Hypothesis Testing

Hypothesis Testing#

As we previously determined, the following metrics have a right-skewed distribution:

  • from_purchase_to_approved_hours

  • total_payment

  • delivery_time_days

  • total_weight_kg

  • avg_products_price

  • total_freight_value

Given the skewness of these metrics and the fact that most of our hypotheses will involve more than two categories, we will use regression analysis to test our hypotheses.

Regression analysis utilizes the full variance of the data when building a model.

To account for the right-skewness, we will employ a Generalized Linear Model (GLM) regression with a Gamma distribution and a log-link function.

For multiple comparisons, we will apply the Holm correction.

Time Patterns#

Are orders processed longer at night?

For each time of day N (except Sunday):

  • \(H_{0}^{N}:\) The mean order processing time at night equals the mean order processing time during time period N.

  • \(H_{1}^{N}:\) The mean order processing time at night does not equal the mean order processing time during time period N.

df_sales.assign(from_purchase_to_approved_hours = lambda x: x.from_purchase_to_approved_hours + 1e-6).stats.glm(
    formula='from_purchase_to_approved_hours ~ C(purchase_time_of_day, Treatment(reference="Night"))'
    , family=sm.families.Gamma(link=sm.families.links.Log())
    , p_adjust='holm'
)
Variance Inflation Factors
Variable VIF
C(purchase_time_of_day, Treatment(reference="Night"))[T.Afternoon] 1.0
C(purchase_time_of_day, Treatment(reference="Night"))[T.Evening] 1.0
C(purchase_time_of_day, Treatment(reference="Night"))[T.Morning] 1.0
Generalized Linear Model Regression Results
Dep. Variable: from_purchase_to_approved_hours No. Observations: 96346
Model: GLM Df Residuals: 96342
Model Family: Gamma Df Model: 3
Link Function: Log Scale: 4.0286
Method: IRLS Log-Likelihood: -2.3764e+05
Date: Tue, 05 Aug 2025 Deviance: 4.4813e+05
Time: 11:55:32 Pearson chi2: 3.88e+05
No. Iterations: 9 Pseudo R-squ. (CS): 0.0008234
Covariance Type: HC3
coef std err t P>|t| [0.025 0.975]
Intercept 2.4603 0.020 122.914 0.000 2.421 2.500
C(purchase_time_of_day, Treatment(reference="Night"))[T.Afternoon] -0.1477 0.023 -6.406 0.000 -0.193 -0.103
C(purchase_time_of_day, Treatment(reference="Night"))[T.Evening] -0.1881 0.023 -8.209 0.000 -0.233 -0.143
C(purchase_time_of_day, Treatment(reference="Night"))[T.Morning] -0.0839 0.024 -3.513 0.000 -0.131 -0.037
Adjusted p-values (method: holm):
  coef p-unc p-corr
Intercept 2.46 0.000 nan
C(purchase_time_of_day, Treatment(reference="Night"))[T.Afternoon] -0.15 0.000 0.000
C(purchase_time_of_day, Treatment(reference="Night"))[T.Evening] -0.19 0.000 0.000
C(purchase_time_of_day, Treatment(reference="Night"))[T.Morning] -0.08 0.000 0.000

Result:

  • At the 0.05 significance level, the mean order processing time at night is statistically significantly different from the mean order processing time at any other time of day.

  • Moreover, the processing time at night is statistically significantly longer than during other periods.

Are orders processed longer on weekdays?

  • H0: The average processing time for orders on weekdays and weekends is the same.

