API Comparison Table - Quick Function Lookup

Overview

This guide helps you quickly find the Real Simple Stats function you need, with comparisons to similar functions in other popular libraries.

Descriptive Statistics

Task

Real Simple Stats

NumPy

SciPy

Pandas

statsmodels

Mean

mean(data)

np.mean(data)

-

df.mean()

-

Median

median(data)

np.median(data)

-

df.median()

-

Mode

mode(data)

-

stats.mode(data)

df.mode()

-

Std Dev

sample_std_dev(data)

np.std(data, ddof=1)

-

df.std()

-

Variance

sample_variance(data)

np.var(data, ddof=1)

-

df.var()

-

Range

data_range(data)

np.ptp(data)

-

df.max() - df.min()

-

IQR

interquartile_range(data)

np.percentile(data, 75) - np.percentile(data, 25)

-

df.quantile(0.75) - df.quantile(0.25)

-

5-Number Summary

five_number_summary(data)

-

-

df.describe()

-

CV

coefficient_of_variation(data)

-

stats.variation(data)

-

-

Example:

import real_simple_stats as rss

data = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
print(rss.mean(data))                    # 5.5
print(rss.five_number_summary(data))     # {'min': 1, 'q1': 3.25, ...}

Probability Distributions

Normal Distribution

Task

Real Simple Stats

SciPy

NumPy

PDF

normal_pdf(x, mu, sigma)

stats.norm.pdf(x, mu, sigma)

-

CDF

normal_cdf(x, mu, sigma)

stats.norm.cdf(x, mu, sigma)

-

Inverse CDF

normal_ppf(p, mu, sigma)

stats.norm.ppf(p, mu, sigma)

-

Z-score

z_score(x, mu, sigma)

(x - mu) / sigma

-

Random samples

-

stats.norm.rvs(mu, sigma, size=n)

np.random.normal(mu, sigma, n)

Binomial Distribution

Task

Real Simple Stats

SciPy

NumPy

PMF

binomial_probability(n, k, p)

stats.binom.pmf(k, n, p)

-

CDF

binomial_cdf(k, n, p)

stats.binom.cdf(k, n, p)

-

Mean

binomial_mean(n, p)

n * p

-

Variance

binomial_variance(n, p)

n * p * (1-p)

-

Other Distributions

Distribution

Real Simple Stats

SciPy Equivalent

Poisson

poisson_pmf(k, lam)

stats.poisson.pmf(k, lam)

Geometric

geometric_pmf(k, p)

stats.geom.pmf(k, p)

Exponential

exponential_pdf(x, lam)

stats.expon.pdf(x, scale=1/lam)

Negative Binomial

negative_binomial_pmf(k, r, p)

stats.nbinom.pmf(k, r, p)

Example:

import real_simple_stats as rss

# Normal distribution
prob = rss.normal_cdf(1.96, 0, 1)  # P(Z ≤ 1.96) ≈ 0.975

# Binomial distribution
prob = rss.binomial_probability(10, 7, 0.5)  # P(X=7) when n=10, p=0.5

🧪 Hypothesis Testing

Test

Real Simple Stats

SciPy

statsmodels

One-sample t-test

one_sample_t_test(data, mu0)

stats.ttest_1samp(data, mu0)

sm.stats.ttest_ind(data, mu0)

Two-sample t-test

two_sample_t_test(data1, data2)

stats.ttest_ind(data1, data2)

sm.stats.ttest_ind(data1, data2)

Paired t-test

paired_t_test(data1, data2)

stats.ttest_rel(data1, data2)

-

Z-test

one_sample_z_test(data, mu0, sigma)

sm.stats.ztest(data, value=mu0)

sm.stats.ztest(data, value=mu0)

Chi-square test

chi_square_statistic(obs, exp)

stats.chisquare(obs, exp)

-

ANOVA

one_way_anova(groups)

stats.f_oneway(*groups)

sm.stats.anova_lm()

Example:

import real_simple_stats as rss

# One-sample t-test
data = [23, 25, 28, 30, 32]
t_stat, p_value = rss.one_sample_t_test(data, mu0=30)
print(f"t = {t_stat:.3f}, p = {p_value:.3f}")

# Two-sample t-test
group1 = [1, 2, 3, 4, 5]
group2 = [3, 4, 5, 6, 7]
t_stat, p_value = rss.two_sample_t_test(group1, group2)

📉 Regression & Correlation

Task

Real Simple Stats

SciPy

scikit-learn

statsmodels

Pearson correlation

pearson_correlation(x, y)

stats.pearsonr(x, y)

-

sm.stats.correlation()

Simple linear regression

linear_regression(x, y)

stats.linregress(x, y)

LinearRegression()

sm.OLS(y, x)

R-squared

coefficient_of_determination(x, y)

linregress(x, y).rvalue**2

model.score(X, y)

results.rsquared

Multiple regression

multiple_regression(X, y)

-

LinearRegression()

sm.OLS(y, X)

Prediction

regression_equation(x, slope, intercept)

slope * x + intercept

model.predict(X)

results.predict(X)

