Comparing Morning and Afternoon GPAs at UW Madison since 2006

This notebook performs a SQL query on the UW Madison database and does a hypothesis test comparing morning and afternoon class GPAs.

$H_0$ = There is no difference between GPAs of morning and afternoon classes.

$H_A$ = There is a difference between GPAs of morning and afternoon classes.

Import necessary Python libraries and modules

In [1]:
from sqlalchemy import create_engine
from scipy import stats
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
import seaborn as sns

Query the database and create dataframes of morning and afternoon classes

In [2]:
engine = create_engine('postgresql:///uw_madison')
In [3]:
morning_df = pd.read_sql('SELECT * FROM morning_classes_gpas;', engine)
morning_df.describe()
Out[3]:
section_number section_gpa
count 123451.000000 123451.000000
mean 7.673555 3.373092
std 13.850752 0.366443
min 1.000000 0.000000
25% 1.000000 3.117647
50% 2.000000 3.395833
75% 8.000000 3.666667
max 234.000000 3.996503
In [4]:
afternoon_df = pd.read_sql('SELECT * FROM afternoon_classes_gpas;', engine)
afternoon_df.describe()
Out[4]:
section_number section_gpa
count 166296.000000 166296.000000
mean 7.026675 3.389228
std 11.750693 0.371208
min 1.000000 0.000000
25% 1.000000 3.121739
50% 2.000000 3.416667
75% 8.000000 3.695652
max 211.000000 3.998418

Remove the classes where the average GPA was 4.0 and only look at GPAs

In [5]:
morning_minus_four_os = morning_df.loc[morning_df['section_gpa'] != 4.0]['section_gpa']
morning_minus_four_os.describe()
Out[5]:
count    123451.000000
mean          3.373092
std           0.366443
min           0.000000
25%           3.117647
50%           3.395833
75%           3.666667
max           3.996503
Name: section_gpa, dtype: float64
In [6]:
afternoon_minus_four_os = afternoon_df.loc[afternoon_df['section_gpa'] != 4.0]['section_gpa']
afternoon_minus_four_os.describe()
Out[6]:
count    166296.000000
mean          3.389228
std           0.371208
min           0.000000
25%           3.121739
50%           3.416667
75%           3.695652
max           3.998418
Name: section_gpa, dtype: float64

Choose 2,000 random classes from each population to do the hypothesis testing on

In [7]:
morning_choice = np.random.choice(morning_minus_four_os, size=2000, replace=False)
afternoon_choice = np.random.choice(afternoon_minus_four_os, size=2000, replace=False)

Generate histogram plots for GPAs

In [8]:
fig, ax = plt.subplots()
ax.hist(morning_choice, alpha=0.5, color='#1f77b4', bins=50, range=(1.0, 4.0), label='Morning Classes')
ax.axvline(morning_choice.mean(), alpha=1, color='#1f77b4', linestyle='dashed', label='Morning Class Mean')
ax.hist(afternoon_choice, alpha=0.5, bins=50, color='#ff7f0e', range=(1.0, 4.0), label='Afternoon Classes')
ax.axvline(afternoon_choice.mean(), alpha=1, color='#ff7f0e', linestyle='dashed', label='Afternoon Class Mean')
ax.legend()
ax.set_xlabel('GPA');

Perform statistical testing for the hypothesis

In [9]:
stats.ttest_ind(morning_choice, afternoon_choice, equal_var=False)
Out[9]:
Ttest_indResult(statistic=-1.5768663072428946, pvalue=0.1149054103240241)

This shows that there is not a statistically significant difference between the morning and afternoon class GPAs.

Thus, we fail to reject the null hypothesis that grades are the same between the morning and afternoon.