  • H1: The average processing time for orders on weekdays and weekends differs

df_sales.assign(from_purchase_to_approved_hours = lambda x: x.from_purchase_to_approved_hours + 1e-6).stats.glm(
    formula='from_purchase_to_approved_hours ~ C(purchase_day_type, Treatment(reference="Weekday"))'
    , family=sm.families.Gamma(link=sm.families.links.Log())
)

VIF requires at least two predictors. Skipping check.
Generalized Linear Model Regression Results
Dep. Variable: from_purchase_to_approved_hours No. Observations: 96346
Model: GLM Df Residuals: 96344
Model Family: Gamma Df Model: 1
Link Function: Log Scale: 3.9920
Method: IRLS Log-Likelihood: -2.3742e+05
Date: Tue, 05 Aug 2025 Deviance: 4.4728e+05
Time: 11:55:33 Pearson chi2: 3.85e+05
No. Iterations: 9 Pseudo R-squ. (CS): 0.003053
Covariance Type: HC3
coef std err t P>|t| [0.025 0.975]
Intercept 2.2617 0.007 304.098 0.000 2.247 2.276
C(purchase_day_type, Treatment(reference="Weekday"))[T.Weekend] 0.2567 0.015 17.360 0.000 0.228 0.286

Result:

  • At the 0.05 significance level, the mean order processing time on weekdays is statistically significantly different from the mean order processing time on weekends.

  • Moreover, the processing time on weekdays is statistically significantly shorter than on weekends.

Customer Reviews Scores#

Does reviews score of 1 have a higher average order value?

For each rating N (except 1):

  • \(H_{0}^{N}:\) The mean order value for rating 1 equals the mean order value for rating N.

  • \(H_{1}^{N}:\) The mean order value for rating 1 does not equal the mean order value for rating N.

df_sales.stats.glm(
    formula='total_payment ~ C(order_avg_reviews_score, Treatment(reference=1))'
    , family=sm.families.Gamma(link=sm.families.links.Log())
    , p_adjust='holm'
)
Variance Inflation Factors
Variable VIF
C(order_avg_reviews_score, Treatment(reference=1))[T.2] 1.0
C(order_avg_reviews_score, Treatment(reference=1))[T.3] 1.0
C(order_avg_reviews_score, Treatment(reference=1))[T.4] 1.0
C(order_avg_reviews_score, Treatment(reference=1))[T.5] 1.0
Generalized Linear Model Regression Results
Dep. Variable: total_payment No. Observations: 96346
Model: GLM Df Residuals: 96341
Model Family: Gamma Df Model: 4
Link Function: Log Scale: 1.8232
Method: IRLS Log-Likelihood: -6.0315e+05
Date: Tue, 05 Aug 2025 Deviance: 73396.
Time: 11:55:34 Pearson chi2: 1.76e+05
No. Iterations: 8 Pseudo R-squ. (CS): 0.002713
Covariance Type: HC3
coef std err t P>|t| [0.025 0.975]
Intercept 5.2693 0.016 328.951 0.000 5.238 5.301
C(order_avg_reviews_score, Treatment(reference=1))[T.2] -0.1362 0.029 -4.685 0.000 -0.193 -0.079
C(order_avg_reviews_score, Treatment(reference=1))[T.3] -0.2514 0.021 -12.106 0.000 -0.292 -0.211
C(order_avg_reviews_score, Treatment(reference=1))[T.4] -0.2260 0.019 -12.086 0.000 -0.263 -0.189
C(order_avg_reviews_score, Treatment(reference=1))[T.5] -0.2177 0.017 -12.821 0.000 -0.251 -0.184
Adjusted p-values (method: holm):
  coef p-unc p-corr
Intercept 5.27 0.000 nan
C(order_avg_reviews_score, Treatment(reference=1))[T.2] -0.14 0.000 0.000
C(order_avg_reviews_score, Treatment(reference=1))[T.3] -0.25 0.000 0.000
C(order_avg_reviews_score, Treatment(reference=1))[T.4] -0.23 0.000 0.000
C(order_avg_reviews_score, Treatment(reference=1))[T.5] -0.22 0.000 0.000

Result:

  • At the 0.05 significance level, the mean order value for rating 1 is statistically significantly different from the mean order value for any other rating.

