scipy.stats

The scipy.stats module is part of the broader SciPy library for scientific computing in Python. It provides functionality for working with various probability distributions, conducting hypothesis tests, and computing descriptive statistics. By leveraging scipy.stats, data scientists and analysts can quickly explore their data, model it using theoretical distributions, and draw meaningful conclusions through statistical inference.

Probability Distributions

scipy.stats provides a wide range of distributions (e.g., Normal, Exponential, Binomial) with methods to work with them. For example, for the Normal distribution:

stats.norm.pdf(x)       # Probability Density Function
stats.norm.cdf(x)       # Cumulative Distribution Function
stats.norm.rvs(size=n)  # Generate random samples

• pdf: Returns the probability density function (PDF) value at a given point for continuous distributions..
• cdf: Gives the probability that a random variable is less than or equal to a certain value.
• rvs: Draws random samples from the specified distribution.

These methods can be used with other distributions available in scipy.stats by replacing norm with the desired distribution (e.g., expon, binom).

Descriptive Statistics

Compute common statistical measures with both numpy and scipy.stats:

np.mean(data)
np.median(data)
stats.mode(data)
stats.describe(data)

• mean(): Computes the average value of the data.
• median(): Finds the middle value separating the higher and lower halves of the data.
• mode(): Returns the most frequently occurring value (for multi-modal data, it returns the smallest mode).
• describe(): Provides a quick summary of the data, including count, min, max, mean, variance, skewness, and kurtosis.

Note: While mean and median are part of numpy, mode and describe belong to scipy.stats.

Hypothesis Testing

Perform a variety of statistical tests to assess differences or relationships:

stats.ttest_ind(group1, group2)       # Independent t-test
stats.chisquare(observed, expected)   # Chi-square test
stats.mannwhitneyu(group1, group2)    # Mann-Whitney U test

• ttest_ind(): Checks if the means of two independent samples differ significantly.
• chisquare(): Compares observed frequencies to expected frequencies for a goodness-of-fit test.
• mannwhitneyu(): Tests for differences in the distribution of two independent samples (non-parametric).

Correlation and Regression

Evaluate relationships between variables:

stats.pearsonr(x, y)   # Pearson correlation
stats.spearmanr(x, y)  # Spearman rank correlation
stats.kendalltau(x, y) # Kendall’s Tau correlation

• pearsonr(): Measures linear correlation between two datasets.
• spearmanr(): Measures rank-based correlation, less sensitive to non-linear relationships.
• kendalltau(): Measures the association between two measured quantities using rank correlation.