# Chi-squared Test (χ²0, χ²e & H0) Calculator

getcalc.com's **Chi-squared (χ²) Test calculator** is an online statistics & *probability *tool to estimate χ²-statistic (χ²_{0}), χ²-critical value (χ²_{e}) & test of hypothesis (H_{0}) to check if the test of significance between two nonuniform datasets is accepted or rejected under null hypothesis in statistics & probability experiments.

## Why χ²-Test & Formula

**Chi-squared (χ ^{2}) Test** is a technique used in probability & statistics to check if the results of χ²-distribution is statistically significant under null hypothesis. χ²-distribution is a collection of data which is not uniformly distributed over the period of time. Chi-squared test requires χ²-statistic χ²

_{0}& critical (table) value of χ²-distribution χ²

_{e}at a stated level of significance (α = 1%, 2%, 3%, 4%, 5%, 10%, 25%, 5% etc or α = 0.01, 0.02, 0.03, 0.04, 0.05, 0.1, 0.25, 0.5 etc) for the test of hypothesis (H

_{0}) in statistics & probability surveys or experiments to analyze samples which is not distributed uniformly or normally. Critical value of χ

^{2}from χ

^{2}-distribution table represents the rejection area of distribution. The estimated value of χ² or chi-squared statistic (χ²

_{0}) is compared with the critical value from χ²-distribution p-value table at a stated level of significance to check if the test of null hypothesis accepted in statistical experiments. Users may use this below χ²-test calculator to estimate χ²-statistic (χ²

_{0}), critical value (χ²

_{e}) & hypothesis test (H

_{0}) to test the significance between two or more samples which are not normally or uniformly distributed over time.

**Inference**The below statements show when to accept or reject null hypothesis H

_{0}in χ²-test

__For null hypothesis H__

_{0}:If F

_{0}< F

_{e}then the null hypothesis H

_{0}is accepted.

It states that there is no significance difference between χ²-statistic & expected (critical) value of χ².

If χ²

_{0}> χ²

_{e}then the null hypothesis H

_{0}is rejected.

It states that there is significance difference between χ²-statistic & expected or critical value of χ².

**Formula :**The below is the mathematical representation for χ²-test formula to estimate the quality of

*variances*among two or more samples which are not normally or uniformly distributed over time to predict the characteristics of population parameters of a unknown distribution.

^{2}) test formula for test of significance

## Solved Example Problems with Solutions

The below are the solved example problems for χ²-Test with step by step solution to analyze the two set of irregularly (nonuniform) distributed samples. Users may refer the below estimations to know what formula & input parameters are being used in the respective chi-squared calculations.