  • Moreover, the mean order value for rating 1 is statistically significantly higher than for other ratings.

Are orders with review score of 1 delivered longer?

For each rating N (except 1):

  • \(H_{0}^{N}:\) The mean delivery time for rating 1 equals the mean delivery time for rating N.

  • \(H_{1}^{N}:\) The mean delivery time for rating 1 does not equal the mean delivery time for rating N.

df_sales.stats.glm(
    formula='delivery_time_days ~ C(order_avg_reviews_score, Treatment(reference=1))'
    , family=sm.families.Gamma(link=sm.families.links.Log())
    , p_adjust='holm'
)
Variance Inflation Factors
Variable VIF
C(order_avg_reviews_score, Treatment(reference=1))[T.2] 1.0
C(order_avg_reviews_score, Treatment(reference=1))[T.3] 1.0
C(order_avg_reviews_score, Treatment(reference=1))[T.4] 1.0
C(order_avg_reviews_score, Treatment(reference=1))[T.5] 1.0
Generalized Linear Model Regression Results
Dep. Variable: delivery_time_days No. Observations: 96211
Model: GLM Df Residuals: 96206
Model Family: Gamma Df Model: 4
Link Function: Log Scale: 0.44468
Method: IRLS Log-Likelihood: -3.1745e+05
Date: Tue, 05 Aug 2025 Deviance: 37991.
Time: 11:55:35 Pearson chi2: 4.28e+04
No. Iterations: 7 Pseudo R-squ. (CS): 0.1121
Covariance Type: HC3
coef std err t P>|t| [0.025 0.975]
Intercept 3.0591 0.008 393.622 0.000 3.044 3.074
C(order_avg_reviews_score, Treatment(reference=1))[T.2] -0.2406 0.016 -15.280 0.000 -0.271 -0.210
C(order_avg_reviews_score, Treatment(reference=1))[T.3] -0.4029 0.011 -36.655 0.000 -0.424 -0.381
C(order_avg_reviews_score, Treatment(reference=1))[T.4] -0.5502 0.009 -59.917 0.000 -0.568 -0.532
C(order_avg_reviews_score, Treatment(reference=1))[T.5] -0.6922 0.008 -84.196 0.000 -0.708 -0.676
Adjusted p-values (method: holm):
  coef p-unc p-corr
Intercept 3.06 0.000 nan
C(order_avg_reviews_score, Treatment(reference=1))[T.2] -0.24 0.000 0.000
C(order_avg_reviews_score, Treatment(reference=1))[T.3] -0.40 0.000 0.000
C(order_avg_reviews_score, Treatment(reference=1))[T.4] -0.55 0.000 0.000
C(order_avg_reviews_score, Treatment(reference=1))[T.5] -0.69 0.000 0.000

Result:

  • At the 0.05 significance level, the mean delivery time for rating 1 is statistically significantly different from the mean delivery time for any other rating.

  • Moreover, the mean delivery time for rating 1 is statistically significantly longer than for other ratings.

Installments#

Are installment orders processed faster?

  • \(H_{0}:\) The mean processing time of installment-based orders equals the mean processing time of non-installment orders.

  • \(H_{1}:\) The mean processing time of installment-based orders does not equal the mean processing time of non-installment orders.

df_sales.assign(from_purchase_to_approved_hours = lambda x: x.from_purchase_to_approved_hours + 1e-6).stats.glm(
    formula='from_purchase_to_approved_hours ~ C(order_has_installment, Treatment(reference="Has Installments"))'
    , family=sm.families.Gamma(link=sm.families.links.Log())
)

