Python

Dataset/Data Sources

• Environmental Dataset
• Breast Cancer Dataset

Statistical tests

• They evaluate whether data patterns are meaningful or merely the result of random chance.
• They work by establishing a null hypothesis ((H_{0})) of no effect and computing a p-value.
• A p-value below a chosen significance threshold (typically (\alpha = 0.05)) rejects (H_{0}), indicating statistically significant findings

Core Python Ecosystem for Testing

• Python relies on three specialized open-source libraries to execute these tests:

scipy.stats:

• The primary engine for traditional hypothesis testing, probability distributions, and descriptive calculations.

statsmodels:

• Focused on comprehensive statistical modeling, providing in-depth regression diagnostics, generalized linear models (GLMs), and time-series tests.

pingouin:

• A user-friendly, high-level package that extends scipy by automatically appending statistical power, confidence intervals, and effect sizes directly into Pandas DataFrame

Test Category	Purpose	Assumed Constraints	Python Method
Shapiro-Wilk	Evaluates whether a sample is normally distributed.	Continuous numeric metrics.	scipy.stats.shapiro
Independent t-test	Compares means across two completely distinct groups.	Normally distributed continuous variables.	scipy.stats.ttest_ind
Paired t-test	Compares group means across matched or repeated intervals.	Paired numeric observations from one entity type.	scipy.stats.ttest_rel
Mann-Whitney U	Compares rankings between two independent populations.	Non-parametric (does not assume normal distribution).	scipy.stats.mannwhitneyu
One-Way ANOVA	Compares means across three or more unique groups.	Normally distributed metrics with equal variances.	scipy.stats.f_oneway
Chi-Square ($\chi^{2}$)	Tests independence between structural categorical fields.	Frequency cell counts exceed minimum thresholds.	scipy.stats.chi2_contingency
Pearson Correlation	Measures strength of a linear relationship between two variables.	Normally distributed continuous values.	scipy.stats.pearsonr
Spearman Correlation	Measures a monotonic relationship between two variables.	Non-parametric, ordinal, or non-linear continuous data.	scipy.stats.spearmanr

Regression Test / Model	Purpose	Assumed Constraints	Python Method
Simple Linear Regression	Models relationship between one predictor and one dependent variable.	Linearity, homoscedasticity, independent and normal residuals.	statsmodels.api.OLS
Multiple Linear Regression	Predicts a continuous outcome using multiple explanatory variables.	No severe multicollinearity among predictor variables.	statsmodels.formula.api.ols
Logistic Regression	Predicts the probability of a binary or categorical outcome.	Independence of errors, absence of high multicollinearity.	statsmodels.api.Logit / Logit.from_formula