Teaching Ratings¶
Run in Google ColabObjective: Analyze the evaluation of professors with different characteristics and determine whether there are external influences on their teaching evaluation scores.
Import libraries¶
In [1]:
from scipy.stats import norm, levene, ttest_ind, f_oneway, chi2_contingency, pearsonr
import statsmodels.api as sm
from statsmodels.formula.api import ols
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
sns.set_style('whitegrid')
Load the dataset¶
In [2]:
file_url = 'https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ST0151EN-SkillsNetwork/labs/teachingratings.csv'
df = pd.read_csv(file_url).loc[:, :"prof"]
df.head()
Out[2]:
| minority | age | gender | credits | beauty | eval | division | native | tenure | students | allstudents | prof | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | yes | 36 | female | more | 0.289916 | 4.3 | upper | yes | yes | 24 | 43 | 1 |
| 1 | yes | 36 | female | more | 0.289916 | 3.7 | upper | yes | yes | 86 | 125 | 1 |
| 2 | yes | 36 | female | more | 0.289916 | 3.6 | upper | yes | yes | 76 | 125 | 1 |
| 3 | yes | 36 | female | more | 0.289916 | 4.4 | upper | yes | yes | 77 | 123 | 1 |
| 4 | no | 59 | male | more | -0.737732 | 4.5 | upper | yes | yes | 17 | 20 | 2 |
Understand the dataset¶
| Variable | Description |
|---|---|
| minority | Does the instructor belong to a minority (non-Caucasian) group? |
| age | The instructor's age |
| gender | Indicating whether the instructor was male or female. |
| credits | Is the course a single-credit elective? |
| beauty | Rating of the instructor's physical appearance by a panel of six students averaged across the six panelists and standardized to have a mean of zero. |
| eval | Course overall teaching evaluation score, on a scale of 1 (very unsatisfactory) to 5 (excellent). |
| division | Is the course an upper or lower division course? |
| native | Is the instructor a native English speaker? |
| tenure | Is the instructor on a tenure track? |
| students | Number of students that participated in the evaluation. |
| allstudents | Number of students enrolled in the course. |
| prof | Indicating instructor identifier. |
In [3]:
df.info()
<class 'pandas.core.frame.DataFrame'> RangeIndex: 463 entries, 0 to 462 Data columns (total 12 columns): # Column Non-Null Count Dtype --- ------ -------------- ----- 0 minority 463 non-null object 1 age 463 non-null int64 2 gender 463 non-null object 3 credits 463 non-null object 4 beauty 463 non-null float64 5 eval 463 non-null float64 6 division 463 non-null object 7 native 463 non-null object 8 tenure 463 non-null object 9 students 463 non-null int64 10 allstudents 463 non-null int64 11 prof 463 non-null int64 dtypes: float64(2), int64(4), object(6) memory usage: 43.5+ KB
Visualize the dataset¶
In [4]:
number_features = df.columns.size - 1
grid_rows = int(np.ceil(number_features / 3))
fig, axs = plt.subplots(grid_rows, 3, figsize=(15, 5 * grid_rows))
for ax, feature in zip(axs.flatten(), df.columns[:number_features]):
if df[feature].dtype == 'O':
labels, sizes = np.unique(df[feature], return_counts=True)
sns.barplot(x=labels, y=sizes, hue=labels, ax=ax, legend=False)
ax.set_xlabel("")
ax.set_title(feature)
else:
sns.histplot(data=df, x=feature, ax=ax)
ax.set_xlabel("")
ax.set_title(feature)
for ax in axs.flatten()[number_features:]:
ax.axis("off")
plt.tight_layout()
plt.show()
Analysis¶
Does the average beauty score vary by gender?¶
In [5]:
df_subset = df.drop_duplicates(subset=['prof'])
gender_beauty_mean = df_subset.groupby('gender')["beauty"].mean().round(2)
print(gender_beauty_mean)
plt.figure()
sns.histplot(data=df_subset, x="beauty", hue="gender")
plt.axvline(gender_beauty_mean["female"], color="blue", linestyle='dashed', linewidth=2)
plt.axvline(gender_beauty_mean["male"], color="orange", linestyle='dashed', linewidth=2)
