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276 Statistics for Environmental Science and Management, Second Edition
Critical Values for the F-Distribution
Table A2.4
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60 |
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30 |
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20 |
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15 |
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12 |
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10 |
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9 |
1 |
8 |
ν |
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7 |
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6 |
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5 |
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4 |
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3 |
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2 |
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1 |
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2 |
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ν |
252.2 |
19.48 |
8.57 |
5.69 |
4.43 |
3.74 |
3.30 |
3.01 |
2.79 |
2.62 |
2.49 |
2.38 |
2.30 |
2.22 |
2.16 |
2.11 |
250.1 |
19.46 |
8.62 |
5.75 |
4.50 |
3.81 |
3.38 |
3.08 |
2.86 |
2.70 |
2.57 |
2.47 |
2.38 |
2.31 |
2.25 |
2.19 |
248.0 |
19.45 |
8.66 |
5.80 |
4.56 |
3.87 |
3.45 |
3.15 |
2.94 |
2.77 |
2.65 |
2.54 |
2.46 |
2.39 |
2.33 |
2.28 |
246.0 |
19.43 |
8.70 |
5.86 |
4.62 |
3.94 |
3.51 |
3.22 |
3.01 |
2.85 |
2.72 |
2.62 |
2.53 |
2.46 |
2.40 |
2.35 |
243.9 |
19.41 |
8.75 |
5.91 |
4.68 |
4.00 |
3.58 |
3.28 |
3.07 |
2.91 |
2.79 |
2.69 |
2.60 |
2.53 |
2.48 |
2.43 |
241.9 |
19.40 |
8.79 |
5.96 |
4.74 |
4.06 |
3.64 |
3.35 |
3.14 |
2.98 |
2.85 |
2.75 |
2.67 |
2.60 |
2.54 |
2.49 |
240.5 |
19.39 |
8.81 |
6.00 |
4.77 |
4.10 |
3.68 |
3.39 |
3.18 |
3.02 |
2.90 |
2.80 |
2.71 |
2.65 |
2.59 |
2.54 |
238.9 |
19.37 |
8.85 |
6.04 |
4.82 |
4.15 |
3.73 |
3.44 |
3.23 |
3.07 |
2.95 |
2.85 |
2.77 |
2.70 |
2.64 |
2.59 |
236.8 |
19.35 |
8.89 |
6.09 |
4.88 |
4.21 |
3.79 |
3.50 |
3.29 |
3.14 |
3.01 |
2.91 |
2.83 |
2.76 |
2.71 |
2.66 |
234.0 |
19.33 |
8.94 |
6.16 |
4.95 |
4.28 |
3.87 |
3.58 |
3.37 |
3.22 |
3.10 |
3.00 |
2.92 |
2.85 |
2.79 |
2.74 |
230.2 |
19.30 |
9.01 |
6.26 |
5.05 |
4.39 |
3.97 |
3.69 |
3.48 |
3.33 |
3.20 |
3.11 |
3.03 |
2.96 |
2.90 |
2.85 |
224.6 |
19.25 |
9.12 |
6.39 |
5.19 |
4.53 |
4.12 |
3.84 |
3.63 |
3.48 |
3.36 |
3.26 |
3.18 |
3.11 |
3.06 |
3.01 |
215.7 |
19.16 |
9.28 |
6.59 |
5.41 |
4.76 |
4.35 |
4.07 |
3.86 |
3.71 |
3.59 |
3.49 |
3.41 |
3.34 |
3.29 |
3.24 |
199.5 |
19.00 |
9.55 |
6.94 |
5.79 |
5.14 |
4.74 |
4.46 |
4.26 |
4.10 |
3.98 |
3.89 |
3.81 |
3.74 |
3.68 |
3.63 |
161.5 |
18.51 |
10.13 |
7.71 |
6.61 |
5.99 |
5.59 |
5.32 |
5.12 |
4.97 |
4.84 |
4.75 |
4.67 |
4.60 |
4.54 |
4.49 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
Statistical Tables |
277 |
2.062.15 |
2.022.11 |
1.982.07 |
1.952.04 |
1.922.01 |
1.891.98 |
1.871.96 |
1.841.94 |
1.821.92 |
1.801.90 |
1.791.88 |
1.771.87 |
1.751.85 |
1.741.84 |
1.641.74 |
1.531.65 |
1.431.55 |
distributions-F |
vand |
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=4df,then |
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2.452.492.38 2.31 2.23 |
2.412.462.34 2.27 2.19 |
2.382.422.31 2.23 2.16 |
2.352.392.28 2.20 2.12 |
2.322.372.25 2.18 2.10 |
2.302.342.23 2.15 2.07 |
2.282.322.20 2.13 2.05 |
2.262.302.18 2.11 2.03 |
2.242.282.17 2.09 2.01 |
2.222.272.15 2.07 1.99 |
2.202.252.13 2.06 1.97 |
2.192.242.12 2.04 1.96 |
2.182.222.11 2.03 1.95 |
2.172.212.09 2.02 1.93 |
2.082.122.00 1.92 1.84 |
1.992.041.92 1.84 1.75 |
1.911.961.83 1.75 1.66 |
0.05probabilitybyrandomvaluesfrom |
2 |
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example,Fordenominator.ifFhasv |
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10 = |
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2.812.973.20 2.70 2.61 2.55 |
2.772.933.16 2.66 2.58 2.51 |
2.742.903.13 2.63 2.54 2.48 |
2.712.873.10 2.60 2.51 2.45 |
2.692.843.07 2.57 2.49 2.42 |
2.662.823.05 2.55 2.46 2.40 |
2.642.803.03 2.53 2.44 2.38 |
2.622.783.01 2.51 2.42 2.36 |
2.602.762.99 2.49 2.41 2.34 |
