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

Chi-squared (χ²) 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 χ²₀ & 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 (H₀) in statistics & probability surveys or experiments to analyze samples which is not distributed uniformly or normally. Critical value of χ² from χ²-distribution table represents the rejection area of distribution. The estimated value of χ² or chi-squared statistic (χ²₀) 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 (χ²₀), critical value (χ²_e) & hypothesis test (H₀) 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 H₀ in χ²-test
For null hypothesis H₀ :
If F₀ < F_e then the null hypothesis H₀ is accepted.
It states that there is no significance difference between χ²-statistic & expected (critical) value of χ².
If χ²₀ > χ²_e then the null hypothesis H₀ 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.