plt.show()
gender female 0.25 male -0.03 Name: beauty, dtype: float64
What is the percentage of males and females that are tenured professors?¶
In [6]:
gender_tenure_count = df[df.tenure == 'yes'].drop_duplicates(subset=['prof']).groupby('gender')["tenure"].count()
labels = gender_tenure_count.keys()
sizes = gender_tenure_count.values
fig, ax = plt.subplots()
ax.pie(sizes, textprops={'color': "w", 'fontsize': '12'}, autopct=lambda pct: "{:.2f}%\n({:d})".format(pct, round(pct/100 * sum(sizes))))
ax.legend(labels)
ax.set_title("Tenured professors")
plt.show()
What is the percentage of professors from minority and non-minority groups that are tenured?¶
In [7]:
minority_tenure_count = df[df.tenure == 'yes'].drop_duplicates(subset=['prof']).groupby('minority')["tenure"].count()
labels = ["non-minority" if i == "no" else "minority" for i in minority_tenure_count.keys()]
sizes = minority_tenure_count.values
fig, ax = plt.subplots()
ax.pie(sizes, textprops={'color': "w", 'fontsize': '12'}, autopct=lambda pct: "{:.2f}%\n({:d})".format(pct, round(pct/100 * sum(sizes))))
ax.legend(labels)
plt.title("Tenured professors")
plt.show()
Does the average age vary by tenure?¶
In [8]:
df_subset = df.drop_duplicates(subset=['prof'])
tenure_age_mean = df_subset.groupby('tenure')["age"].mean().round(2)
print(tenure_age_mean)
plt.figure()
sns.histplot(data=df_subset, x="age", hue="tenure")
plt.axvline(tenure_age_mean["yes"], color="blue", linestyle="dashed", linewidth=2)
plt.axvline(tenure_age_mean["no"], color="orange", linestyle="dashed", linewidth=2)
plt.show()
tenure no 49.27 yes 47.23 Name: age, dtype: float64
What is the average evaluation score for tenured professors?¶
In [9]:
tenure_eval_mean = df.groupby('tenure')["eval"].mean().round(2)
print(tenure_eval_mean)
plt.figure()
sns.histplot(data=df, x="eval", hue="tenure")
plt.axvline(tenure_eval_mean["yes"], color="blue", linestyle="dashed", linewidth=2)
plt.axvline(tenure_eval_mean["no"], color="orange", linestyle="dashed", linewidth=2)
plt.show()
tenure no 4.13 yes 3.96 Name: eval, dtype: float64
Do instructors teaching lower-division courses receive higher average teaching evaluations?¶
In [10]:
division_eval_mean = df.groupby('division')["eval"].mean().round(2)
print(division_eval_mean)
plt.figure()
sns.histplot(data=df, x="eval", hue="division")
plt.axvline(division_eval_mean["lower"], color="orange", linestyle="dashed", linewidth=2)
plt.axvline(division_eval_mean["upper"], color="blue", linestyle="dashed", linewidth=2)
plt.show()
division lower 4.09 upper 3.95 Name: eval, dtype: float64
Do beauty scores vary by course credits?¶
In [11]:
print(df.groupby('credits')["beauty"].describe().round(2).iloc[:, 1:])
plt.figure()
sns.boxplot(x="credits", y='beauty', hue="credits", data=df)
plt.show()
mean std min 25% 50% 75% max credits more 0.02 0.80 -1.45 -0.66 -0.07 0.56 1.97 single -0.27 0.58 -0.66 -0.58 -0.53 -0.29 1.15
What is the number of courses taught by gender?¶
In [12]:
courses_gender_count = df["gender"].value_counts()
print(courses_gender_count)
plt.figure()
sns.countplot(data=df, x="gender", hue="gender")
plt.show()
gender male 268 female 195 Name: count, dtype: int64
What is the number of professors by gender and tenure?¶
In [13]:
df_subset = df.drop_duplicates(subset=['prof'])
gender_tenure_count = df_subset.groupby("gender")["tenure"].value_counts()
print(gender_tenure_count)
plt.figure()
sns.countplot(data=df_subset, x="gender", hue="tenure")
plt.show()
gender tenure
female yes 32
no 8
male yes 47
no 7
Name: count, dtype: int64
Does the average evaluation score vary by gender?¶
In [14]:
gender_eval_mean = df.groupby('gender')["eval"].mean().round(2)
print(gender_eval_mean)
plt.figure()
sns.histplot(data=df, x="eval", hue="gender")
