CHI-SQUARED $(\chi^2)$ DISTRIBUTION
The percentage at the top of the table is equal to the AREA to the LEFT of $\chi^2$; where $\chi^2$ is located both along the horizontal axis and in the table body.
$$
\begin{array}
{r|@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }}\\
\ \\
df&0.1\%&0.5\%&1.0\%&2.5\%&5.0\%&10.0\%&12.5\%&20.0\%&25.0\%&33.3\%&50.0\%\\ \hline
\ \\
1&0.000&0.000&0.000&0.001&0.004&0.016&0.025&0.064&0.102&0.186&0.455\\
2&0.002&0.010&0.020&0.051&0.103&0.211&0.267&0.446&0.575&0.811&1.386\\
3&0.024&0.072&0.115&0.216&0.352&0.584&0.692&1.005&1.213&1.568&2.366\\
4&0.091&0.207&0.297&0.484&0.711&1.064&1.219&1.649&1.923&2.378&3.357\\
5&0.210&0.412&0.554&0.831&1.145&1.610&1.808&2.343&2.675&3.216&4.351\\
6&0.381&0.676&0.872&1.237&1.635&2.204&2.441&3.070&3.455&4.074&5.348\\
7&0.598&0.989&1.239&1.690&2.167&2.833&3.106&3.822&4.255&4.945&6.346\\
8&0.857&1.344&1.646&2.180&2.733&3.490&3.797&4.594&5.071&5.826&7.344\\
9&1.152&1.735&2.088&2.700&3.325&4.168&4.507&5.380&5.899&6.716&8.343\\
10&1.479&2.156&2.558&3.247&3.940&4.865&5.234&6.179&6.737&7.612&9.342\\
11&1.834&2.603&3.053&3.816&4.575&5.578&5.975&6.989&7.584&8.514&10.341\\
12&2.214&3.074&3.571&4.404&5.226&6.304&6.729&7.807&8.438&9.420&11.340\\
13&2.617&3.565&4.107&5.009&5.892&7.042&7.493&8.634&9.299&10.331&12.340\\
14&3.041&4.075&4.660&5.629&6.571&7.790&8.266&9.467&10.165&11.245&13.339\\
15&3.483&4.601&5.229&6.262&7.261&8.547&9.048&10.307&11.037&12.163&14.339\\
16&3.942&5.142&5.812&6.908&7.962&9.312&9.837&11.152&11.912&13.083&15.338\\
17&4.416&5.697&6.408&7.564&8.672&10.085&10.633&12.002&12.792&14.006&16.338\\
18&4.905&6.265&7.015&8.231&9.390&10.865&11.435&12.857&13.675&14.931&17.338\\
19&5.407&6.844&7.633&8.907&10.117&11.651&12.242&13.716&14.562&15.859&18.338\\
20&5.921&7.434&8.260&9.591&10.851&12.443&13.055&14.578&15.452&16.788&19.337\\
21&6.447&8.034&8.897&10.283&11.591&13.240&13.873&15.445&16.344&17.720&20.337\\
22&6.983&8.643&9.542&10.982&12.338&14.041&14.695&16.314&17.240&18.653&21.337\\
23&7.529&9.260&10.196&11.689&13.091&14.848&15.521&17.187&18.137&19.587&22.337\\
24&8.085&9.886&10.856&12.401&13.848&15.659&16.351&18.062&19.037&20.523&23.337\\
25&8.649&10.520&11.524&13.120&14.611&16.473&17.184&18.940&19.939&21.461&24.337\\
26&9.222&11.160&12.198&13.844&15.379&17.292&18.021&19.820&20.843&22.399&25.336\\
27&9.803&11.808&12.879&14.573&16.151&18.114&18.861&20.703&21.749&23.339&26.336\\
28&10.391&12.461&13.565&15.308&16.928&18.939&19.704&21.588&22.657&24.280
&27.336\\
29&10.986&13.121&14.256&16.047&17.708&19.768&20.550&22.475&23.567&25.222
&28.336\\
30&11.588&13.787&14.953&16.791&18.493&20.599&21.399&23.364&24.478&26.165
&29.336\\
35&14.688&17.192&18.509&20.569&22.465&24.797&25.678&27.836&29.054&30.894
&34.336\\
40&17.916&20.707&22.164&24.433&26.509&29.051&30.008&32.345&33.660&35.643
&39.335\\
45&21.251&24.311&25.901&28.366&30.612&33.350&34.379&36.884&38.291&40.407
&44.335\\
50&24.674&27.991&29.707&32.357&34.764&37.689&38.785&41.449&42.942&45.184
&49.335\\
55&28.173&31.735&33.570&36.398&38.958&42.060&43.220&46.036&47.610&49.972
&54.335\\
60&31.738&35.534&37.485&40.482&43.188&46.459&47.680&50.641&52.294&54.770
&59.335