VIF requires at least two predictors. Skipping check.
Generalized Linear Model Regression Results
Dep. Variable: from_purchase_to_approved_hours No. Observations: 96346
Model: GLM Df Residuals: 96344
Model Family: Gamma Df Model: 1
Link Function: Log Scale: 5.3357
Method: IRLS Log-Likelihood: -2.4076e+05
Date: Tue, 05 Aug 2025 Deviance: 4.1670e+05
Time: 11:55:36 Pearson chi2: 5.14e+05
No. Iterations: 9 Pseudo R-squ. (CS): 0.05990
Covariance Type: HC3
coef std err t P>|t| [0.025 0.975]
Intercept 1.5922 0.013 124.214 0.000 1.567 1.617
C(order_has_installment, Treatment(reference="Has Installments"))[T.No Installments] 1.1739 0.015 80.109 0.000 1.145 1.203

Result:

  • At the 0.05 significance level, the mean order processing time for installment payments is statistically significantly different from the mean order processing time for non-installment payments.

  • Moreover, the mean order processing time for installment payments is statistically significantly shorter than for non-installment payments.

Do installment orders have a higher average order value?

  • \(H_{0}:\) The mean order value of installment-based orders equals the mean order value of non-installment orders.

  • \(H_{1}:\) The mean order value of installment-based orders does not equal the mean order value of non-installment orders.

df_sales.stats.glm(
    formula='total_payment ~ C(order_has_installment, Treatment(reference="Has Installments"))'
    , family=sm.families.Gamma(link=sm.families.links.Log())
)

VIF requires at least two predictors. Skipping check.
Generalized Linear Model Regression Results
Dep. Variable: total_payment No. Observations: 96346
Model: GLM Df Residuals: 96344
Model Family: Gamma Df Model: 1
Link Function: Log Scale: 1.8866
Method: IRLS Log-Likelihood: -6.0313e+05
Date: Tue, 05 Aug 2025 Deviance: 68063.
Time: 11:55:37 Pearson chi2: 1.82e+05
No. Iterations: 7 Pseudo R-squ. (CS): 0.03146
Covariance Type: HC3
coef std err t P>|t| [0.025 0.975]
Intercept 5.2843 0.006 952.606 0.000 5.273 5.295
C(order_has_installment, Treatment(reference="Has Installments"))[T.No Installments] -0.4950 0.009 -55.592 0.000 -0.512 -0.478

Result:

  • At the 0.05 significance level, the mean order value for installment payments is statistically significantly different from the mean order value for non-installment payments.

  • Moreover, the mean order value for installment payments is statistically significantly higher than for non-installment payments.

Do installment orders have a higher average order weight?

  • \(H_{0}:\) The mean weight of installment-based orders equals the mean weight of non-installment orders.

  • \(H_{1}:\) The mean weight of installment-based orders does not equal the mean weight of non-installment orders.

df_sales.assign(total_weight_kg = lambda x: x.total_weight_kg + 1e-6).stats.glm(
    formula='total_weight_kg ~ C(order_has_installment, Treatment(reference="Has Installments"))'
    , family=sm.families.Gamma(link=sm.families.links.Log())
)

VIF requires at least two predictors. Skipping check.
Generalized Linear Model Regression Results
Dep. Variable: total_weight_kg No. Observations: 96346
Model: GLM Df Residuals: 96344
Model Family: Gamma Df Model: 1
Link Function: Log Scale: 4.1103
Method: IRLS Log-Likelihood: -1.9360e+05
Date: Tue, 05 Aug 2025 Deviance: 1.8836e+05
Time: 11:55:38 Pearson chi2: 3.96e+05
No. Iterations: 8 Pseudo R-squ. (CS): 0.01172
Covariance Type: HC3
coef std err t P>|t| [0.025 0.975]
Intercept 1.0603 0.008 129.641 0.000 1.044 1.076
C(order_has_installment, Treatment(reference="Has Installments"))[T.No Installments] -0.4431 0.013 -33.710 0.000 -0.469 -0.417

Result:

  • At the 0.05 significance level, the mean order weight for installment payments is statistically significantly different from the mean order weight for non-installment payments.