plt.axvline(gender_eval_mean["female"], color="blue", linestyle='dashed', linewidth=2)
plt.axvline(gender_eval_mean["male"], color="orange", linestyle='dashed', linewidth=2)
plt.show()
gender female 3.90 male 4.07 Name: eval, dtype: float64
What is the average age by gender?¶
In [15]:
df_subset = df.drop_duplicates(subset=['prof'])
gender_eval_mean = df_subset.groupby('gender')["age"].mean().round(2)
print(gender_eval_mean)
plt.figure()
sns.histplot(data=df_subset, x="age", hue="gender")
plt.axvline(gender_eval_mean["female"], color="blue", linestyle='dashed', linewidth=2)
plt.axvline(gender_eval_mean["male"], color="orange", linestyle='dashed', linewidth=2)
plt.show()
gender female 44.95 male 49.48 Name: age, dtype: float64
What is the average age by gender and tenure?¶
In [16]:
df_subset = df.drop_duplicates(subset=['prof'])
print(df_subset.groupby(['tenure', "gender"])["age"].describe().round(2).iloc[:, 1:])
plt.figure()
sns.boxplot(x="tenure", y="age", hue="gender", data=df_subset)
plt.show()
mean std min 25% 50% 75% max
tenure gender
no female 48.88 7.14 38.0 45.00 51.0 53.00 57.0
male 49.71 8.56 37.0 46.00 48.0 54.00 63.0
yes female 43.97 9.16 29.0 35.75 43.0 51.25 62.0
male 49.45 11.19 32.0 40.50 50.0 59.50 73.0
Do native professors have higher beauty scores?¶
In [17]:
df_subset = df.drop_duplicates(subset=['prof'])
native_beauty_mean = df_subset.groupby('native')["beauty"].mean().round(2)
print(native_beauty_mean)
plt.figure()
sns.histplot(data=df_subset, x="beauty", hue="native")
plt.axvline(native_beauty_mean["yes"], color="blue", linestyle="dashed", linewidth=2)
plt.axvline(native_beauty_mean["no"], color="orange", linestyle="dashed", linewidth=2)
plt.show()
native no -0.09 yes 0.10 Name: beauty, dtype: float64
What is the average age of professors from minority and non-minority groups?¶
In [18]:
df_subset = df.drop_duplicates(subset=['prof'])
print(df_subset.groupby(["minority"])["age"].describe().round(2).iloc[:, 1:])
plt.figure()
sns.boxplot(x="minority", y="age", hue="minority", data=df_subset)
plt.show()
mean std min 25% 50% 75% max minority no 48.24 10.43 31.0 39.00 49.0 57.00 73.0 yes 42.83 7.73 29.0 35.75 43.5 47.75 54.0
What is the number of professors by gender from minority and non-minority groups?¶
In [19]:
df_subset = df.drop_duplicates(subset=['prof'])
gender_minority_count = df_subset.groupby("gender")["minority"].value_counts()
print(gender_minority_count)
plt.figure()
sns.countplot(data=df_subset, x="gender", hue="minority")
plt.show()
gender minority
female no 32
yes 8
male no 50
yes 4
Name: count, dtype: int64
What is the probability of receiving an evaluation score greater than 4.5?¶
In [20]:
eval_statistics = df["eval"].describe().round(2).iloc[1:]
probability = norm.cdf((4.5 - eval_statistics["mean"]) / eval_statistics["std"])
print(eval_statistics)
print("\n\033[1mProbability\033[0m = {:.2f}%".format(100*(1 - probability)))
plt.figure()
sns.boxplot(x='eval', data=df)
plt.show()
mean 4.00
std 0.55
min 2.10
25% 3.60
50% 4.00
75% 4.40
max 5.00
Name: eval, dtype: float64
Probability = 18.17%
What is the probability of receiving an evaluation score greater than 3.5 and less than 4.2?¶
In [21]:
probability_1 = norm.cdf((3.5 - eval_statistics["mean"]) / eval_statistics["std"])
probability_2 = norm.cdf((4.2 - eval_statistics["mean"]) / eval_statistics["std"])
print("\033[1mProbability\033[0m = {:.2f}%".format(100*(probability_2 - probability_1)))
Probability = 46.03%
Using t-test, does gender affect teaching evaluation scores?¶
For the t-test for independent samples, the following assumptions must be met:
- One independent, categorical variable with two levels or groups.
- One dependent continuous variable.
- There is no relationship between the observations in each group.
- The dependent variable must follow a normal distribution.
