e-12 0.149 0.882 -1.33e-11 1.54e-11
x1 -4.927e-16 3.61e-15 -0.136 0.892 -7.63e-15 6.64e-15
x2 1.0000 5.31e-15 1.88e+14 0.000 1.000 1.000
x3 -6.87e-16 5.48e-15 -0.125 0.900 -1.15e-14 1.01e-14
x4 -2.526e-15 7.47e-14 -0.034 0.973 -1.5e-13 1.45e-13
x5 -5.052e-15 7.46e-14 -0.068 0.946 -1.52e-13 1.42e-13
x6 1.887e-15 7.37e-14 0.026 0.980 -1.44e-13 1.47e-13
x7 1.665e-15 7.37e-14 0.023 0.982 -1.44e-13 1.47e-13
x8 -2.22e-16 7.48e-14 -0.003 0.998 -1.48e-13 1.48e-13
x9 1.665e-16 7.42e-14 0.002 0.998 -1.46e-13 1.47e-13
x10 -7.216e-16 7.43e-14 -0.010 0.992 -1.48e-13 1.46e-13
x11 1.332e-15 7.77e-14 0.017 0.986 -1.52e-13 1.55e-13
x12 -9.714e-16 7.45e-14 -0.013 0.990 -1.48e-13 1.46e-13
x13 4.441e-16 7.42e-14 0.006 0.995 -1.46e-13 1.47e-13
x14 1.11e-15 7.36e-14 0.015 0.988 -1.44e-13 1.47e-13
x15 -3.608e-16 7.44e-14 -0.005 0.996 -1.47e-13 1.47e-13
x16 0 7.38e-14 0 1.000 -1.46e-13 1.46e-13
x17 6.106e-16 7.34e-14 0.008 0.993 -1.44e-13 1.46e-13
x18 5.551e-16 7.37e-14 0.008 0.994 -1.45e-13 1.46e-13
x19 -3.331e-16 7.75e-14 -0.004 0.997 -1.54e-13 1.53e-13
x20 -5.551e-16 7.37e-14 -0.008 0.994 -1.46e-13 1.45e-13
x21 4.58e-16 7.46e-14 0.006 0.995 -1.47e-13 1.48e-13
x22 -1.416e-15 7.42e-14 -0.019 0.985 -1.48e-13 1.45e-13
x23 -1.11e-15 7.51e-14 -0.015 0.988 -1.5e-13 1.47e-13
x24 -2.22e-16 7.4e-14 -0.003 0.998 -1.46e-13 1.46e-13
x25 0 7.4e-14 0 1.000 -1.46e-13 1.46e-13
x26 9.992e-16 7.46e-14 0.013 0.989 -1.46e-13 1.48e-13
x27 -9.298e-16 7.47e-14 -0.012 0.990 -1.49e-13 1.47e-13
x28 -1.998e-15 7.52e-14 -0.027 0.979 -1.51e-13 1.47e-13
x29 5.412e-16 7.48e-14 0.007 0.994 -1.47e-13 1.48e-13
x30 -9.437e-16 7.44e-14 -0.013 0.990 -1.48e-13 1.46e-13
x31 7.91e-16 7.37e-14 0.011 0.991 -1.45e-13 1.46e-13
x32 9.021e-16 7.46e-14 0.012 0.990 -1.47e-13 1.48e-13
x33 8.327e-17 7.43e-14 0.001 0.999 -1.47e-13 1.47e-13
x34 -3.886e-16 7.43e-14 -0.005 0.996 -1.47e-13 1.46e-13
x35 -1.776e-15 7.48e-14 -0.024 0.981 -1.5e-13 1.46e-13
x36 1.554e-15 7.36e-14 0.021 0.983 -1.44e-13 1.47e-13
x37 1.221e-15 7.45e-14 0.016 0.987 -1.46e-13 1.48e-13
x38 -4.996e-16 7.44e-14 -0.007 0.995 -1.47e-13 1.46e-13
x39 1.166e-15 7.41e-14 0.016 0.987 -1.45e-13 1.48e-13
x40 1.665e-16 7.39e-14 0.002 0.998 -1.46e-13 1.46e-13
x41 -3.886e-16 7.67e-14 -0.005 0.996 -1.52e-13 1.51e-13
x42 0 7.36e-14 0 1.000 -1.46e-13 1.46e-13
x43 2.776e-17 7.68e-14 0.000 1.000 -1.52e-13 1.52e-13
x44 -1.166e-15 7.66e-14 -0.015 0.988 -1.53e-13 1.5e-13
x45 -1.11e-16 7.52e-14 -0.001 0.999 -1.49e-13 1.49e-13
x46 1.178e-15 7.46e-14 0.016 0.987 -1.46e-13 1.48e-13
x47 8.882e-16 7.5e-14 0.012 0.991 -1.47e-13 1.49e-13
x48 -2.581e-15 7.61e-14 -0.034 0.973 -1.53e-13 1.48e-13
x49 -2.914e-16 7.36e-14 -0.004 0.997 -1.46e-13 1.45e-13
x50 8.327e-16 7.42e-14 0.011 0.991 -1.46e-13 1.48e-13
x51 -6.661e-16 7.46e-14 -0.009 0.993 -1.48e-13 1.47e-13
x52 -2.22e-16 7.38e-14 -0.003 0.998 -1.46e-13 1.46e-13
x53 7.008e-16 7.37e-14 0.010 0.992 -1.45e-13 1.46e-13
Omnibus: 7.634 Durbin-Watson: 0.002
Prob(Omnibus): 0.022 Jarque-Bera (JB): 7.586
Skew: 0.469 Prob(JB): 0.0225
Kurtosis: 3.117 Cond. No. 2.01e+06


