Scientific Computing & Statistics (SciPy & Statsmodels)

Introduction

NumPy gives you fast arrays and basic linear algebra, but most real data science work needs more: optimization routines, statistical tests, signal processing, and interpretable statistical models with p-values and confidence intervals. That is where SciPy and Statsmodels come in.

In this lesson you will install both libraries, run a real hypothesis test with scipy.stats, and fit a linear regression with statsmodels that prints a full R-style summary table.

What is SciPy?

SciPy (Scientific Python) is a library built directly on top of NumPy arrays. Where NumPy gives you the array data structure and basic operations, SciPy adds entire submodules of specialized algorithms: scipy.optimize for optimization and curve fitting, scipy.linalg for advanced linear algebra, scipy.signal for signal processing, scipy.integrate for numerical integration, and scipy.stats for probability distributions and statistical tests.

In practice, if you find yourself needing a statistical test, an optimizer, or an algorithm from a numerical methods textbook, SciPy almost certainly already has it implemented and tested.

Installing SciPy

SciPy is installed with pip like any other package. It depends on NumPy, which pip will install automatically if it is not already present.

pip install scipy

Example: A t-test with scipy.stats

A very common real-world task is comparing two groups of numbers to see if their averages are meaningfully different, or if the difference could just be random noise. An independent two-sample t-test answers exactly this question.

from scipy import stats

# Test scores for two different teaching methods
method_a = [78, 82, 88, 91, 74, 86, 79, 84]
method_b = [85, 90, 95, 92, 88, 91, 89, 94]

t_statistic, p_value = stats.ttest_ind(method_a, method_b)

print(f"t-statistic: {t_statistic:.3f}")
print(f"p-value: {p_value:.4f}")

if p_value < 0.05:
    print("The difference between the groups is statistically significant.")
else:
    print("No statistically significant difference was found.")

A p-value below 0.05 conventionally means the observed difference is unlikely to be pure chance, so here method B's scores are significantly higher than method A's. scipy.stats has dozens of similar tests: chi-square, ANOVA, correlation tests, and more, all following the same pattern of returning a statistic and a p-value.

What is Statsmodels?

Statsmodels focuses on statistical modeling rather than prediction accuracy alone. Where scikit-learn is built for training a model and generating predictions efficiently, statsmodels is built for understanding a model: it produces detailed output tables with coefficients, standard errors, t-statistics, p-values, and confidence intervals, similar to what you would get from R.

This makes statsmodels the go-to library when the goal is explaining a relationship in data (for example, in economics, social science, or A/B test analysis) rather than only maximizing predictive accuracy.

Installing Statsmodels

pip install statsmodels

Example: OLS Linear Regression

Ordinary Least Squares (OLS) regression is the classic starting point for statistical modeling. The example below fits hours studied against exam scores and prints the full summary table.

import statsmodels.api as sm
import numpy as np

hours_studied = np.array([1, 2, 3, 4, 5, 6, 7, 8])
exam_score = np.array([52, 58, 63, 68, 74, 78, 85, 90])

# statsmodels requires an explicit constant (intercept) term
X = sm.add_constant(hours_studied)

model = sm.OLS(exam_score, X)
results = model.fit()

print(results.summary())

The coefficient on x1 (5.4762) means each additional hour studied is associated with roughly 5.48 more exam points, and the near-zero P>|t| value tells you this relationship is highly statistically significant.

SciPy vs Statsmodels vs Scikit-learn

Common Mistakes

Best Practices

Frequently Asked Questions

Key Takeaways

Summary

SciPy and statsmodels round out the classic Python statistics toolkit: SciPy for general scientific computing and quick statistical tests, and statsmodels for detailed, explainable statistical models. Together with NumPy and pandas, they form the foundation most other data science libraries are built on.