- Assumption of homogeneity of variance.
State the hypothesis:
- $H_0: µ_1 = µ_2$ (There is no difference in evaluation scores between male and females)
- $H_1: µ_1 ≠ µ_2$ (There is a difference in evaluation scores between male and females)
In [22]:
df.groupby("gender")["eval"].describe()
Out[22]:
| count | mean | std | min | 25% | 50% | 75% | max | |
|---|---|---|---|---|---|---|---|---|
| gender | ||||||||
| female | 195.0 | 3.901026 | 0.538803 | 2.3 | 3.6 | 3.90 | 4.3 | 4.9 |
| male | 268.0 | 4.069030 | 0.556652 | 2.1 | 3.7 | 4.15 | 4.5 | 5.0 |
Use the Levene's test to test the null hypothesis that all input samples are from populations with equal variances.
In [23]:
levene(df[df['gender'] == 'female']['eval'],
df[df['gender'] == 'male']['eval'],
center='mean')
Out[23]:
LeveneResult(statistic=np.float64(0.19032922435292574), pvalue=np.float64(0.6628469836244741))
Since the p-value is greater than 0.05, we can assume equality of variance.
In [24]:
ttest_ind(df[df['gender'] == 'female']['eval'],
df[df['gender'] == 'male']['eval'],
equal_var=True)
Out[24]:
TtestResult(statistic=np.float64(-3.249937943510772), pvalue=np.float64(0.0012387609449522217), df=np.float64(461.0))
Answer: Since the p-value is less than 0.05, we can reject the null hypothesis as there is enough proof that there is a statistical difference in teaching evaluations based on gender.
Using ANOVA test, do beauty scores vary by age?¶
The data must be grouped into categories as the one-way ANOVA can't work with continuous variable, then the categories will be professors that are:
- 40 years and younger.
- Between 40 and 60 years.
- 60 years and older.
State the hypothesis:
- $H_0: µ_1 = µ_2 = µ_3$ (The three population means are equal)
- $H_1:$ At least one of the means differ.
In [25]:
df.loc[(df['age'] <= 40), 'age_group'] = '40 years and younger'
df.loc[(df['age'] > 40) & (df['age'] < 60), 'age_group'] = 'between 40 and 60 years'
df.loc[(df['age'] >= 60), 'age_group'] = '60 years and older'
In [26]:
df.groupby("age_group")["beauty"].describe()
Out[26]:
| count | mean | std | min | 25% | 50% | 75% | max | |
|---|---|---|---|---|---|---|---|---|
| age_group | ||||||||
| 40 years and younger | 113.0 | 0.336196 | 0.913748 | -1.450494 | -0.326015 | 0.289916 | 1.070944 | 1.970023 |
| 60 years and older | 77.0 | -0.423557 | 0.548289 | -1.422919 | -0.733091 | -0.395397 | -0.056677 | 0.588569 |
| between 40 and 60 years | 273.0 | -0.019693 | 0.728354 | -1.090389 | -0.583587 | -0.083601 | 0.420400 | 1.774334 |
Test for equality of variance.
In [27]:
levene(df[df['age_group'] == '40 years and younger']['beauty'],
df[df['age_group'] == 'between 40 and 60 years']['beauty'],
df[df['age_group'] == '60 years and older']['beauty'],
center='mean')
Out[27]:
LeveneResult(statistic=np.float64(11.769735544673434), pvalue=np.float64(1.0350399938234537e-05))
Since the p-value is less than 0.05, the variances are not equal.
In [28]:
f_oneway(df[df['age_group'] == '40 years and younger']['beauty'],
df[df['age_group'] == 'between 40 and 60 years']['beauty'],
df[df['age_group'] == '60 years and older']['beauty'])
Out[28]:
F_onewayResult(statistic=np.float64(23.552552376353074), pvalue=np.float64(1.8271127151948056e-10))
Answer: Since the p-value is less than 0.05, we reject the null hypothesis as there is significant evidence that at least one of the means differs.
Using ANOVA test, do teaching evaluation scores vary by age?¶
State the hypothesis:
- $H_0: µ_1 = µ_2 = µ_3$ (The three population means are equal)
- $H_1:$ At least one of the means differ.
