Crate hypors

Crate hypors 

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§HypoRS: A Statistical Hypothesis Testing Library

hypors is a Rust library designed for performing a variety of hypothesis tests, including t-tests, z-tests, proportion tests, ANOVA, Chi-square tests, and Mann-Whitney tests. This library utilizes the polars crate for data manipulation and the statrs crate for statistical distributions.

§Overview

The library is organized into the following key modules:

  • common - Contains shared utilities and helper functions for statistical calculations, including confidence intervals and p-values.
  • t - Implements various t-tests, including one-sample, two-sample paired, and two-sample independent t-tests.
  • z - Implements z-tests for one-sample and two-sample scenarios, supporting both paired and independent tests.
  • proportion - Implements tests for proportions, including one-sample and two-sample proportion tests.
  • anova - Implements one-way ANOVA tests for comparing means across multiple groups.
  • chi_square - Implements Chi-square tests for categorical data analysis.
  • mann_whitney - Implements the Mann-Whitney U test for comparing two independent samples.

§Sample Size Calculations

Each of the parametrized tests have the faculty to also calculate minimum sample sizes required based on the Alpha and Power values.

§Hypothesis Tests

§T-Tests

Example of performing a one-sample t-test:

use hypors::{t::t_test, common::TailType};

let data = [1.2, 2.3, 1.9, 2.5, 2.8];
let population_mean = 2.0;
let tail = TailType::Two;
let alpha = 0.05;

let result = t_test(data, population_mean, tail, alpha).unwrap();
println!("Test Statistic: {}", result.test_statistic);
println!("P-value: {}", result.p_value);
println!("Confidence Interval: {:?}", result.confidence_interval);
println!("Reject Null Hypothesis: {}", result.reject_null);
§Features
  • One-sample t-test: Tests whether the mean of a single sample differs from a specified population mean.
  • Two-sample paired t-test: Tests whether the means of two related samples differ.
  • Two-sample independent t-test: Tests whether the means of two unrelated samples differ, supporting both pooled and unpooled variances (Welch’s t-test).
  • Sample Size Calculation: Use t_sample_size to determine the required sample size for specified power and significance levels.

§Z-Tests

Example of performing a one-sample z-test:

use hypors::{z::z_test, common::TailType};

let data = vec![1.5, 2.3, 2.7, 2.8, 3.1];
let population_mean = 2.0;
let population_std_dev = 0.5;
let tail = TailType::Two;
let alpha = 0.05;

let result = z_test(data, population_mean, population_std_dev, tail, alpha).unwrap();
println!("Z Statistic: {}", result.test_statistic);
println!("P-value: {}", result.p_value);
println!("Confidence Interval: {:?}", result.confidence_interval);
println!("Reject Null Hypothesis: {}", result.reject_null);
§Features
  • One-sample z-test: Tests whether the mean of a single sample differs from a specified population mean when the population standard deviation is known.
  • Two-sample paired z-test: Tests whether the means of two related samples differ when the population standard deviation of the differences is known.
  • Two-sample independent z-test: Tests whether the means of two unrelated samples differ, with options for pooled or unpooled variances, assuming known population standard deviations.
  • Sample Size Calculation: Use z_sample_size to determine the required sample size for specified power and significance levels.

§Proportion Tests

Example of performing a one-sample proportion test:

use hypors::{proportion::z_test, common::TailType};

let successes = vec![1, 1, 0, 1, 0]; // Number of successes
let population_proportion = 0.25; // Population proportion
let tail = TailType::Right;
let alpha = 0.05;

let result = z_test(successes, population_proportion, tail, alpha).unwrap();
println!("Test Statistic: {}", result.test_statistic);
println!("P-value: {}", result.p_value);
println!("Confidence Interval: {:?}", result.confidence_interval);
println!("Reject Null Hypothesis: {}", result.reject_null);
§Features
  • One-sample proportion test: Tests whether the proportion of successes in a single sample differs from a specified population proportion.
  • Two-sample proportion test: Tests whether the proportions of successes in two independent samples differ.
  • Sample Size Calculation: Use prop_sample_size to determine the required sample size for specified power and significance levels.

§ANOVA

Example of performing a one-way ANOVA test:

use hypors::anova::anova;

let group1 = vec![1.5, 2.5, 1.8];
let group2 = vec![2.3, 2.9, 3.0];
let group3 = vec![1.9, 2.2, 2.5];
let alpha = 0.05;

let result = anova(&[group1, group2, group3], alpha).unwrap();
println!("F Statistic: {}", result.test_statistic);
println!("P-value: {}", result.p_value);
println!("Reject Null Hypothesis: {}", result.reject_null);
§Features
  • One-way ANOVA: Tests whether at least one group mean differs from the others across multiple groups.
  • Sample Size Calculation: Use f_sample_size to determine the required sample size for specified power and significance levels.

§Chi-Square Tests

Example of performing a Chi-square test for Goodness of Fit:

use hypors::chi_square::goodness_of_fit;

let observed = vec![10, 20, 30]; // Observed frequencies
let expected = vec![15, 15, 30]; // Expected frequencies
let alpha = 0.05;

let result = goodness_of_fit(observed, expected, alpha).unwrap();
println!("Chi-Square Statistic: {}", result.test_statistic);
println!("P-value: {}", result.p_value);
println!("Reject Null Hypothesis: {}", result.reject_null);
§Features
  • Chi-square variance test: Tests whether the variance of the distribution differs from the expected variance.
  • Chi-square test for independence: Tests whether two categorical variables are independent of each other.
  • Chi-square goodness-of-fit test: Tests whether the observed frequency distribution differs from the expected distribution.
  • Sample Size Calculation: Use chi2_sample_size_gof, chi2_sample_size_ind,chi2_sample_size_variance to determine the required sample sizes for the different implementations respectively.

§Mann-Whitney U Test

Example of performing the Mann-Whitney U test:

use hypors::mann_whitney::u_test;
use hypors::common::TailType;

let group1 = vec![1.2, 2.3, 3.1];
let group2 = vec![2.5, 3.0, 3.8];
let alpha = 0.05;

let result = u_test(group1, group2, alpha, TailType::Two).unwrap();
println!("U Statistic: {}", result.test_statistic);
println!("P-value: {}", result.p_value);
println!("Reject Null Hypothesis: {}", result.reject_null);
§Features
  • Mann-Whitney U test: A non-parametric test used to determine whether there is a difference between two independent samples. This test is particularly useful when the data does not follow a normal distribution.

§Common Features

  • Customizable tail type: Supports left-tailed, right-tailed, and two-tailed tests for both t-tests and z-tests.
  • Confidence interval calculation: Returns confidence intervals for all tests.

§Usage with Polars

The library is designed to work with Vectors, arrays, and iterators of numeric data types. It can also be integrated with the polars crate for more complex data manipulation tasks. However, due to frequent minor version updates in polars, data should be converted to a compatible format (e.g., Vec<f64>) before and after usage.

§Crate Dependencies

This library relies on the following crates:

  • statrs for statistical distributions.
  • serde for object serialization and deserialization.

§Error Handling

The library uses PolarsError to handle errors that arise during data manipulation (e.g., failure to compute mean or variance). Each test function returns a Result<TestResult, PolarsError> type, where TestResult encapsulates the outcome of the hypothesis test.

§License

This project is licensed under the MIT License.

Modules§

anova
Analysis of Variance (ANOVA) Tests
chi_square
Chi Square Tests
common
Common Utilities
mann_whitney
Mann-Whitney U Tests
proportion
Tests of Proportion
t
Student T Tests
z
Z Tests