Skip to main content
Statistics LibreTexts

A.3: Table of Chi-square critical values

  1. Last updated
  2. Save as PDF
  • Page ID
    45297

    • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    \( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

    ( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\id}{\mathrm{id}}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\kernel}{\mathrm{null}\,}\)

    \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\)

    \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\)

    \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    \( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

    \( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

    \( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vectorC}[1]{\textbf{#1}} \)

    \( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

    \( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

    \( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

    \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    \(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)
    Chi-square distribution curve with the upper tail highlighted.
    Figure \(\PageIndex{1}\).
    \(\alpha\)(1) 0.25 0.1 0.05 0.025 0.01 0.005 0.0025 0.001 0.0005
    DF/1 1.323 2.706 3.841 5.024 6.635 7.879 9.141 10.828 12.116
    2 2.773 4.605 5.991 7.378 9.210 10.597 11.983 13.816 15.202
    3 4.108 6.251 7.815 9.348 11.345 12.838 14.320 16.266 17.730
    4 5.385 7.779 9.488 11.143 13.277 14.860 16.424 18.467 19.997
    5 6.626 9.236 11.070 12.833 15.086 16.750 18.386 20.515 22.105
    6 7.841 10.645 12.592 14.449 16.812 18.548 20.249 22.458 24.103
    7 9.037 12.017 14.067 16.013 18.475 20.278 22.040 24.322 26.018
    8 10.219 13.362 15.507 17.535 20.090 21.955 23.774 26.124 27.868
    9 11.389 14.684 16.919 19.023 21.666 23.589 25.462 27.877 29.666
    10 12.549 15.987 18.307 20.483 23.209 25.188 27.112 29.588 31.420
    11 13.701 17.275 19.675 21.920 24.725 26.757 28.729 31.264 33.137
    12 14.845 18.549 21.026 23.337 26.217 28.300 30.318 32.909 34.821
    13 15.984 19.812 22.362 24.736 27.688 29.819 31.883 34.528 36.478
    14 17.117 21.064 23.685 26.119 29.141 31.319 33.426 36.123 38.109
    15 18.245 22.307 24.996 27.488 30.578 32.801 34.950 37.697 39.719
    16 19.369 23.542 26.296 28.845 32.000 34.267 36.456 39.252 41.308
    17 20.489 24.769 27.587 30.191 33.409 35.718 37.946 40.790 42.879
    18 21.605 25.989 28.869 31.526 34.805 37.156 39.422 42.312 44.434
    19 22.718 27.204 30.144 32.852 36.191 38.582 40.885 43.820 45.973
    20 23.828 28.412 31.410 34.170 37.566 39.997 42.336 45.315 47.498
    21 24.935 29.615 32.671 35.479 38.932 41.401 43.775 46.797 49.011
    22 26.039 30.813 33.924 36.781 40.289 42.796 45.204 48.268 50.511
    23 27.141 32.007 35.172 38.076 41.638 44.181 46.623 49.728 52.000
    24 28.241 33.196 36.415 39.364 42.980 45.559 48.034 51.179 53.479
    25 29.339 34.382 37.652 40.646 44.314 46.928 49.435 52.620 54.947
    26 30.435 35.563 38.885 41.923 45.642 48.290 50.829 54.052 56.407
    27 31.528 36.741 40.113 43.195 46.963 49.645 52.215 55.476 57.858
    28 32.620 37.916 41.337 44.461 48.278 50.993 53.594 56.892 59.300
    29 33.711 39.087 42.557 45.722 49.588 52.336 54.967 58.301 60.735
    30 34.800 40.256 43.773 46.979 50.892 53.672 56.332 59.703 62.162
    35 40.223 46.059 49.802 53.203 57.342 60.275 63.076 66.619 69.199
    40 45.616 51.805 55.758 59.342 63.691 66.766 69.699 73.402 76.095
    50 56.334 63.167 67.505 71.420 76.154 79.490 82.664 86.661 89.561

    R command

    qchisq(c(alpha), df=df, lower.tail=FALSE)

    where alpha is one-tailed probability, df is number of degrees of freedom, and lower.tail=FALSE means each cell is to be read as equal to or greater than the critical value.

    This page titled A.3: Table of Chi-square critical values is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Michael R Dohm via source content that was edited to the style and standards of the LibreTexts platform.