In [29]:
df.groupby("age_group")["eval"].describe()
Out[29]:
| count | mean | std | min | 25% | 50% | 75% | max | |
|---|---|---|---|---|---|---|---|---|
| age_group | ||||||||
| 40 years and younger | 113.0 | 4.002655 | 0.505763 | 2.7 | 3.6 | 4.1 | 4.4 | 4.8 |
| 60 years and older | 77.0 | 3.894805 | 0.626371 | 2.2 | 3.4 | 4.0 | 4.4 | 4.9 |
| between 40 and 60 years | 273.0 | 4.025641 | 0.551537 | 2.1 | 3.7 | 4.0 | 4.5 | 5.0 |
In [30]:
levene(df[df['age_group'] == '40 years and younger']['eval'],
df[df['age_group'] == 'between 40 and 60 years']['eval'],
df[df['age_group'] == '60 years and older']['eval'],
center='mean')
Out[30]:
LeveneResult(statistic=np.float64(3.123930368994838), pvalue=np.float64(0.04491850441786862))
In [31]:
f_oneway(df[df['age_group'] == '40 years and younger']['eval'],
df[df['age_group'] == 'between 40 and 60 years']['eval'],
df[df['age_group'] == '60 years and older']['eval'])
Out[31]:
F_onewayResult(statistic=np.float64(1.6792657352642264), pvalue=np.float64(0.1876521827204442))
Answer: Since the p-value is greater than 0.05, we cannot reject the null hypothesis as there is no significant evidence that at least one of the means differs.
Using chi-square, is there an association between tenure and gender?¶
State the hypothesis:
- $H_0:$ The proportion of professors who are tenured is independent of gender.
- $H_1:$ The proportion of professors who are tenured is associated with gender.
In [32]:
cross_tenure_gender = pd.crosstab(df['tenure'], df['gender'])
cross_tenure_gender
Out[32]:
| gender | female | male |
|---|---|---|
| tenure | ||
| no | 50 | 52 |
| yes | 145 | 216 |
In [33]:
chi2_contingency(cross_tenure_gender, correction=False)
Out[33]:
Chi2ContingencyResult(statistic=np.float64(2.557051129789522), pvalue=np.float64(0.10980322511302845), dof=1, expected_freq=array([[ 42.95896328, 59.04103672],
[152.04103672, 208.95896328]]))
Answer: Since the p-value is greater than 0.05, we cannot reject the null hypothesis as there is no sufficient evidence that professors are tenured as a result of gender.
Using Pearson correlation, is teaching evaluation score correlated with beauty score?¶
State the hypothesis:
- $H_0:$ Teaching evaluation score is not correlated with beauty score.
- $H_1:$ Teaching evaluation score is correlated with beauty score.
In [34]:
sns.lmplot(data=df, x="beauty", y="eval", line_kws={"color": "red"})
plt.show()
In [35]:
pearsonr(df['beauty'], df['eval'])
Out[35]:
PearsonRResult(statistic=np.float64(0.18903909084045212), pvalue=np.float64(4.247115419813557e-05))
Answer: Since the p-value is less than 0.05, we reject the null hypothesis as there exists a relationship between beauty and teaching evaluation score.
Using t-test, does tenure affect teaching evaluation scores?¶
State the hypothesis
- $H_0: µ_1 = µ_2$ (There is no difference in evaluation scores between tenure and non-tenure)
- $H_1: µ_1 ≠ µ_2$ (There is a difference in evaluation scores between tenure and non-tenure)
In [36]:
df.groupby("tenure")["eval"].describe()
Out[36]:
| count | mean | std | min | 25% | 50% | 75% | max | |
|---|---|---|---|---|---|---|---|---|
| tenure | ||||||||
| no | 102.0 | 4.133333 | 0.556747 | 2.8 | 3.7 | 4.2 | 4.6 | 5.0 |
| yes | 361.0 | 3.960111 | 0.549104 | 2.1 | 3.6 | 4.0 | 4.4 | 5.0 |
In [37]:
ttest_ind(df[df['tenure'] == 'yes']['eval'],
df[df['tenure'] == 'no']['eval'],
equal_var=True)
Out[37]:
TtestResult(statistic=np.float64(-2.8046798258451777), pvalue=np.float64(0.005249471210198792), df=np.float64(461.0))
Answer: Since the p-value is less than 0.05, we reject the null hypothesis as there evidence that being tenured affects teaching evaluation scores.
Using chi-square, is there an association between age and tenure?¶
State the hypothesis:
- $H_0:$ There is no association between age and tenure.
- $H_1:$ There is an association between age and tenure.