Example:

import real_simple_stats as rss

x = [1, 2, 3, 4, 5]
y = [2, 4, 5, 4, 5]

# Correlation
r = rss.pearson_correlation(x, y)
print(f"Correlation: {r:.3f}")

# Regression
slope, intercept, r_value, p_value, std_err = rss.linear_regression(x, y)
print(f"y = {slope:.2f}x + {intercept:.2f}")

# Prediction
y_pred = rss.regression_equation(6, slope, intercept)

🔄 Time Series Analysis

Task

Real Simple Stats

pandas

statsmodels

Moving average

moving_average(data, window, 'simple')

df.rolling(window).mean()

-

Exponential MA

moving_average(data, window, 'exponential')

df.ewm(span=window).mean()

-

Autocorrelation

autocorrelation(data, max_lag)

pd.Series(data).autocorr(lag)

sm.tsa.acf(data)

Partial ACF

partial_autocorrelation(data, max_lag)

-

sm.tsa.pacf(data)

Linear trend

linear_trend(data)

-

sm.tsa.deterministic.DeterministicTerm()

Detrend

detrend(data, 'linear')

-

sm.tsa.detrend(data)

Seasonal decompose

seasonal_decompose(data, period)

-

sm.tsa.seasonal_decompose()

Differencing

difference(data, lag, order)

df.diff(lag)

-

Example:

import real_simple_stats as rss

data = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

# Moving average
ma = rss.moving_average(data, window_size=3, method='simple')

# Autocorrelation
acf = rss.autocorrelation(data, max_lag=5)

# Trend analysis
slope, intercept, r2 = rss.linear_trend(data)

Resampling Methods

Method

Real Simple Stats

scikit-learn

scipy

Bootstrap

bootstrap(data, statistic, n_iterations)

-

-

Bootstrap CI

Returns confidence_interval

-

-

Permutation test

permutation_test(data1, data2, statistic)

permutation_test()

-

Jackknife

jackknife(data, statistic)

-

-

Cross-validation

cross_validate(X, y, model_fn, k_folds)

cross_val_score()

-

Stratified split

stratified_split(X, y, test_size)

train_test_split(stratify=y)

-

Example:

import real_simple_stats as rss
import numpy as np

data = [1, 2, 3, 4, 5]

# Bootstrap confidence interval
result = rss.bootstrap(data, np.mean, n_iterations=1000)
print(f"95% CI: {result['confidence_interval']}")

# Permutation test
group1 = [1, 2, 3, 4, 5]
group2 = [3, 4, 5, 6, 7]
result = rss.permutation_test(group1, group2,
                               lambda d1, d2: np.mean(d1) - np.mean(d2))
print(f"p-value: {result['p_value']:.3f}")

Effect Sizes

Effect Size

Real Simple Stats

Other Libraries

Cohen’s d

cohens_d(group1, group2)

pg.compute_effsize() (pingouin)

Hedges’ g

hedges_g(group1, group2)

pg.compute_effsize(eftype='hedges')

Glass’s Δ

glass_delta(group1, group2)

-

Eta-squared

eta_squared(groups)

pg.anova()['np2']

Partial η²

partial_eta_squared(groups)

-

Omega-squared

omega_squared(groups)

-

Cramér’s V

cramers_v(contingency_table)

scipy.stats.contingency.association()

Phi coefficient

phi_coefficient(table)

-

Odds ratio

odds_ratio(table)

statsmodels.stats.contingency_tables

Relative risk

relative_risk(table)

-

Cohen’s h

cohens_h(p1, p2)

-

Interpretation

interpret_effect_size(es, measure)

-

Example:

import real_simple_stats as rss

group1 = [1, 2, 3, 4, 5]
group2 = [3, 4, 5, 6, 7]

# Cohen's d
d = rss.cohens_d(group1, group2)
interpretation = rss.interpret_effect_size(d, 'd')
print(f"Cohen's d = {d:.3f} ({interpretation})")

# Cramér's V for categorical data
table = [[10, 20], [30, 40]]
v = rss.cramers_v(table)
print(f"Cramér's V = {v:.3f}")

🔬 Power Analysis

Analysis

Real Simple Stats

statsmodels

G*Power

t-test power

power_t_test(delta, power, sig_level)

sm.stats.TTestPower()

Manual

Proportion test

power_proportion_test(p1, p2, power)

sm.stats.proportion_effectsize()

Manual

ANOVA power

power_anova(effect_size, k, power)

sm.stats.FTestAnovaPower()

Manual

Correlation power

power_correlation(r, power, sig_level)

-

Manual

Min detectable effect

minimum_detectable_effect(n, power)

-

Manual

Sample size summary

sample_size_summary(test_type, params)

-

-

Example:

import real_simple_stats as rss

# Calculate required sample size for t-test
result = rss.power_t_test(delta=0.5, power=0.8, sig_level=0.05)
print(f"Required n per group: {result['n']}")

# Calculate power for given sample size
result = rss.power_t_test(delta=0.5, n=64, sig_level=0.05)
print(f"Statistical power: {result['power']:.3f}")

