Distinctive Analytics

To perform ANCOVA (Analysis of Covariance) with a dataset that includes multiple types of variables, you’ll need to ensure your dependent variable is continuous, and you can include categorical variables as factors. Below is an example using the statsmodels library in Python:

Mock Dataset

Let’s create a dataset with a mix of variable types:

import numpy as np
import statsmodels.api as sm
from statsmodels.formula.api import ols

# Generating a larger sample dataset
np.random.seed(0)
data = pd.DataFrame({
    'continuous_var': np.random.uniform(1, 10, 100),
    'categorical_var': np.random.choice(['A', 'B', 'C'], 100),
    'binary_var': np.random.choice([0, 1], 100),
    'discrete_var': np.random.choice([1, 2, 3], 100),
    'ordinal_var': np.random.choice(['low', 'medium', 'high'], 100),
    'interval_var': np.random.uniform(10, 30, 100),
    'ratio_var': np.random.uniform(100, 300, 100),
    'dependent_var': np.random.uniform(5, 20, 100)
})

# Convert categorical variables to category dtype
data['categorical_var'] = data['categorical_var'].astype('category')
data['ordinal_var'] = pd.Categorical(data['ordinal_var'], categories=['low', 'medium', 'high'], ordered=True)
data.head()

Performing ANCOVA with multiple categorical variables

We’ll perform ANCOVA with dependent_var as the dependent variable, continuous_var and ratio_var as covariates, and categorical_var as a factor:

data['categorical_var'] = data['categorical_var'].astype('category')
data['ordinal_var'] = pd.Categorical(data['ordinal_var'], categories=['low', 'medium', 'high'], ordered=True)

# Defining the formula for ANCOVA
formula = 'dependent_var ~ C(categorical_var) + continuous_var + ratio_var'

# Fitting the model
model = ols(formula, data=data).fit()

# Performing ANCOVA
anova_table = sm.stats.anova_lm(model, typ=2)
print(anova_table)

Explanation:

• Formula: The formula ‘dependent_var ~ C(categorical_var) + continuous_var + ratio_var‘
• ols: specifies that dependent_var is the dependent variable, categorical_var is a categorical factor (notated by C() ), and continuous_var and ratio_var are covariates.
• anova_lm: This function performs the ANCOVA and returns the results in an ANOVA table format.

You can add more variables to the formula as needed, ensuring that you correctly specify categorical variables with C()

Check out the following examples for numerous variable types

Example 1: Education Dataset

Dataset

• Dependent Variable: Test Scores
• Covariates: Hours of Study, Previous Grades
• Factors: Teaching Method, Gender

Test Scores

Dependent Variables

Hours of Study

Covariates

Previous Grades

Covariates

Teaching Methods

Categorical

Gender

Categorical

import pandas as pd
import numpy as np
import statsmodels.api as sm
from statsmodels.formula.api import ols

# Example dataset
data = pd.DataFrame({
    'test_scores': [80, 85, 88, 90, 85, 80, 95, 90, 88, 85],
    'hours_of_study': [10, 12, 14, 16, 12, 10, 18, 14, 15, 13],
    'previous_grades': [75, 80, 85, 90, 80, 75, 95, 85, 88, 83],
    'teaching_method': ['Traditional', 'Traditional', 'Online', 'Online', 'Traditional', 'Traditional', 'Online', 'Online', 'Traditional', 'Online'],
    'gender': ['M', 'F', 'M', 'F', 'F', 'M', 'M', 'F', 'F', 'M']
})

# Convert categorical variables to category dtype
data['teaching_method'] = data['teaching_method'].astype('category')
data['gender'] = data['gender'].astype('category')

# Defining the formula for ANCOVA
formula = 'test_scores ~ C(teaching_method) + C(gender) + hours_of_study + previous_grades'

# Fitting the model
model = ols(formula, data=data).fit()

# Performing ANCOVA
anova_table = sm.stats.anova_lm(model, typ=2)
print(anova_table)

Example 2: Health Dataset

Dataset

• Dependent Variable: Blood Pressure
• Covariates: Age, Exercise Hours per Week
• Factors: Diet Type, Smoking Status

Test Scores

Dependent Variables

Age

Covariates

Exercise per Week

Covariates

Diet Type

Categorical

Smoking Status

Categorical

import statsmodels.api as sm
from statsmodels.formula.api import ols

# Example dataset
data = pd.DataFrame({
    'blood_pressure': [120, 130, 125, 135, 128, 122, 138, 140, 126, 129],
    'age': [25, 35, 45, 55, 30, 40, 50, 60, 28, 33],
    'exercise_hours': [5, 3, 4, 2, 6, 4, 2, 1, 5, 3],
    'diet_type': ['Vegetarian', 'Non-Vegetarian', 'Vegetarian', 'Non-Vegetarian', 'Vegetarian', 'Non-Vegetarian', 'Vegetarian', 'Non-Vegetarian', 'Vegetarian', 'Non-Vegetarian'],
    'smoking_status': ['Non-Smoker', 'Smoker', 'Non-Smoker', 'Smoker', 'Non-Smoker', 'Smoker', 'Non-Smoker', 'Smoker', 'Non-Smoker', 'Smoker']
})
data
# Convert categorical variables to category dtype
data['diet_type'] = data['diet_type'].astype('category')
data['smoking_status'] = data['smoking_status'].astype('category')

# Defining the formula for ANCOVA
formula = 'blood_pressure ~ C(diet_type) + C(smoking_status) + age + exercise_hours'

# Fitting the model
model = ols(formula, data=data).fit()

# Performing ANCOVA
anova_table = sm.stats.anova_lm(model, typ=2)
print(anova_table)

Example 3: Marketing Dataset

Dataset

• Dependent Variable: Sales
• Covariates: Advertising Spend
• Factors: Region, Campaign Type

Sales

Dependent Variables

Advertising Spend

Covariates

Region

Categorical

Campaign Type

Categorical

import statsmodels.api as sm
from statsmodels.formula.api import ols

# Example dataset
data = pd.DataFrame({
    'sales': [200, 220, 210, 230, 225, 215, 240, 235, 220, 210],
    'advertising_spend': [5000, 6000, 5500, 6500, 6200, 5800, 7000, 6800, 6200, 5900],
    'region': ['North', 'South', 'North', 'South', 'North', 'South', 'North', 'South', 'North', 'South'],
    'campaign_type': ['Online', 'Offline', 'Online', 'Offline', 'Online', 'Offline', 'Online', 'Offline', 'Online', 'Offline']
})

# Convert categorical variables to category dtype
data['region'] = data['region'].astype('category')
data['campaign_type'] = data['campaign_type'].astype('category')

# Defining the formula for ANCOVA
formula = 'sales ~ C(region) + C(campaign_type) + advertising_spend'

# Fitting the model
model = ols(formula, data=data).fit()

# Performing ANCOVA
anova_table = sm.stats.anova_lm(model, typ=2)
print(anova_table)

Conclusion:

These examples demonstrate the flexibility of ANCOVA in handling datasets with a mix of covariates and factors. By correctly specifying the model formula and using the appropriate statistical methods, researchers can gain valuable insights into how different types of variables influence the dependent variable. Whether in education, health, or marketing, ANCOVA provides a robust framework for adjusting for covariates while examining the effects of categorical factors, leading to more precise and meaningful analyses.