Table of critical values for the F distribution (for use with ANOVA): How to use this table:
Table of critical values for the F distribution (for use with ANOVA):
How to use this table:
There are two tables here. The first one gives critical values of F at the p = 0.05 level of significance. The second table gives critical values of F at the p = 0.01 level of significance.
- Obtain your F-ratio. This has (x,y) degrees of freedom associated with it.
- Go along x columns, and down y rows. The point of intersection is your critical F-ratio.
- If your obtained value of F is equal to or larger than this critical F-value, then your result is significant at that level of probability.
An example: I obtain an F ratio of 3.96 with (2, 24) degrees of freedom.
I go along 2 columns and down 24 rows. The critical value of F is 3.40. My obtained F-ratio
is larger than this, and so I conclude that my obtained F-ratio is likely to occur by chance with a p<.05.
Critical values of F for the 0.05 significance level:
|
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
|
1 |
161.45 |
199.50 |
215.71 |
224.58 |
230.16 |
233.99 |
236.77 |
238.88 |
240.54 |
241.88 |
|
2 |
18.51 |
19.00 |
19.16 |
19.25 |
19.30 |
19.33 |
19.35 |
19.37 |
19.39 |
19.40 |
|
3 |
10.13 |
9.55 |
9.28 |
9.12 |
9.01 |
8.94 |
8.89 |
8.85 |
8.81 |
8.79 |
|
4 |
7.71 |
6.94 |
6.59 |
6.39 |
6.26 |
6.16 |
6.09 |
6.04 |
6.00 |
5.96 |
|
5 |
6.61 |
5.79 |
5.41 |
5.19 |
5.05 |
4.95 |
4.88 |
4.82 |
4.77 |
4.74 |
|
6 |
5.99 |
5.14 |
4.76 |
4.53 |
4.39 |
4.28 |
4.21 |
4.15 |
4.10 |
4.06 |
|
7 |
5.59 |
4.74 |
4.35 |
4.12 |
3.97 |
3.87 |
3.79 |
3.73 |
3.68 |
3.64 |
|
8 |
5.32 |
4.46 |
4.07 |
3.84 |
3.69 |
3.58 |
3.50 |
3.44 |
3.39 |
3.35 |
|
9 |
5.12 |
4.26 |
3.86 |
3.63 |
3.48 |
3.37 |
3.29 |
3.23 |
3.18 |
3.14 |
|
10 |
4.97 |
4.10 |
3.71 |
3.48 |
3.33 |
3.22 |
3.14 |
3.07 |
3.02 |
2.98 |
|
11 |
4.84 |
3.98 |
3.59 |
3.36 |
3.20 |
3.10 |
3.01 |
2.95 |
2.90 |
2.85 |
|
12 |
4.75 |
3.89 |
3.49 |
3.26 |
3.11 |
3.00 |
2.91 |
2.85 |
2.80 |
2.75 |
|
13 |
4.67 |
3.81 |
3.41 |
3.18 |
3.03 |
2.92 |
2.83 |
2.77 |
2.71 |
2.67 |
|
14 |
4.60 |
3.74 |
3.34 |
3.11 |
2.96 |
2.85 |
2.76 |
2.70 |
2.65 |
2.60 |
|
15 |
4.54 |
3.68 |
3.29 |
3.06 |
2.90 |
2.79 |
2.71 |
2.64 |
2.59 |
2.54 |
|
16 |
4.49 |
3.63 |
3.24 |
3.01 |
2.85 |
2.74 |
2.66 |
2.59 |
2.54 |
2.49 |
|
17 |
4.45 |
3.59 |
3.20 |
2.97 |
2.81 |
2.70 |
2.61 |
2.55 |
2.49 |
2.45 |
|
18 |
4.41 |
3.56 |
3.16 |
2.93 |
2.77 |
2.66 |
2.58 |
2.51 |
2.46 |
2.41 |
|
19 |
4.38 |
3.52 |
3.13 |
2.90 |
2.74 |
2.63 |
2.54 |
2.48 |
2.42 |
2.38 |
|
20 |
4.35 |
3.49 |
3.10 |
2.87 |
2.71 |
2.60 |
2.51 |
2.45 |
2.39 |
2.35 |
|
21 |
4.33 |
3.47 |
3.07 |
2.84 |
2.69 |
2.57 |
2.49 |
2.42 |
2.37 |
2.32 |
|
22 |
4.30 |
3.44 |
3.05 |
2.82 |
2.66 |
2.55 |
2.46 |
2.40 |
2.34 |
2.30 |
|
23 |
4.28 |
3.42 |
3.03 |
2.80 |
2.64 |
2.53 |
2.44 |
2.38 |
2.32 |
2.28 |
|
24 |
4.26 |
3.40 |
3.01 |
2.78 |
2.62 |
2.51 |
2.42 |
2.36 |
2.30 |
2.26 |
|
25 |
4.24 |
3.39 |
2.99 |
2.76 |
2.60 |
2.49 |
2.41 |
2.34 |
2.28 |