  • Moreover, the mean order weight for installment payments is statistically significantly higher than for non-installment payments.

Do installment orders have a higher average product price in the order?

  • \(H_{0}:\) The mean product price in orders with installment payments equals the mean product price in orders without installment payments.

  • \(H_{1}:\) The mean product price in orders with installment payments does not equal the mean product price in orders without installment payments.

df_sales.stats.glm(
    formula='avg_products_price ~ C(order_has_installment, Treatment(reference="Has Installments"))'
    , family=sm.families.Gamma(link=sm.families.links.Log())
)

VIF requires at least two predictors. Skipping check.
Generalized Linear Model Regression Results
Dep. Variable: avg_products_price No. Observations: 96346
Model: GLM Df Residuals: 96344
Model Family: Gamma Df Model: 1
Link Function: Log Scale: 2.1777
Method: IRLS Log-Likelihood: -5.8102e+05
Date: Tue, 05 Aug 2025 Deviance: 83596.
Time: 11:55:38 Pearson chi2: 2.10e+05
No. Iterations: 8 Pseudo R-squ. (CS): 0.03467
Covariance Type: HC3
coef std err t P>|t| [0.025 0.975]
Intercept 5.0635 0.006 802.494 0.000 5.051 5.076
C(order_has_installment, Treatment(reference="Has Installments"))[T.No Installments] -0.5597 0.010 -58.672 0.000 -0.578 -0.541

Result:

  • At the 0.05 significance level, the mean product price in orders with installment payments is statistically significantly different from the mean product price in orders without installment payments.

  • Moreover, the mean product price in orders with installment payments is statistically significantly higher than in orders without installment payments.

Do installment orders have a higher average delivery cost?

  • \(H_{0}:\) The mean delivery cost for orders with installment payments equals the mean delivery cost for orders without installment payments.

  • \(H_{1}:\) The mean delivery cost for orders with installment payments does not equal the mean delivery cost for orders without installment payments.

df_sales.assign(total_freight_value = lambda x: x.total_freight_value + 1e-6).stats.glm(
    formula='total_freight_value ~ C(order_has_installment, Treatment(reference="Has Installments"))'
    , family=sm.families.Gamma(link=sm.families.links.Log())
)

VIF requires at least two predictors. Skipping check.
Generalized Linear Model Regression Results
Dep. Variable: total_freight_value No. Observations: 96346
Model: GLM Df Residuals: 96344
Model Family: Gamma Df Model: 1
Link Function: Log Scale: 0.89391
Method: IRLS Log-Likelihood: -3.9351e+05
Date: Tue, 05 Aug 2025 Deviance: 46190.
Time: 11:55:39 Pearson chi2: 8.61e+04
No. Iterations: 7 Pseudo R-squ. (CS): 0.01284
Covariance Type: HC3
coef std err t P>|t| [0.025 0.975]
Intercept 3.2249 0.004 800.485 0.000 3.217 3.233
C(order_has_installment, Treatment(reference="Has Installments"))[T.No Installments] -0.2155 0.006 -35.256 0.000 -0.227 -0.204

Result:

  • At the 0.05 significance level, the mean delivery cost for orders with installment payments is statistically significantly different from the mean delivery cost for orders without installment payments.

  • Moreover, the mean delivery cost for orders with installment payments is statistically significantly higher than for orders without installment payments.

Order Processing and Delivery#

Do delayed orders have a higher average order value?

  • \(H_{0}:\) The mean value of delayed orders equals the mean value of non-delayed orders.