In [38]:
cross_tenure_age = pd.crosstab(df['tenure'], df['age_group'])
cross_tenure_age
Out[38]:
| age_group | 40 years and younger | 60 years and older | between 40 and 60 years |
|---|---|---|---|
| tenure | |||
| no | 15 | 7 | 80 |
| yes | 98 | 70 | 193 |
In [39]:
chi2_contingency(cross_tenure_age, correction=True)
Out[39]:
Chi2ContingencyResult(statistic=np.float64(20.957740803528935), pvalue=np.float64(2.8124473945785386e-05), dof=2, expected_freq=array([[ 24.89416847, 16.96328294, 60.1425486 ],
[ 88.10583153, 60.03671706, 212.8574514 ]]))
Answer: Since the p-value is less than 0.05, we reject the null hypothesis as there is evidence of an association between age and tenure.
Using chi-square, is there an association between visible minorities and tenure?¶
State the hypothesis:
- $H_0:$ There is no association between tenure and visible minorities.
- $H_1:$ There is an association between tenure and visible minorities.
In [40]:
cross_minority_tenure = pd.crosstab(df['minority'], df['tenure'])
cross_minority_tenure
Out[40]:
| tenure | no | yes |
|---|---|---|
| minority | ||
| no | 92 | 307 |
| yes | 10 | 54 |
In [41]:
chi2_contingency(cross_minority_tenure, correction=True)
Out[41]:
Chi2ContingencyResult(statistic=np.float64(1.3675127484429763), pvalue=np.float64(0.24223968800237178), dof=1, expected_freq=array([[ 87.90064795, 311.09935205],
[ 14.09935205, 49.90064795]]))
Answer: Since the p-value is greater than 0.05, we cannot reject the null hypothesis as there is no evidence of an association between visible minorities and tenure.
Using regression with t-test, does gender affect teaching evaluation scores?¶
State the hypothesis:
- $H_0: β_1$ = 0 (Gender has no effect on teaching evaluation scores)
- $H_1: β_1$ is not equal to 0 (Gender has an effect on teaching evaluation scores)
In [42]:
# X is the input variables (or independent variables)
X = df['gender'].map({"female": 1, "male": 0})
# y is the target/dependent variable
y = df['eval']
# Add an intercept (beta_0) to our model
X = sm.add_constant(X)
# Ordinary Least Squares
model = sm.OLS(y, X).fit()
# Print out the statistics
model.summary()
Out[42]:
| Dep. Variable: | eval | R-squared: | 0.022 |
|---|---|---|---|
| Model: | OLS | Adj. R-squared: | 0.020 |
| Method: | Least Squares | F-statistic: | 10.56 |
| Date: | Thu, 29 May 2025 | Prob (F-statistic): | 0.00124 |
| Time: | 02:23:20 | Log-Likelihood: | -378.50 |
| No. Observations: | 463 | AIC: | 761.0 |
| Df Residuals: | 461 | BIC: | 769.3 |
| Df Model: | 1 | ||
| Covariance Type: | nonrobust |
| coef | std err | t | P>|t| | [0.025 | 0.975] | |
|---|---|---|---|---|---|---|
| const | 4.0690 | 0.034 | 121.288 | 0.000 | 4.003 | 4.135 |
| gender | -0.1680 | 0.052 | -3.250 | 0.001 | -0.270 | -0.066 |
| Omnibus: | 17.625 | Durbin-Watson: | 1.209 |
|---|---|---|---|
| Prob(Omnibus): | 0.000 | Jarque-Bera (JB): | 18.970 |
| Skew: | -0.496 | Prob(JB): | 7.60e-05 |
| Kurtosis: | 2.981 | Cond. No. | 2.47 |
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
Answer: Since the p-value is less than 0.05, we reject the null hypothesis as there is evidence that there is a difference in mean evaluation scores based on gender. The coefficient -0.1680 means that females get 0.168 scores less than men.
Using regression with ANOVA, do beauty scores vary by age?¶
State the hypothesis:
- $H_0: µ_1 = µ_2 = µ_3$ (The three population means are equal)
- $H_1:$ At least one of the means differ.