\end{array}
$$
$$
\begin{array}
{r|@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r@{\ }r}
\ \\
df&60.0\%&66.7\%&75.0\%&80.0\%&87.5\%&90.0\%&95.0\%&97.5\%&99.0\%&99.5\%
&99.9\%\\ \hline
\ \\
1&0.708&0.936&1.323&1.642&2.354&2.706&3.841&5.024&6.635&7.879&10.828\\
2&1.833&2.197&2.773&3.219&4.159&4.605&5.991&7.378&9.210&10.597&13.816\\
3&2.946&3.405&4.108&4.642&5.739&6.251&7.815&9.348&11.345&12.838&16.266\\
4&4.045&4.579&5.385&5.989&7.214&7.779&9.488&11.143&13.277&14.860&18.467\\
5&5.132&5.730&6.626&7.289&8.625&9.236&11.070&12.833&15.086&16.750&20.515\\
6&6.211&6.867&7.841&8.558&9.992&10.645&12.592&14.449&16.812&18.548&22.458\\
7&7.283&7.992&9.037&9.803&11.326&12.017&14.067&16.013&18.475&20.278&24.322\\
8&8.351&9.107&10.219&11.030&12.636&13.362&15.507&17.535&20.090&21.955&26.125\\
9&9.414&10.215&11.389&12.242&13.926&14.684&16.919&19.023&21.666&23.589
&27.877\\
10&10.473&11.317&12.549&13.442&15.198&15.987&18.307&20.483&23.209&25.188
&29.588\\
11&11.530&12.414&13.701&14.631&16.457&17.275&19.675&21.920&24.725&26.757
&31.264\\
12&12.584&13.506&14.845&15.812&17.703&18.549&21.026&23.337&26.217&28.300
&32.910\\
13&13.636&14.595&15.984&16.985&18.939&19.812&22.362&24.736&27.688&29.819
&34.528\\
14&14.685&15.680&17.117&18.151&20.166&21.064&23.685&26.119&29.141&31.319
&36.123\\
15&15.733&16.761&18.245&19.311&21.384&22.307&24.996&27.488&30.578&32.801
&37.697\\
16&16.780&17.840&19.369&20.465&22.595&23.542&26.296&28.845&32.000&34.267
&39.252\\
17&17.824&18.917&20.489&21.615&23.799&24.769&27.587&30.191&33.409&35.718
&40.790\\
18&18.868&19.991&21.605&22.760&24.997&25.989&28.869&31.526&34.805&37.156
&42.312\\
19&19.910&21.063&22.718&23.900&26.189&27.204&30.144&32.852&36.191&38.582
&43.820\\
20&20.951&22.133&23.828&25.038&27.376&28.412&31.410&34.170&37.566&39.997
&45.315\\
21&21.991&23.201&24.935&26.171&28.559&29.615&32.671&35.479&38.932&41.401
&46.797\\
22&23.031&24.268&26.039&27.301&29.737&30.813&33.924&36.781&40.289&42.796
&48.268\\
23&24.069&25.333&27.141&28.429&30.911&32.007&35.172&38.076&41.638&44.181
&49.728\\
24&25.106&26.397&28.241&29.553&32.081&33.196&36.415&39.364&42.980&45.559
&51.179\\
25&26.143&27.459&29.339&30.675&33.247&34.382&37.652&40.646&44.314&46.928
&52.620\\
26&27.179&28.520&30.435&31.795&34.410&35.563&38.885&41.923&45.642&48.290
&54.052\\
27&28.214&29.580&31.528&32.912&35.570&36.741&40.113&43.195&46.963&49.645
&55.476\\
28&29.249&30.639&32.620&34.027&36.727&37.916&41.337&44.461&48.278&50.993
&56.892\\
29&30.283&31.697&33.711&35.139&37.881&39.087&42.557&45.722&49.588&52.336
&58.301\\
30&31.316&32.754&34.800&36.250&39.033&40.256&43.773&46.979&50.892&53.672
&59.703\\
35&36.475&38.024&40.223&41.778&44.753&46.059&49.802&53.203&57.342&60.275
&66.619\\
40&41.622&43.275&45.616&47.269&50.424&51.805&55.758&59.342&63.691&66.766
&73.402\\
45&46.761&48.510&50.985&52.729&56.052&57.505&61.656&65.410&69.957&73.166
&80.077\\
50&51.892&53.733&56.334&58.164&61.647&63.167&67.505&71.420&76.154&79.490
&86.661\\
55&57.016&58.945&61.665&63.577&67.211&68.796&73.311&77.380&82.292&85.749
&93.168\\
60&62.135&64.147&66.981&68.972&72.751&74.397&79.082&83.298&88.379&91.952
&99.607
\end{array}
$$