  • \(H_{1}:\) The mean value of delayed orders does not equal the mean value of non-delayed orders.

df_sales.stats.glm(
    formula='total_payment ~ C(is_delayed, Treatment(reference="Delayed"))'
    , family=sm.families.Gamma(link=sm.families.links.Log())
)
Variance Inflation Factors
Variable VIF
C(is_delayed, Treatment(reference="Delayed"))[T.Missing Delivery Dt] 1.0
C(is_delayed, Treatment(reference="Delayed"))[T.Not Delayed] 1.0
Generalized Linear Model Regression Results
Dep. Variable: total_payment No. Observations: 96346
Model: GLM Df Residuals: 96343
Model Family: Gamma Df Model: 2
Link Function: Log Scale: 1.8743
Method: IRLS Log-Likelihood: -6.0438e+05
Date: Tue, 05 Aug 2025 Deviance: 73819.
Time: 11:55:40 Pearson chi2: 1.81e+05
No. Iterations: 7 Pseudo R-squ. (CS): 0.0002999
Covariance Type: HC3
coef std err t P>|t| [0.025 0.975]
Intercept 5.1518 0.016 332.268 0.000 5.121 5.182
C(is_delayed, Treatment(reference="Delayed"))[T.Missing Delivery Dt] 0.0089 0.123 0.072 0.942 -0.233 0.251
C(is_delayed, Treatment(reference="Delayed"))[T.Not Delayed] -0.0850 0.016 -5.253 0.000 -0.117 -0.053

Result:

  • At the 0.05 significance level, the mean value of delayed orders is statistically significantly different from the mean value of non-delayed orders.

  • Moreover, the mean value of delayed orders is statistically significantly higher than of non-delayed orders.

Do delayed orders have a higher average order weight?

  • \(H_{0}:\) The mean weight of delayed orders equals the mean weight of non-delayed orders.

  • \(H_{1}:\) The mean weight of delayed orders does not equal the mean weight of non-delayed orders.

df_sales.assign(total_weight_kg = lambda x: x.total_weight_kg + 1e-6).stats.glm(
    formula='total_weight_kg ~ C(is_delayed, Treatment(reference="Delayed"))'
    , family=sm.families.Gamma(link=sm.families.links.Log())
)
Variance Inflation Factors
Variable VIF
C(is_delayed, Treatment(reference="Delayed"))[T.Missing Delivery Dt] 1.0
C(is_delayed, Treatment(reference="Delayed"))[T.Not Delayed] 1.0
Generalized Linear Model Regression Results
Dep. Variable: total_weight_kg No. Observations: 96346
Model: GLM Df Residuals: 96343
Model Family: Gamma Df Model: 2
Link Function: Log Scale: 3.9901
Method: IRLS Log-Likelihood: -1.9283e+05
Date: Tue, 05 Aug 2025 Deviance: 1.9292e+05
Time: 11:55:41 Pearson chi2: 3.84e+05
No. Iterations: 8 Pseudo R-squ. (CS): 0.0002701
Covariance Type: HC3
coef std err t P>|t| [0.025 0.975]
Intercept 0.9750 0.023 42.661 0.000 0.930 1.020
C(is_delayed, Treatment(reference="Delayed"))[T.Missing Delivery Dt] -0.3118 0.161 -1.938 0.053 -0.627 0.004
C(is_delayed, Treatment(reference="Delayed"))[T.Not Delayed] -0.1152 0.024 -4.836 0.000 -0.162 -0.069

Result:

  • At the 0.05 significance level, the mean weight of delayed orders is statistically significantly different from the mean weight of non-delayed orders.

  • Moreover, the mean weight of delayed orders is statistically significantly higher than that of non-delayed orders.

Do delayed orders have a higher average product price in the order?

  • \(H_{0}:\) The mean product price in delayed orders equals the mean product price in non-delayed orders.

