Find Critical Value of χ² for Chi-squared Test

Chi-squared distribution table & how to use instructions to quickly find the critical value of χ² 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 in statistics & probability surveys or experiments to analyze samples which are not normally or uniformly distributed. The degrees of freedom is used to refer the χ²-table values for the specified level of significance such as 1%, 2%, 3%, 5%, 10% etc. It's generally represented by χ²_e. Critical value of χ² from χ²-distribution table represents the rejection area of distribution. The estimated value of χ² or χ²-statistic (χ²₀) is compared with the critical value of χ² from Chi-squared distribution table to check the significance of results. For locating the χ²_e (critical value of χ²) in the table quickly, users can supply the values of degrees of freedom (df) and significance level (α) directly in the above χ²-table calculator. F-table to find the critical value of F is also available in pdf format too, users may download this table in pdf format to refer it later offline.

How to Find Critical Region in χ²-Test

Users may use this below χ²-table calculator or refer the rows & columns value of χ²-distribution table for a stated level of significance to find the critical region of χ²-distribution.
by Using Calculator
Supply or select the values of degrees of freedom (df), and significance level (α) directly to the χ²-table calculator and hit on "LOCATE" to address the corresponding critical value of χ².

by Using χ²-Distribution Table
Refer the row & column meeting point of degrees of freedom at a specified level of significance (α = α = 0.1%, 0.5%, 5%, 2.5%, 5%, 10% or α = 0.001, 0.005, 0.01, 0.025, 0.05, 0.1). The point where the row & column meets for the corresponding input value is the critical value of χ² or the rejection area of χ²-distribution.

Inference

The below statements show when to accept or reject null hypothesis H₀ in χ²-test

For null hypothesis H₀ :
If χ²₀ < χ²_e then the null hypothesis H₀ is accepted.
It states that there is no significance difference between χ²-statistic & expected 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 value of χ².