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 2.01e+06. This might indicate that there are
strong multicollinearity or other numerical problems.
In [278]:
# create statsmodel for reading data female
p_reading_F = sm.OLS(train_data['READING_GROWTH_F'].tolist(), sm.add_constant(X_reading_F)).fit()
p_reading_F.summary()
Out[278]:
OLS Regression Results
Dep. Variable: y R-squared: 1.000
Model: OLS Adj. R-squared: 1.000
Method: Least Squares F-statistic: 6.839e+27
Date: Mon, 16 May 2022 Prob (F-statistic): 0.00
Time: 15:54:27 Log-Likelihood: 5952.7
No. Observations: 204 AIC: -1.180e+04
Df Residuals: 150 BIC: -1.162e+04
Df Model: 53
Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975]
const 1.734e-12 4.2e-12 0.413 0.680 -6.56e-12 1e-11
x1 -8.882e-16 2.09e-15 -0.426 0.671 -5.01e-15 3.23e-15
x2 5.135e-16 3.07e-15 0.167 0.867 -5.55e-15 6.58e-15
x3 1.0000 3.16e-15 3.16e+14 0.000 1.000 1.000
x4 2.054e-15 4.31e-14 0.048 0.962 -8.32e-14 8.73e-14
x5 -7.772e-16 4.31e-14 -0.018 0.986 -8.59e-14 8.44e-14
x6 -2.776e-16 4.26e-14 -0.007 0.995 -8.44e-14 8.38e-14
x7 1.499e-15 4.26e-14 0.035 0.972 -8.26e-14 8.56e-14
x8 9.992e-16 4.32e-14 0.023 0.982 -8.44e-14 8.64e-14
x9 2.359e-15 4.28e-14 0.055 0.956 -8.23e-14 8.7e-14
x10 1.776e-15 4.29e-14 0.041 0.967 -8.3e-14 8.66e-14
x11 4.441e-16 4.49e-14 0.010 0.992 -8.83e-14 8.92e-14
x12 -2.22e-16 4.3e-14 -0.005 0.996 -8.52e-14 8.48e-14
x13 -1.221e-15 4.29e-14 -0.028 0.977 -8.59e-14 8.35e-14
x14 -7.772e-16 4.25e-14 -0.018 0.985 -8.48e-14 8.32e-14
x15 1.554e-15 4.3e-14 0.036 0.971 -8.33e-14 8.64e-14
x16 9.714e-16 4.26e-14 0.023 0.982 -8.33e-14 8.52e-14
x17 7.355e-16 4.24e-14 0.017 0.986 -8.31e-14 8.45e-14
x18 9.992e-16 4.26e-14 0.023 0.981 -8.31e-14 8.51e-14
x19 8.882e-16 4.48e-14 0.020 0.984 -8.76e-14 8.94e-14
x20 1.138e-15 4.26e-14 0.027 0.979 -8.3e-14 8.53e-14
x21 -1.665e-15 4.31e-14 -0.039 0.969 -8.68e-14 8.35e-14