  • \(H_{1}:\) The mean product price in delayed orders does not equal the mean product price in non-delayed orders.

df_sales.stats.glm(
    formula='avg_products_price ~ C(is_delayed, Treatment(reference="Delayed"))'
    , family=sm.families.Gamma(link=sm.families.links.Log())
)
Variance Inflation Factors
Variable VIF
C(is_delayed, Treatment(reference="Delayed"))[T.Missing Delivery Dt] 1.0
C(is_delayed, Treatment(reference="Delayed"))[T.Not Delayed] 1.0
Generalized Linear Model Regression Results
Dep. Variable: avg_products_price No. Observations: 96346
Model: GLM Df Residuals: 96343
Model Family: Gamma Df Model: 2
Link Function: Log Scale: 2.2900
Method: IRLS Log-Likelihood: -5.8480e+05
Date: Tue, 05 Aug 2025 Deviance: 90898.
Time: 11:55:41 Pearson chi2: 2.21e+05
No. Iterations: 8 Pseudo R-squ. (CS): 0.0004556
Covariance Type: HC3
coef std err t P>|t| [0.025 0.975]
Intercept 4.9336 0.018 278.035 0.000 4.899 4.968
C(is_delayed, Treatment(reference="Delayed"))[T.Missing Delivery Dt] 0.0848 0.140 0.607 0.544 -0.189 0.358
C(is_delayed, Treatment(reference="Delayed"))[T.Not Delayed] -0.1134 0.018 -6.146 0.000 -0.150 -0.077

Result:

  • At the 0.05 significance level, the mean product price in delayed orders is statistically significantly different from the mean product price in non-delayed orders.

  • Moreover, the mean product price in delayed orders is statistically significantly higher than in non-delayed orders.

Do delayed orders have a higher average delivery cost?

  • \(H_{0}:\) The mean delivery cost for delayed orders equals the mean delivery cost for non-delayed orders.

  • \(H_{1}:\) The mean delivery cost for delayed orders does not equal the mean delivery cost for non-delayed orders.

df_sales.assign(total_freight_value = lambda x: x.total_freight_value + 1e-6).stats.glm(
    formula='total_freight_value ~ C(is_delayed, Treatment(reference="Delayed"))'
    , family=sm.families.Gamma(link=sm.families.links.Log())
)
Variance Inflation Factors
Variable VIF
C(is_delayed, Treatment(reference="Delayed"))[T.Missing Delivery Dt] 1.0
C(is_delayed, Treatment(reference="Delayed"))[T.Not Delayed] 1.0
Generalized Linear Model Regression Results
Dep. Variable: total_freight_value No. Observations: 96346
Model: GLM Df Residuals: 96343
Model Family: Gamma Df Model: 2
Link Function: Log Scale: 0.89540
Method: IRLS Log-Likelihood: -3.9415e+05
Date: Tue, 05 Aug 2025 Deviance: 47250.
Time: 11:55:42 Pearson chi2: 8.63e+04
No. Iterations: 7 Pseudo R-squ. (CS): 0.0006139
Covariance Type: HC3
coef std err t P>|t| [0.025 0.975]
Intercept 3.2036 0.010 305.611 0.000 3.183 3.224
C(is_delayed, Treatment(reference="Delayed"))[T.Missing Delivery Dt] -0.1191 0.085 -1.408 0.159 -0.285 0.047
C(is_delayed, Treatment(reference="Delayed"))[T.Not Delayed] -0.0847 0.011 -7.727 0.000 -0.106 -0.063

Result:

  • At the 0.05 significance level, the mean delivery cost in delayed orders is statistically significantly different from the mean delivery cost in non-delayed orders.

  • Moreover, the mean delivery cost in delayed orders is statistically significantly higher than in non-delayed orders.

Does delivery delay affect the distribution of order ratings?

  • \(H_{0}:\) The distribution of order ratings is identical for delayed and non-delayed orders.

  • \(H_{1}:\) The distribution of order ratings differs between delayed and non-delayed orders.

We will use:

  • OrderedModel, since the rating is an ordinal variable.