In [43]:
model = ols('beauty ~ age_group', data=df).fit()
anova_table = sm.stats.anova_lm(model)
anova_table
Out[43]:
| df | sum_sq | mean_sq | F | PR(>F) | |
|---|---|---|---|---|---|
| age_group | 2.0 | 26.691809 | 13.345905 | 23.552552 | 1.827113e-10 |
| Residual | 460.0 | 260.656087 | 0.566644 | NaN | NaN |
Answer: Since the p-value is less than 0.05, we reject the null hypothesis as there is significant evidence that at least one of the means differs.
Using regression with t-test, does tenure affect beauty scores?¶
State the hypothesis:
- $H_0:$ The average beauty scores for tenured and non-tenured instructors are equal.
- $H_1:$ There is a difference in the average beauty scores for tenured and non-tenured instructors.
In [44]:
# X is the input variables (or independent variables)
X = df['tenure'].map({"yes": 1, "no": 0})
# y is the target/dependent variable
y = df['beauty']
# Add an intercept (beta_0) to our model
X = sm.add_constant(X)
# Ordinary Least Squares
model = sm.OLS(y, X).fit()
# Print out the statistics
model.summary()
Out[44]:
| Dep. Variable: | beauty | R-squared: | 0.000 |
|---|---|---|---|
| Model: | OLS | Adj. R-squared: | -0.002 |
| Method: | Least Squares | F-statistic: | 0.1689 |
| Date: | Thu, 29 May 2025 | Prob (F-statistic): | 0.681 |
| Time: | 02:23:20 | Log-Likelihood: | -546.45 |
| No. Observations: | 463 | AIC: | 1097. |
| Df Residuals: | 461 | BIC: | 1105. |
| Df Model: | 1 | ||
| Covariance Type: | nonrobust |
| coef | std err | t | P>|t| | [0.025 | 0.975] | |
|---|---|---|---|---|---|---|
| const | 0.0284 | 0.078 | 0.363 | 0.717 | -0.125 | 0.182 |
| tenure | -0.0364 | 0.089 | -0.411 | 0.681 | -0.210 | 0.138 |
| Omnibus: | 23.184 | Durbin-Watson: | 0.461 |
|---|---|---|---|
| Prob(Omnibus): | 0.000 | Jarque-Bera (JB): | 23.229 |
| Skew: | 0.507 | Prob(JB): | 9.03e-06 |
| Kurtosis: | 2.583 | Cond. No. | 4.05 |
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
Answer: Since the p-value is greater than 0.05, we cannot reject the null hypothesis as there is no evidence that the mean difference of tenured and untenured instructors are different.
Using regression with t-test, are more students assigned to native professors?¶
State the hypothesis:
- $H_0:$ The average number of students assigned to native english speakers vs non-native english speakers are equal.
- $H_1:$ There is a difference in the average number of students assigned to native english speakers vs non-native English speakers.
In [45]:
# X is the input variables (or independent variables)
X = df["native"].map({"yes": 1, "no": 0})
# y is the target/dependent variable
y = df['allstudents']
# Add an intercept (beta_0) to our model
X = sm.add_constant(X)
# Ordinary Least Squares
model = sm.OLS(y, X).fit()
# Print out the statistics
model.summary()
Out[45]:
| Dep. Variable: | allstudents | R-squared: | 0.007 |
|---|---|---|---|
| Model: | OLS | Adj. R-squared: | 0.005 |
| Method: | Least Squares | F-statistic: | 3.476 |
| Date: | Thu, 29 May 2025 | Prob (F-statistic): | 0.0629 |
| Time: | 02:23:20 | Log-Likelihood: | -2654.2 |
| No. Observations: | 463 | AIC: | 5312. |
| Df Residuals: | 461 | BIC: | 5321. |
| Df Model: | 1 | ||
| Covariance Type: | nonrobust |
| coef | std err | t | P>|t| | [0.025 | 0.975] | |
|---|---|---|---|---|---|---|
| const | 29.6071 | 14.150 | 2.092 | 0.037 | 1.802 | 57.413 |
| native | 27.2158 | 14.598 | 1.864 | 0.063 | -1.471 | 55.902 |
| Omnibus: | 429.792 | Durbin-Watson: | 0.708 |
|---|---|---|---|
| Prob(Omnibus): | 0.000 | Jarque-Bera (JB): | 10527.126 |
| Skew: | 4.129 | Prob(JB): | 0.00 |
| Kurtosis: | 24.852 | Cond. No. | 8.01 |
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
Answer: Since the p-value is greater than 0.05, we cannot reject the null hypothesis as there is no evidence that being a native english speaker or a non-native english speaker affects the number of students assigned.