x22 0 4.28e-14 0 1.000 -8.46e-14 8.46e-14
x23 -1.11e-15 4.34e-14 -0.026 0.980 -8.68e-14 8.46e-14
x24 0 4.27e-14 0 1.000 -8.45e-14 8.45e-14
x25 4.025e-16 4.28e-14 0.009 0.993 -8.41e-14 8.49e-14
x26 1.665e-15 4.31e-14 0.039 0.969 -8.35e-14 8.68e-14
x27 1.11e-15 4.32e-14 0.026 0.980 -8.42e-14 8.64e-14
x28 1.554e-15 4.35e-14 0.036 0.972 -8.43e-14 8.74e-14
x29 1.332e-15 4.32e-14 0.031 0.975 -8.41e-14 8.67e-14
x30 -7.772e-16 4.3e-14 -0.018 0.986 -8.57e-14 8.42e-14
x31 5.412e-16 4.26e-14 0.013 0.990 -8.36e-14 8.47e-14
x32 1.443e-15 4.31e-14 0.033 0.973 -8.37e-14 8.66e-14
x33 9.992e-16 4.29e-14 0.023 0.981 -8.38e-14 8.58e-14
x34 1.61e-15 4.29e-14 0.038 0.970 -8.31e-14 8.64e-14
x35 1.055e-15 4.32e-14 0.024 0.981 -8.44e-14 8.65e-14
x36 -5.551e-16 4.25e-14 -0.013 0.990 -8.46e-14 8.35e-14
x37 1.069e-15 4.3e-14 0.025 0.980 -8.4e-14 8.61e-14
x38 4.996e-16 4.3e-14 0.012 0.991 -8.44e-14 8.54e-14
x39 1.11e-15 4.28e-14 0.026 0.979 -8.35e-14 8.57e-14
x40 8.882e-16 4.27e-14 0.021 0.983 -8.34e-14 8.52e-14
x41 -1.776e-15 4.43e-14 -0.040 0.968 -8.93e-14 8.58e-14
x42 3.331e-16 4.25e-14 0.008 0.994 -8.37e-14 8.44e-14
x43 8.882e-16 4.44e-14 0.020 0.984 -8.68e-14 8.86e-14
x44 1.776e-15 4.43e-14 0.040 0.968 -8.57e-14 8.92e-14
x45 8.327e-16 4.35e-14 0.019 0.985 -8.5e-14 8.67e-14
x46 1.887e-15 4.31e-14 0.044 0.965 -8.32e-14 8.7e-14
x47 -1.665e-16 4.33e-14 -0.004 0.997 -8.58e-14 8.55e-14
x48 1.11e-16 4.39e-14 0.003 0.998 -8.67e-14 8.69e-14
x49 2.359e-16 4.25e-14 0.006 0.996 -8.38e-14 8.42e-14
x50 -1.11e-15 4.29e-14 -0.026 0.979 -8.58e-14 8.36e-14
x51 4.441e-16 4.31e-14 0.010 0.992 -8.47e-14 8.56e-14
x52 4.857e-17 4.26e-14 0.001 0.999 -8.41e-14 8.42e-14
x53 4.441e-16 4.26e-14 0.010 0.992 -8.37e-14 8.46e-14
Omnibus: 21.730 Durbin-Watson: 0.014
Prob(Omnibus): 0.000 Jarque-Bera (JB): 48.054
Skew: -0.479 Prob(JB): 3.67e-11
Kurtosis: 5.176 Cond. No. 2.01e+06


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 2.01e+06. This might indicate that there are
strong multicollinearity or other numerical problems.

Creating statsmodel for math data MALE:

In [279]:
p_math_M = sm.OLS(train_data['MATHEMATICS_GROWTH_M'].tolist(), sm.add_constant(X_math_M)).fit()
p_math_M.summary()
Out[279]:
OLS Regression Results
Dep. Variable: y R-squared: 0.670
Model: OLS Adj. R-squared: 0.554
Method: Least Squares F-statistic: 5.752
Date: Mon, 16 May 2022 Prob (F-statistic): 1.56e-17
Time: 15:54:27 Log-Likelihood: -376.61
No. Observations: 204 AIC: 861.2
Df Residuals: 150 BIC: 1040.
Df Model: 53
Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975]
const 117.5397 125.080 0.940 0.349 -129.607 364.686
x1 -0.0576 0.062 -0.926 0.356 -0.180 0.065
x2 0.3180 0.091 3.476 0.001 0.137 0.499
x3 0.3177 0.094 3.369 0.001 0.131 0.504
x4 -1.4225 1.285 -1.107 0.270 -3.962 1.117
x5 3.1146 1.284 2.425 0.016 0.577 5.652
x6 -3.5234 1.268 -2.778 0.006 -6.030 -1.017
x7 -1.8293 1.268 -1.442 0.151 -4.336 0.677
x8 -0.1490 1.288 -0.116 0.908 -2.695 2.397
x9 -3.8198 1.277 -2.991 0.003 -6.343 -1.296
x10 -1.1491 1.279 -0.898 0.371 -3.677 1.379
x11 2.2971 1.339 1.716 0.088 -0.348 4.942
x12 -2.8757 1.282 -2.243 0.026 -5.409 -0.342
x13 -2.3738 1.278 -1.858 0.065 -4.899 0.151
x14 -0.1356 1.267 -0.107 0.915 -2.640 2.369
x15 -1.9904 1.280 -1.555 0.122 -4.520 0.540
x16 -2.6261 1.271 -2.067 0.040 -5.137 -0.115
x17 0.6589 1.264 0.521 0.603 -1.839 3.157
x18 -0.7734 1.268 -0.610 0.543 -3.280 1.733
x19 -1.5014 1.335 -1.125 0.263 -4.139 1.137
x20 -0.0465 1.270 -0.037 0.971 -2.556 2.463
x21 -1.8506 1.285 -1.440 0.152 -4.389 0.688
x22 -2.6491 1.277 -2.075 0.040 -5.172 -0.126
x23 -2.3291 1.293 -1.801 0.074 -4.884 0.226
x24 -1.6936 1.274 -1.329 0.186 -4.211 0.824
x25 -1.9787 1.274 -1.553 0.123 -4.497 0.539
x26 -1.7051 1.285 -1.327 0.186 -4.243 0.833
x27 1.4538 1.286 1.130 0.260 -1.088 3.995
x28 -1.0252 1.295 -0.792 0.430 -3.584 1.534
x29 -3.3990 1.288 -2.638 0.009 -5.945 -0.853
x30 0.8181 1.282 0.638 0.524 -1.714 3.351
x31 -2.7382 1.269 -2.158 0.033 -5.245 -0.231
x32 -2.4202 1.285 -1.884 0.062 -4.959 0.118
x33 -1.7168 1.279 -1.343 0.181 -4.243 0.810
x34 0.5097 1.279 0.399 0.691 -2.017 3.036
x35 -3.1723 1.289 -2.462 0.015 -5.719 -0.626
x36 -2.6356 1.267 -2.079 0.039 -5.140 -0.131
x37 -1.5813 1.283 -1.233 0.220 -4.116 0.953
x38 -1.5579 1.281 -1.216 0.226 -4.089 0.973
x39 -1.0230 1.276 -0.802 0.424 -3.545 1.499
x40 -2.5464 1.272 -2.001 0.047 -5.060 -0.032
x41 -3.2262 1.321 -2.442 0.016 -5.836 -0.616
x42 -1.4554 1.268 -1.148 0.253 -3.961 1.050
x43 -0.6487 1.323 -0.491 0.624 -3.262 1.964
x44 -1.7071 1.319 -1.294 0.198 -4.314 0.900
x45 2.4655 1.295 1.903 0.059 -0.094 5.025
x46 0.2481 1.284 0.193 0.847 -2.288 2.785
x47 -1.1353 1.292 -0.879 0.381 -3.688 1.417
x48 -3.3077 1.310 -2.525 0.013 -5.896 -0.720
x49 -0.9320 1.267 -0.735 0.463 -3.436 1.572
x50 -0.3292 1.278 -0.258 0.797 -2.855 2.196
x51 -0.4551 1.285 -0.354 0.724 -2.993 2.083
x52 -2.4436 1.270 -1.924 0.056 -4.953 0.066
x53 -0.7150 1.269 -0.563 0.574 -3.223 1.793
Omnibus: 8.941 Durbin-Watson: 1.507
Prob(Omnibus): 0.011 Jarque-Bera (JB): 9.440
Skew: -0.408 Prob(JB): 0.00891
Kurtosis: 3.667 Cond. No. 2.01e+06


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 2.01e+06. This might indicate that there are
strong multicollinearity or other numerical problems.

Create statsmodel for math data FEMALE:

In [280]:
p_math_F = sm.OLS(train_data['MATHEMATICS_GROWTH_F'].tolist(), sm.add_constant(X_math_F)).fit()
p_math_F.summary()
Out[280]:
OLS Regression Results
Dep. Variable: y R-squared: 0.559
Model: OLS Adj. R-squared: 0.403
Method: Least Squares F-statistic: 3.585
Date: Mon, 16 May 2022 Prob (F-statistic): 5.14e-10
Time: 15:54:27 Log-Likelihood: -388.09
No. Observations: 204 AIC: 884.2
Df Residuals: 150 BIC: 1063.
Df Model: 53
Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975]
const -57.9757 132.324 -0.438 0.662 -319.436 203.484
x1 0.0298 0.066 0.453 0.651 -0.100 0.160
x2 0.1847 0.097 1.909 0.058 -0.007 0.376
x3 0.3334 0.100 3.343 0.001 0.136 0.531
x4 -1.7418 1.360 -1.281 0.202 -4.429 0.945
x5 1.5459 1.359 1.138 0.257 -1.139 4.231
x6 -1.0370 1.342 -0.773 0.441 -3.688 1.614
x7 -2.1577 1.342 -1.608 0.110 -4.809 0.494
x8 -1.0663 1.363 -0.782 0.435 -3.760 1.627
x9 -3.0842 1.351 -2.283 0.024 -5.754 -0.415
x10 -0.2419 1.353 -0.179 0.858 -2.916 2.432
x11 1.6009 1.416 1.131 0.260 -1.197 4.399
x12 -1.9549 1.356 -1.441 0.152 -4.635 0.725
x13 -2.0926 1.352 -1.548 0.124 -4.764 0.579
x14 0.1947 1.341 0.145 0.885 -2.455 2.844
x15 -2.7136 1.355 -2.003 0.047 -5.390 -0.037
x16 -1.2318 1.344 -0.916 0.361 -3.888 1.424
x17 0.1295 1.337 0.097 0.923 -2.513 2.772
x18 -1.5370 1.342 -1.145 0.254 -4.188 1.114
x19 -1.9098 1.412 -1.352 0.178 -4.701 0.881
x20 -0.2228 1.343 -0.166 0.868 -2.877 2.432
x21 -1.9812 1.359 -1.458 0.147 -4.667 0.704
x22 -0.7047 1.351 -0.522 0.603 -3.374 1.964
x23 -3.0565 1.368 -2.234 0.027 -5.760 -0.353
x24 -2.4268 1.348 -1.800 0.074 -5.090 0.237
x25 -1.4637 1.348 -1.086 0.279 -4.127 1.200
x26 -0.7883 1.359 -0.580 0.563 -3.474 1.897
x27 1.0913 1.361 0.802 0.424 -1.597 3.780
x28 -1.6865 1.370 -1.231 0.220 -4.394 1.021
x29 -2.5663 1.363 -1.883 0.062 -5.260 0.127
x30 -0.9269 1.356 -0.684 0.495 -3.606 1.752
x31 -2.5373 1.342 -1.890 0.061 -5.190 0.115
x32 -2.8898 1.359 -2.126 0.035 -5.576 -0.204
x33 -1.5382 1.353 -1.137 0.257 -4.211 1.135
x34 0.2120 1.353 0.157 0.876 -2.461 2.885
x35 -2.3533 1.363 -1.726 0.086 -5.047 0.340
x36 -3.5553 1.341 -2.652 0.009 -6.205 -0.906
x37 -1.1957 1.357 -0.881 0.380 -3.877 1.486
x38 -0.6587 1.355 -0.486 0.628 -3.336 2.019
x39 -1.0102 1.350 -0.748 0.456 -3.678 1.658
x40 -0.7972 1.346 -0.592 0.555 -3.457 1.862
x41 -2.2233 1.398 -1.591 0.114 -4.985 0.538
x42 0.3977 1.342 0.296 0.767 -2.253 3.048
x43 0.0349 1.399 0.025 0.980 -2.730 2.799
x44 -1.6134 1.396 -1.156 0.250 -4.371 1.144
x45 2.3412 1.370 1.708 0.090 -0.367 5.049
x46 0.1377 1.358 0.101 0.919 -2.546 2.821
x47 -1.9913 1.367 -1.457 0.147 -4.692 0.709
x48 -3.3074 1.386 -2.387 0.018 -6.045 -0.569
x49 0.6847 1.341 0.511 0.610 -1.965 3.334
x50 -1.2321 1.352 -0.911 0.364 -3.904 1.440
x51 0.4617 1.359 0.340 0.735 -2.224 3.147
x52 -1.1396 1.344 -0.848 0.398 -3.795 1.515
x53 -0.3887 1.343 -0.290 0.773 -3.041 2.264
Omnibus: 0.595 Durbin-Watson: 1.221
Prob(Omnibus): 0.743 Jarque-Bera (JB): 0.729
Skew: -0.083 Prob(JB): 0.695
Kurtosis: 2.758 Cond. No. 2.01e+06