Bayesian Statistics

Method

Real Simple Stats

PyMC

Stan

Beta-Binomial update

beta_binomial_update(α, β, k, n)

Manual

Manual

Normal-Normal update

normal_normal_update(μ₀, σ₀², data, σ²)

Manual

Manual

Gamma-Poisson update

gamma_poisson_update(α, β, data)

Manual

Manual

Credible interval

credible_interval(dist, params, cred)

pm.hdi()

Manual

HDI

highest_density_interval(samples, cred)

pm.hdi()

Manual

Bayes factor

bayes_factor(L_H1, L_H0, prior_odds)

Manual

Manual

Posterior predictive

posterior_predictive(dist, params, n)

pm.sample_posterior_predictive()

Manual

Example:

import real_simple_stats as rss

# Update Beta prior with binomial data
prior_alpha, prior_beta = 1, 1  # Uniform prior
successes, trials = 7, 10

post_alpha, post_beta = rss.beta_binomial_update(prior_alpha, prior_beta,
                                                   successes, trials)

# Calculate credible interval
lower, upper = rss.credible_interval('beta',
                                      {'alpha': post_alpha, 'beta': post_beta},
                                      0.95)
print(f"95% Credible Interval: [{lower:.3f}, {upper:.3f}]")

📐 Multivariate Analysis

Method

Real Simple Stats

scikit-learn

statsmodels

Multiple regression

multiple_regression(X, y)

LinearRegression()

sm.OLS()

PCA

pca(X, n_components)

PCA()

-

Factor analysis

factor_analysis(X, n_factors)

FactorAnalysis()

-

Canonical correlation

canonical_correlation(X, Y)

CCA()

-

Mahalanobis distance

mahalanobis_distance(X, point)

-

-

Example:

import real_simple_stats as rss

X = [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6]]
y = [2, 4, 5, 4, 5]

# Multiple regression
result = rss.multiple_regression(X, y)
print(f"R² = {result['r_squared']:.3f}")
print(f"Coefficients: {result['coefficients']}")

# PCA
result = rss.pca(X, n_components=2)
print(f"Explained variance: {result['explained_variance']}")

🔍 Quick Lookup by Use Case

“I want to…”

…compare two groups

  • two_sample_t_test(group1, group2) - Test for mean difference

  • cohens_d(group1, group2) - Calculate effect size

  • permutation_test(group1, group2, statistic) - Non-parametric test

…analyze relationships

  • pearson_correlation(x, y) - Linear correlation

  • linear_regression(x, y) - Fit regression line

  • coefficient_of_determination(x, y) - R² value

…work with time series

  • moving_average(data, window) - Smooth data

  • autocorrelation(data, max_lag) - Find patterns

  • seasonal_decompose(data, period) - Decompose components

…calculate confidence

  • confidence_interval_known_std(mean, std, n, conf) - Known σ

  • confidence_interval_unknown_std(mean, std, n, conf) - Unknown σ

  • bootstrap(data, statistic, n_iterations) - Bootstrap CI

…plan a study

  • power_t_test(delta, power, sig_level) - Sample size for t-test

  • required_sample_size(confidence, width, std) - CI-based planning

  • slovins_formula(N, e) - Survey sample size

…do Bayesian analysis

  • beta_binomial_update(α, β, k, n) - Update beliefs

  • credible_interval(dist, params, cred) - Bayesian CI

  • bayes_factor(L_H1, L_H0) - Compare hypotheses

📚 Function Categories

By Statistical Domain

Descriptive Statistics: mean, median, mode, sample_std_dev, sample_variance, five_number_summary, interquartile_range, coefficient_of_variation

Probability: normal_pdf, normal_cdf, binomial_probability, poisson_pmf, geometric_pmf, exponential_pdf

Inference: one_sample_t_test, two_sample_t_test, paired_t_test, one_sample_z_test, chi_square_statistic, one_way_anova

Regression: linear_regression, multiple_regression, pearson_correlation, coefficient_of_determination

Time Series: moving_average, autocorrelation, seasonal_decompose, detrend, difference

Resampling: bootstrap, permutation_test, jackknife, cross_validate

Effect Sizes: cohens_d, eta_squared, cramers_v, odds_ratio

Power Analysis: power_t_test, power_anova, minimum_detectable_effect

Bayesian: beta_binomial_update, credible_interval, bayes_factor

Multivariate: pca, factor_analysis, canonical_correlation

Learning Path

Beginner → Intermediate → Advanced

  1. Start here: mean, median, std_dev, normal_cdf

  2. Then learn: t_test, linear_regression, confidence_interval

  3. Next: bootstrap, effect_sizes, power_analysis

  4. Advanced: time_series, bayesian_stats, multivariate

Tips

  • All functions return simple Python types (floats, lists, dicts) - no custom objects

  • Type hints included for better IDE support

  • Comprehensive docstrings with examples in every function

  • Consistent naming - functions do what their names say

  • Educational focus - designed for learning and teaching

See also: