# Chi-squared distribution

The chi-squared distribution can be derived from the normal distribution. It results from the sum of n normally distributed random variables, where n is the number of degrees of freedom. The critical chi-square value for a given degree of freedom can be read from the chi-square table.

If a hypothesis is to be tested with the chi-squared test, we have to compare the calculated chi-squared value resulting from the test with the critical value. Depending on the significance level alpha, the critical value can be read from the chi-squared table below. Usually the significance level alpha is 0.05. If the calculated chi-squared value is lower than the critical value, the null hypothesis can be mantained.

The chi-squared calculator on DATAtab gives can have important values automatically. If you need help, take a look at the example of the chi-squared test.

=

## Table of chi-squared distribution

Significance level Alpha 0.995 0.975 0.2 0.1 0.05 0.025 0.02 0.01 0.005 0.002 0.001
Degrees of freedom
1 00.0011.6422.7063.8415.0245.4126.6357.8799.5510.828
2 0.010.0513.2194.6055.9917.3787.8249.2110.59712.42913.816
3 0.0720.2164.6426.2517.8159.3489.83711.34512.83814.79616.266
4 0.2070.4845.9897.7799.48811.14311.66813.27714.8616.92418.467
5 0.4120.8317.2899.23611.0712.83313.38815.08616.7518.90720.515
6 0.6761.2378.55810.64512.59214.44915.03316.81218.54820.79122.458
7 0.9891.699.80312.01714.06716.01316.62218.47520.27822.60124.322
8 1.3442.1811.0313.36215.50717.53518.16820.0921.95524.35226.124
9 1.7352.712.24214.68416.91919.02319.67921.66623.58926.05627.877
10 2.1563.24713.44215.98718.30720.48321.16123.20925.18827.72229.588
11 2.6033.81614.63117.27519.67521.9222.61824.72526.75729.35431.264
12 3.0744.40415.81218.54921.02623.33724.05426.21728.330.95732.909
13 3.5655.00916.98519.81222.36224.73625.47227.68829.81932.53534.528
14 4.0755.62918.15121.06423.68526.11926.87329.14131.31934.09136.123
15 4.6016.26219.31122.30724.99627.48828.25930.57832.80135.62837.697
16 5.1426.90820.46523.54226.29628.84529.6333234.26737.14639.252
17 5.6977.56421.61524.76927.58730.19130.99533.40935.71838.64840.79
18 6.2658.23122.7625.98928.86931.52632.34634.80537.15640.13642.312
19 6.8448.90723.927.20430.14432.85233.68736.19138.58241.6143.82
20 7.4349.59125.03828.41231.4134.1735.0237.56639.99743.07245.315
21 8.03410.28326.17129.61532.67135.47936.34338.93241.40144.52246.797
22 8.64310.98227.30130.81333.92436.78137.65940.28942.79645.96248.268
23 9.2611.68928.42932.00735.17238.07638.96841.63844.18147.39149.728
24 9.88612.40129.55333.19636.41539.36440.2742.9845.55948.81251.179
25 10.5213.1230.67534.38237.65240.64641.56644.31446.92850.22352.62
26 11.1613.84431.79535.56338.88541.92342.85645.64248.2951.62754.052
27 11.80814.57332.91236.74140.11343.19544.1446.96349.64553.02355.476
28 12.46115.30834.02737.91641.33744.46145.41948.27850.99354.41156.892
29 13.12116.04735.13939.08742.55745.72246.69349.58852.33655.79258.301
30 13.78716.79136.2540.25643.77346.97947.96250.89253.67257.16759.703
40 20.70724.43347.26951.80555.75859.34260.43663.69166.76670.61873.402
50 27.99132.35758.16463.16767.50571.4272.61376.15479.4983.65786.661
60 35.53440.48268.97274.39779.08283.29884.5888.37991.95296.40499.607
70 43.27548.75879.71585.52790.53195.02396.388100.425104.215108.929112.317
80 51.17257.15390.40596.578101.879106.629108.069112.329116.321121.28124.839
90 59.19665.647101.054107.565113.145118.136119.648124.116128.299133.489137.208
100 67.32874.222111.667118.498124.342129.561131.142135.807140.169145.577149.449

The chi-square distribution table can thus be used to determine whether the alternative hypothesis is mantained or rejected.

Cite DATAtab: DATAtab Team (2024). DATAtab: Online Statistics Calculator. DATAtab e.U. Graz, Austria. URL https://datatab.net