Hypothesis Testing, Confidence Intervals, and Effect Size with Python

The article introduces statistical analysis for data science, focusing on hypothesis testing, confidence intervals, and effect size, and demonstrates how to implement each method using Python libraries such as pandas, scipy, and seaborn.

It starts by defining hypothesis testing, describing null (H0) and alternative (H1) hypotheses, and provides simple examples such as comparing view counts across Zhihu accounts or checking whether gas emissions meet regulatory standards.

For the chi‑square test, the author shows how to create a cross‑tabulation with pandas.crosstab, then runs scipy.stats.chi2_contingency to obtain the test statistic, p‑value, and degrees of freedom, interpreting a p‑value smaller than 0.05 as evidence against H0.

Code example for the chi‑square preparation:

import pandas as pd<br>import numpy as np<br>data = pd.read_excel("path_to_file.xlsx")  # read data file<br>a = pd.crosstab(index=data["平台"], columns=data["菜系"], margins=True)  # cross‑tabulation<br>print(a)

Next, the tutorial covers the one‑sample t‑test. After checking normality with the Shapiro‑Wilk test ( stats.shapiro), the author uses stats.ttest_1samp to compare the sample mean against a target value, adjusts the p‑value for a one‑tailed test, and concludes based on the 0.05 significance level.

Normality test code:

from scipy import stats<br>stats.shapiro(data)  # returns statistic and p‑value

One‑sample t‑test code:

from scipy import stats<br>stats.ttest_1samp(data, 20)  # compare against 20 ppm

The article then explains how to compute a confidence interval: it looks up the t‑value for 95% confidence (df = n‑1), calculates the standard error with stats.sem, and builds the interval around the sample mean.

Standard error code:

from scipy import stats<br>stats.sem(data)  # standard error of the mean

Effect size (Cohen's d) is introduced to assess practical significance. The author computes d as the difference between the sample mean and the target divided by the sample standard deviation.

Effect size code: d = (data.mean() - 20) / data.std() # d ≈ -0.94 Finally, the tutorial presents the two‑sample t‑test, outlining its assumptions (normality, independence, equal variances). It demonstrates variance homogeneity testing with Levene’s test ( stats.levene) and then runs the two‑sample t‑test, interpreting a p‑value greater than 0.05 as no significant difference.

Levene’s test and two‑sample t‑test code:

from scipy import stats<br>leneneTestRes = stats.levene(sample1, sample2)<br>print(leneneTestRes)<br>t_stat, p_val = stats.ttest_ind(sample1, sample2, equal_var=True)

Throughout the article, images of data tables, test results, and plots are included to illustrate each step.