2.24 |
|
26 |
4.23 |
3.37 |
2.98 |
2.74 |
2.59 |
2.47 |
2.39 |
2.32 |
2.27 |
2.22 |
|
27 |
4.21 |
3.35 |
2.96 |
2.73 |
2.57 |
2.46 |
2.37 |
2.31 |
2.25 |
2.20 |
|
28 |
4.20 |
3.34 |
2.95 |
2.71 |
2.56 |
2.45 |
2.36 |
2.29 |
2.24 |
2.19 |
|
29 |
4.18 |
3.33 |
2.93 |
2.70 |
2.55 |
2.43 |
2.35 |
2.28 |
2.22 |
2.18 |
|
30 |
4.17 |
3.32 |
2.92 |
2.69 |
2.53 |
2.42 |
2.33 |
2.27 |
2.21 |
2.17 |
|
31 |
4.16 |
3.31 |
2.91 |
2.68 |
2.52 |
2.41 |
2.32 |
2.26 |
2.20 |
2.15 |
|
32 |
4.15 |
3.30 |
2.90 |
2.67 |
2.51 |
2.40 |
2.31 |
2.24 |
2.19 |
2.14 |
|
33 |
4.14 |
3.29 |
2.89 |
2.66 |
2.50 |
2.39 |
2.30 |
2.24 |
2.18 |
2.13 |
|
34 |
4.13 |
3.28 |
2.88 |
2.65 |
2.49 |
2.38 |
2.29 |
2.23 |
2.17 |
2.12 |
|
35 |
4.12 |
3.27 |
2.87 |
2.64 |
2.49 |
2.37 |
2.29 |
2.22 |
2.16 |
2.11 |
The estimated equation by OLS is:
GPA = 0.73+0.44HS+0.04A+0.01AS-0.07S+0.14PC+0.01D+0.01B+0.16F+0.08HR-0.01MR
(.76) (.10) (.03) (.01) (.03) (.06) (.06) (.08) (.06) (.23) (.12) (.10)
[1.36] [1.75] [1.32] [1.28] [1.23] [1.11] [1.43] [1.26] [1.47] [4.22] [3.45]
Residual (df) = 129, TSS =19.41, ESS = 14.03
Critical values of F for the 0.01 significance level:
1 2 3 4 5 6 7 8 9 10
1 4052.19 4999.52 5403.34 5624.62 5763.65 5858.97 5928.33 5981.10 6022.50 6055.85
2 98.50 99.00 99.17 99.25 99.30 99.33 99.36 99.37 99.39 99.40
3 34.12 30.82 29.46 28.71 28.24 27.91 27.67 27.49 27.35 27.23
4 21.20 18.00 16.69 15.98 15.52 15.21 14.98 14.80 14.66 14.55
5 16.26 13.27 12.06 11.39 10.97 10.67 10.46 10.29 10.16 10.05
6 13.75 10.93 9.78 9.15 8.75 8.47 8.26 8.10 7.98 7.87
7 12.25 9.55 8.45 7.85 7.46 7.19 6.99 6.84 6.72 6.62
8 11.26 8.65 7.59 7.01 6.63 6.37 6.18 6.03 5.91 5.81
9 10.56 8.02 6.99 6.42 6.06 5.80 5.61 5.47 5.35 5.26
10 10.04 7.56 6.55 5.99 5.64 5.39 5.20 5.06 4.94 4.85
11 9.65 7.21 6.22 5.67 5.32 5.07 4.89 4.74 4.63 4.54
12 9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.50 4.39 4.30
13 9.07 6.70 5.74 5.21 4.86 4.62 4.44 4.30 4.19 4.10
14 8.86 6.52 5.56 5.04 4.70 4.46 4.28 4.14 4.03 3.94
15 8.68 6.36 5.42 4.89 4.56 4.32 4.14 4.00 3.90 3.81
16 8.53 6.23 5.29 4.77 4.44 4.20 4.03 3.89 3.78 3.69
17 8.40 6.11 5.19 4.67 4.34 4.10 3.93 3.79 3.68 3.59
18 8.29 6.01 5.09 4.58 4.25 4.02 3.84 3.71 3.60 3.51
19 8.19 5.93 5.01 4.50 4.17 3.94 3.77 3.63 3.52 3.43
20 8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.46 3.37
21 8.02 5.78 4.87 4.37 4.04 3.81 3.64 3.51 3.40 3.31
22 7.95 5.72 4.82 4.31 3.99 3.76 3.59 3.45 3.35 3.26
23 7.88 5.66 4.77 4.26 3.94 3.71 3.54 3.41 3.30 3.21
24 7.82 5.61 4.72 4.22 3.90 3.67 3.50 3.36 3.26 3.17
25 7.77 5.57 4.68 4.18 3.86 3.63 3.46 3.32 3.22 3.13
26 7.72 5.53 4.64 4.14 3.82 3.59 3.42 3.29 3.18 3.09
27 7.68 5.49 4.60 4.11 3.79 3.56 3.39 3.26 3.15 3.06
28 7.64 5.45 4.57 4.07 3.75 3.53 3.36 3.23 3.12 3.03
29 7.60 5.42 4.54 4.05 3.73 3.50 3.33 3.20 3.09 3.01
30 7.56 5.39 4.51 4.02 3.70 3.47 3.31 3.17 3.07 2.98
31 7.53 5.36 4.48 3.99 3.68 3.45 3.28 3.15 3.04 2.96
32 7.50 5.34 4.46 3.97 3.65 3.43 3.26 3.13 3.02 2.93
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