NUMBAT OER - Open Educational Resources

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 39.000 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 14.540 14.473 14.419
4 12.218 10.649 9.979 9.604 9.364 9.197 9.074 8.980 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 7.260 6.599 6.227 5.988 5.820 5.695 5.600 5.523 5.461
7 8.073 6.542 5.890 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 4.320 4.197 4.102 4.026 3.964
10 6.937 5.456 4.826 4.468 4.236 4.072 3.950 3.855 3.779 3.717
11 6.724 5.256 4.630 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 3.250
14 6.298 4.857 4.242 3.892 3.663 3.501 3.380 3.285 3.209 3.147
15 6.200 4.765 4.153 3.804 3.576 3.415 3.293 3.199 3.123 3.060
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 4.560 3.954 3.608 3.382 3.221 3.100 3.005 2.929 2.866
19 5.922 4.508 3.903 3.559 3.333 3.172 3.051 2.956 2.880 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 4.420 3.819 3.475 3.250 3.090 2.969 2.874 2.798 2.735
22 5.786 4.383 3.783 3.440 3.215 3.055 2.934 2.839 2.763 2.700
23 5.750 4.349 3.750 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 2.640
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 3.670 3.329 3.105 2.945 2.824 2.729 2.653 2.590
27 5.633 4.242 3.647 3.307 3.083 2.923 2.802 2.707 2.631 2.568
28 5.610 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 3.250 3.026 2.867 2.746 2.651 2.575 2.511
31 5.549 4.165 3.573 3.234 3.010 2.851 2.730 2.635 2.558 2.495
32 5.531 4.149 3.557 3.218 2.995 2.836 2.715 2.620 2.543 2.480
33 5.515 4.134 3.543 3.204 2.981 2.822 2.701 2.606 2.529 2.466
34 5.499 4.120 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 2.440
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.