Editing Chi-squared distribution (section)

=== Table of {{math|''χ''<sup>2</sup>}} values vs {{math|''p''}}-values ===
The [[p-value|<math display="inline">p</math>-value]] is the probability of observing a test statistic ''at least'' as extreme in a chi-squared distribution. Accordingly, since the [[cumulative distribution function]] (CDF) for the appropriate degrees of freedom ''(df)'' gives the probability of having obtained a value ''less extreme'' than this point, subtracting the CDF value from 1 gives the ''p''-value. A low ''p''-value, below the chosen significance level, indicates [[statistical significance]], i.e., sufficient evidence to reject the null hypothesis. A significance level of 0.05 is often used as the cutoff between significant and non-significant results.

The table below gives a number of ''p''-values matching to <math> \chi^2 </math> for the first 10 degrees of freedom.
{| class="wikitable"
! Degrees of freedom (df)
!colspan=11| <math> \chi^2 </math> value<ref>[http://www2.lv.psu.edu/jxm57/irp/chisquar.html Chi-Squared Test] {{Webarchive|url=https://web.archive.org/web/20131118011437/http://www2.lv.psu.edu/jxm57/irp/chisquar.html |date=2013-11-18 }} Table B.2. Dr. Jacqueline S. McLaughlin at The Pennsylvania State University. In turn citing: R. A. Fisher and F. Yates, Statistical Tables for Biological Agricultural and Medical Research, 6th ed., Table IV. Two values have been corrected, 7.82 with 7.81 and 4.60 with 4.61</ref>
|-
| style="text-align:center;" | 1
| 0.004
| 0.02
| 0.06
| 0.15
| 0.46
| 1.07
| 1.64
| 2.71
| 3.84
| 6.63
| 10.83
|-
| style="text-align:center;" | 2
| 0.10
| 0.21
| 0.45
| 0.71
| 1.39
| 2.41
| 3.22
| 4.61
| 5.99
| 9.21
| 13.82
|-
| style="text-align:center;" | 3
| 0.35
| 0.58
| 1.01
| 1.42
| 2.37
| 3.66
| 4.64
| 6.25
| 7.81
| 11.34
| 16.27
|-
| style="text-align:center;" | 4
| 0.71
| 1.06
| 1.65
| 2.20
| 3.36
| 4.88
| 5.99
| 7.78
| 9.49
| 13.28
| 18.47
|-
| style="text-align:center;" | 5
| 1.14
| 1.61
| 2.34
| 3.00
| 4.35
| 6.06
| 7.29
| 9.24
| 11.07
| 15.09
| 20.52
|-
| style="text-align:center;" | 6
| 1.63
| 2.20
| 3.07
| 3.83
| 5.35
| 7.23
| 8.56
| 10.64
| 12.59
| 16.81
| 22.46
|-
| style="text-align:center;" | 7
| 2.17
| 2.83
| 3.82
| 4.67
| 6.35
| 8.38
| 9.80
| 12.02
| 14.07
| 18.48
| 24.32
|-
| style="text-align:center;" | 8
| 2.73
| 3.49
| 4.59
| 5.53
| 7.34
| 9.52
| 11.03
| 13.36
| 15.51
| 20.09
| 26.12
|-
| style="text-align:center;" | 9
| 3.32
| 4.17
| 5.38
| 6.39
| 8.34
| 10.66
| 12.24
| 14.68
| 16.92
| 21.67
| 27.88
|-
| style="text-align:center;" | 10
| 3.94
| 4.87
| 6.18
| 7.27
| 9.34
| 11.78
| 13.44
| 15.99
| 18.31
| 23.21
| 29.59
 13.25
|-
! scope="row" style="text-align:right;" | ''p''-value (probability)
| style="background: #ffa2aa" | 0.95
| style="background: #efaaaa" | 0.90
| style="background: #e8b2aa" | 0.80
| style="background: #dfbaaa" | 0.70
| style="background: #d8c2aa" | 0.50
| style="background: #cfcaaa" | 0.30
| style="background: #c8d2aa" | 0.20
| style="background: #bfdaaa" | 0.10
| style="background: #b8e2aa" | 0.05
| style="background: #afeaaa" | 0.01
| style="background: #a8faaa" | 0.001
|}

These values can be calculated evaluating the [[quantile function]] (also known as "inverse CDF" or "ICDF") of the chi-squared distribution;<ref>{{Cite web|url=https://www.r-tutor.com/elementary-statistics/probability-distributions/chi-squared-distribution|title=Chi-squared Distribution &#124; R Tutorial|website=www.r-tutor.com}}</ref> e. g., the {{math|χ<sup>2</sup>}} ICDF for {{math|1=''p'' = 0.05}} and {{math|1=df = 7}} yields {{math|2.1673 ≈ 2.17}} as in the table above, noticing that {{math|1 – ''p''}} is the [[p-value|''p''-value]] from the table.