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 2.01e+06. This might indicate that there are
strong multicollinearity or other numerical problems.

Okay - we have our four models now, each with their statistical analysis done. We can try interpreting these statistics by checking for each gender assumed model, which states had p-values below an assumed bound of 0.05, as those would indicate that for that FEMALE or MALE classification, that some states had more weight in significance on a change in growth for the average reading or math scores.

In [281]:
# accumulate constant names
const_names = train_data.columns[3:].tolist()
const_names.insert(0, 'YEAR')

M_reading_significant = []
F_reading_significant = []

# iterate through p values and if below than 0.05 add const name to reading_significant
for i in range(len(p_reading_M.pvalues) - 1):
    if p_reading_M.pvalues[i + 1] < 0.05:
        M_reading_significant.append(const_names[i])
        
for i in range(len(p_reading_F.pvalues) - 1):
    if p_reading_F.pvalues[i + 1] < 0.05:
        F_reading_significant.append(const_names[i])
        
print("Significant Male reading test constants: " + str(M_reading_significant))
print()

print("Significant Female reading test constants: " + str(F_reading_significant))
print()

M_math_significant = []
F_math_significant = []

# iterate through p values and if below than 0.05 add const name to math_significant
for i in range(len(p_math_M.pvalues) - 1):
    if p_math_M.pvalues[i + 1] < 0.05:
        M_math_significant.append(const_names[i])
        
for i in range(len(p_math_F.pvalues) - 1):
    if p_math_F.pvalues[i + 1] < 0.05:
        F_math_significant.append(const_names[i])
        
print("Significant Male math test constants: " + str(M_math_significant))
print()

print("Significant Female math test constants: " + str(F_math_significant))