(
    df_sales.assign(
        order_avg_reviews_score=lambda x: pd.Categorical(
            x.order_avg_reviews_score,
            categories=[1, 2, 3, 4, 5],
            ordered=True
        )
    )
    .stats.ordered_model(
        formula = 'order_avg_reviews_score ~ C(is_delayed, Treatment(reference="Delayed"))'
    )
)

Optimization terminated successfully.
         Current function value: 1.128950
         Iterations: 37
         Function evaluations: 38
         Gradient evaluations: 38
OrderedModel Results
Dep. Variable: order_avg_reviews_score Log-Likelihood: -1.0877e+05
Model: OrderedModel AIC: 2.176e+05
Method: Maximum Likelihood BIC: 2.176e+05
Date: Tue, 05 Aug 2025
Time: 11:55:51
No. Observations: 96346
Df Residuals: 96340
Df Model: 2
coef std err z P>|z| [0.025 0.975]
C(is_delayed, Treatment(reference="Delayed"))[T.Missing Delivery Dt] -0.9020 0.178 -5.061 0.000 -1.251 -0.553
C(is_delayed, Treatment(reference="Delayed"))[T.Not Delayed] 2.2494 0.023 96.139 0.000 2.204 2.295
1/2 -0.2899 0.022 -13.254 0.000 -0.333 -0.247
2/3 -1.0485 0.018 -58.598 0.000 -1.084 -1.013
3/4 -0.4063 0.011 -37.453 0.000 -0.428 -0.385
4/5 0.0153 0.007 2.248 0.025 0.002 0.029

Result:

  • At the 0.05 significance level, the distribution of order ratings differs between delayed and non-delayed orders.

  • Moreover, non-delayed orders have statistically significantly higher chances of receiving a higher rating.

Are expensive orders delivered longer?

For each order price category N (except expensive):

  • \(H_{0}^{N}:\) The mean delivery cost for the expensive price category equals the mean delivery cost for category N.

  • \(H_{1}^{N}:\) The mean delivery cost for the expensive price category does not equal the mean delivery cost for category N.

df_sales.stats.glm(
    formula='delivery_time_days ~ C(order_total_payment_cat, Treatment(reference="Expensive"))'
    , family=sm.families.Gamma(link=sm.families.links.Log())
    , p_adjust='holm'
)
Variance Inflation Factors
Variable VIF
C(order_total_payment_cat, Treatment(reference="Expensive"))[T.Cheap] 1.0
C(order_total_payment_cat, Treatment(reference="Expensive"))[T.Medium] 1.0
Generalized Linear Model Regression Results
Dep. Variable: delivery_time_days No. Observations: 96211
Model: GLM Df Residuals: 96208
Model Family: Gamma Df Model: 2
Link Function: Log Scale: 0.56639
Method: IRLS Log-Likelihood: -3.2475e+05
Date: Tue, 05 Aug 2025 Deviance: 42404.
Time: 11:55:52 Pearson chi2: 5.45e+04
No. Iterations: 7 Pseudo R-squ. (CS): 0.01226
Covariance Type: HC3
coef std err t P>|t| [0.025 0.975]
Intercept 2.6356 0.006 477.588 0.000 2.625 2.646
C(order_total_payment_cat, Treatment(reference="Expensive"))[T.Cheap] -0.2749 0.008 -34.007 0.000 -0.291 -0.259
C(order_total_payment_cat, Treatment(reference="Expensive"))[T.Medium] -0.1011 0.006 -16.044 0.000 -0.113 -0.089
Adjusted p-values (method: holm):
  coef p-unc p-corr
Intercept 2.64 0.000 nan
C(order_total_payment_cat, Treatment(reference="Expensive"))[T.Cheap] -0.27 0.000 0.000
C(order_total_payment_cat, Treatment(reference="Expensive"))[T.Medium] -0.10 0.000 0.000

Result:

  • At the 0.05 significance level, the mean delivery cost for the high-price order category is statistically significantly different from the mean delivery cost for any other category.

  • Moreover, the mean delivery cost for the high-price category is statistically significantly higher than for other categories.

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