First, use the Critical Significance Level (α) chosen in Step 2 and the between treatment (df1 = number of treatments - 1) and within treatment (df2 = total sample size - number of treatments) degrees of freedom calculated in Step 3 to find the Critical Value of F (Fcritical) using a Critical Value Table such as the one below (e.g. if α = 0.05, df1 = 2 and df2 = 12, then Fcritical = 5.096).

Second, compare Fcritical with the value for the F statistic calculated in Step 3.

Reject your Null Hypothesis if your calculated value is greater than or equal to the Critical value; F ≥ Fcritical (significant result).

Accept your Null Hypothesis if your calculated value is less than the Critical value; F < Fcritical (non-significant result).

For example, if F = 11.791 and Fcritical = 5.096 then reject the Null Hypothesis.

Table of Critical Values for Critical Significance Levels (α) = 0.5 for the F statistic where df1 is the degrees of freedom between treatments (the numerator; the number of treatments - 1) and df2 is the degrees of freedom within treatments (the denominator; the total sample size - number of treatments) for Anova.

 df1 1 2 3 4 5 6 7 8 9 10 df1 1 647.793 799.482 864.151 899.599 921.835 937.114 948.203 956.643 963.279 968.634 2 38.506 39 39.166 39.248 39.298 39.331 39.356 39.373 39.387 39.398 3 17.443 16.044 15.439 15.101 14.885 14.735 14.624 14.54 14.473 14.419 4 12.218 10.649 9.979 9.604 9.364 9.197 9.074 8.98 8.905 8.844 5 10.007 8.434 7.764 7.388 7.146 6.978 6.853 6.757 6.681 6.619 6 8.813 7.26 6.599 6.227 5.988 5.82 5.695 5.6 5.523 5.461 7 8.073 6.542 5.89 5.523 5.285 5.119 4.995 4.899 4.823 4.761 8 7.571 6.059 5.416 5.053 4.817 4.652 4.529 4.433 4.357 4.295 9 7.209 5.715 5.078 4.718 4.484 4.32 4.197 4.102 4.026 3.964 10 6.937 5.456 4.826 4.468 4.236 4.072 3.95 3.855 3.779 3.717 11 6.724 5.256 4.63 4.275 4.044 3.881 3.759 3.664 3.588 3.526 12 6.554 5.096 4.474 4.121 3.891 3.728 3.607 3.512 3.436 3.374 13 6.414 4.965 4.347 3.996 3.767 3.604 3.483 3.388 3.312 3.25 14 6.298 4.857 4.242 3.892 3.663 3.501 3.38 3.285 3.209 3.147 15 6.2 4.765 4.153 3.804 3.576 3.415 3.293 3.199 3.123 3.06 16 6.115 4.687 4.077 3.729 3.502 3.341 3.219 3.125 3.049 2.986 17 6.042 4.619 4.011 3.665 3.438 3.277 3.156 3.061 2.985 2.922 18 5.978 4.56 3.954 3.608 3.382 3.221 3.1 3.005 2.929 2.866 19 5.922 4.508 3.903 3.559 3.333 3.172 3.051 2.956 2.88 2.817 20 5.871 4.461 3.859 3.515 3.289 3.128 3.007 2.913 2.837 2.774 21 5.827 4.42 3.819 3.475 3.25 3.09 2.969 2.874 2.798 2.735 22 5.786 4.383 3.783 3.44 3.215 3.055 2.934 2.839 2.763 2.7 23 5.75 4.349 3.75 3.408 3.183 3.023 2.902 2.808 2.731 2.668 24 5.717 4.319 3.721 3.379 3.155 2.995 2.874 2.779 2.703 2.64 25 5.686 4.291 3.694 3.353 3.129 2.969 2.848 2.753 2.677 2.613 26 5.659 4.265 3.67 3.329 3.105 2.945 2.824 2.729 2.653 2.59 27 5.633 4.242 3.647 3.307 3.083 2.923 2.802 2.707 2.631 2.568 28 5.61 4.221 3.626 3.286 3.063 2.903 2.782 2.687 2.611 2.547 29 5.588 4.201 3.607 3.267 3.044 2.884 2.763 2.669 2.592 2.529 30 5.568 4.182 3.589 3.25 3.026 2.867 2.746 2.651 2.575 2.511 31 5.549 4.165 3.573 3.234 3.01 2.851 2.73 2.635 2.558 2.495 32 5.531 4.149 3.557 3.218 2.995 2.836 2.715 2.62 2.543 2.48 33 5.515 4.134 3.543 3.204 2.981 2.822 2.701 2.606 2.529 2.466 34 5.499 4.12 3.529 3.191 2.968 2.808 2.688 2.593 2.516 2.453 35 5.485 4.106 3.517 3.179 2.956 2.796 2.676 2.581 2.504 2.44 36 5.471 4.094 3.505 3.167 2.944 2.785 2.664 2.569 2.492 2.429 37 5.458 4.082 3.493 3.156 2.933 2.774 2.653 2.558 2.481 2.418 38 5.446 4.071 3.483 3.145 2.923 2.763 2.643 2.548 2.471 2.407 39 5.435 4.061 3.473 3.135 2.913 2.754 2.633 2.538 2.461 2.397 40 5.424 4.051 3.463 3.126 2.904 2.744 2.624 2.529 2.452 2.388

Critical values of the two-tailed F distribution generated using the FINV() function in Microsoft Excel, which returns the inverse of the F probability distribution. Table generated by Toby Carter.