Significant Male reading test constants: ['READING_GROWTH_M']

Significant Female reading test constants: ['READING_GROWTH_F']

Significant Male math test constants: ['READING_GROWTH_M', 'READING_GROWTH_F', 'STATE_ARIZONA', 'STATE_ARKANSAS', 'STATE_CONNECTICUT', 'STATE_FLORIDA', 'STATE_ILLINOIS', 'STATE_MAINE', 'STATE_MONTANA', 'STATE_NEVADA', 'STATE_NEW_YORK', 'STATE_NORTH_CAROLINA', 'STATE_OREGON', 'STATE_PENNSYLVANIA', 'STATE_VERMONT']

Significant Female math test constants: ['READING_GROWTH_F', 'STATE_CONNECTICUT', 'STATE_IDAHO', 'STATE_MARYLAND', 'STATE_NEW_HAMPSHIRE', 'STATE_NORTH_CAROLINA', 'STATE_VERMONT']

It seems that for reading, there the state does not have significance on either gender of FEMALE or MALE in all states. For the math models, certain states within both the FEMALE and MALE models have significant impact on the math listeracy growth in the United States.

Conclusion/Insights Gained

As a reminder, we are defining growth in math literacy as an increase in average math scores for 4th graders on the NAEP test from 2009 to some future year, and the same definition for reading literacy respectively. We wanted to explore how state and gender play a role in math and reading literacy education standards, which our growth metric for different subsets of our population with state and gender interactions measures.

Based on our exploratory analysis of our data, we found that both math and reading literacy are affected by state, and by gender and state in which a student is in, which indicates that education inequality has been persisting since 2009, as the growth metric differs significantly depending on the state given, or the assumed gender (FEMALE or MALE) with a state given. Important to note that this dataset also obfiscates people outside of the male/female classfication, which may not accurately represent their gendered experiences in the American education system.

Analyzing our predictive models based on state for math and reading literacy, our results indicate that the state where a student resides play a role in determining growth in reading and math literacy. We found that in states centered in the midwest such as Arkansas, Indiana, and Colorado, students are predicted to have significant, specifically, negative growth in reading and math based on our p-values for various states for both math and reading literacy growth being below 0.05; hence we can be 95% confident to reject our null hypothesis of there being no relationship between state and math/reading literacy growth, and hence, we can determine that state has played some significant role in differing the growth of literacy for these subjects across the US - indicating that education inequality is persisting across the United States, state by state. This may be because these are more rural areas, which have less access to opportunities that states centered around more urban areas typically have. Performing this type of analysis can be useful when determining curriculums (especially common core which applies nationwide) because there are vast differences in the quality of education administered (see more here). If students in a particular state are less likely to perform well on math and reading test, state-specific policies could and should be introduced to change the current standards of education to lean towards significant positive growth.

Analyzing our predictive models based on state and gender for math/reading literacy, our results indicate to us that there is no significant growth in reading literacy across genders of FEMALE and MALE in the United States. Hence, since our p-values ranged above 0.05 significance level, for reading literacy, we cannot reject the null hypothesis that gender and state interactions play a role with reading literacy growth - indicating that state and gender interaction may not play a large role in reading difference in education inequality. This does differ slightly from our exploratory data analysis which expected differently. For our models of states under the MALE classification, we foud that there is a significant impact on math literacy that is either positive or negative - could be either extreme. Hence, since our p-values ranged below 0.05 significance level for multiple states in both math models of genders, for math iteracy, we can reject the null hypothesis that gender and state interactions play a role with math literacy growth - once again indicating to us that there still exists education inequality in math literacy within gender and state interactions.

We hope that these models curated, and the exploratory data analysis done, can be used by policymakers when determining which states, and which gendered demographics within states, need more support in developing math and reading curriculums and hiring educators. State, and gender within state, play roles in math and reading literacy that must be changed to provide equitable education to everyone.