2.592.742.98 2.47 2.39 2.32 |
2.572.732.96 2.46 2.37 2.31 |
2.562.712.95 2.45 2.36 2.29 |
2.552.702.93 2.43 2.35 2.28 |
2.532.692.92 2.42 2.33 2.27 |
2.452.612.84 2.34 2.25 2.18 |
2.372.532.76 2.25 2.17 2.10 |
2.292.452.68 2.18 2.09 2.02 |
criticalthegivetablethevaluesthatareexceededwith |
1 |
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thein(df)freedomofdegreesnumeratorandv |
0.05.= |
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the in df |
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2 |
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4.45 3.59 |
4.41 3.56 |
4.38 3.52 |
4.35 3.49 |
4.33 3.47 |
4.30 3.44 |
4.28 3.42 |
4.26 3.40 |
4.24 3.39 |
4.23 3.37 |
4.21 3.35 |
4.20 3.34 |
4.18 3.33 |
4.17 3.32 |
4.09 3.23 |
4.00 3.15 |
3.92 3.07 |
Theentriesin |
withv Prob(F>5.96) |
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1 |
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17 |
18 |
19 |
20 |
21 |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
40 |
60 |
120 |
Note: |
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278 Statistics for Environmental Science and Management, Second Edition
Table A2.5
Critical Values for the Durbin-Watson Statistic
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p = 1 |
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p = 2 |
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p = 3 |
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p = 4 |
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p = 5 |
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n |
d1 |
d2 |
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d1 |
d2 |
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d1 |
d2 |
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d1 |
d2 |
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d1 |
d2 |
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15 |
0.95 |
1.22 |
0.83 |
1.41 |
0.71 |
1.61 |
0.59 |
1.84 |
0.48 |
2.09 |
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20 |
1.08 |
1.29 |
0.99 |
1.41 |
0.89 |
1.55 |
0.79 |
1.70 |
0.70 |
1.87 |
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25 |
1.18 |
1.34 |
1.10 |
1.43 |
1.02 |
1.54 |
0.94 |
1.65 |
0.86 |
1.77 |
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30 |
1.25 |
1.38 |
1.18 |
1.46 |
1.12 |
1.54 |
1.05 |
1.63 |
0.98 |
1.73 |
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35 |
1.31 |
1.42 |
1.25 |
1.48 |
1.19 |
1.55 |
1.13 |
1.63 |
1.07 |
1.70 |
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40 |
1.35 |
1.45 |
1.30 |
1.51 |
1.25 |
1.57 |
1.20 |
1.63 |
1.15 |
1.69 |
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45 |
1.39 |
1.48 |
1.34 |
1.53 |
1.30 |
1.58 |
1.25 |
1.63 |
1.21 |
1.69 |
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50 |
1.42 |
1.50 |
1.38 |
1.54 |
1.34 |
1.59 |
1.30 |
1.64 |
1.26 |
1.69 |
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60 |
1.47 |
1.54 |
1.44 |
1.57 |
1.40 |
1.61 |
1.37 |
1.65 |
1.33 |
1.69 |
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70 |
1.51 |
1.57 |
1.48 |
1.60 |
1.45 |
1.63 |
1.42 |
1.66 |
1.39 |
1.70 |
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80 |
1.54 |
1.59 |
1.52 |
1.62 |
1.49 |
1.65 |
1.47 |
1.67 |
1.44 |
1.70 |
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90 |
1.57 |
1.61 |
1.55 |
1.64 |
1.53 |
1.66 |
1.50 |
1.69 |
1.48 |
1.71 |
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100 |
1.59 |
1.63 |
1.57 |
1.65 |
1.55 |
1.67 |
1.53 |
1.70 |
1.51 |
1.72 |
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Note: This table gives bounds for critical values for the Durbin-Watson statistic, V, for a two-sided test (for positive or negative autocorrelation) at the 5% level (n = number of data points, p = number of X variables in the regression). If V is less than 2, then it is definitely significant if V < d1, may be significant if d1 < V < d2, and is not significant if V > d2. If V is greater than 2, then it is definitely significant if 4 − V < d1, may be significant if d1 < 4 − V < d2, and is not significant if 4 − V > d2. For example, if there are n = 30 observations and p = 2 X variables, then to be definitely significant, V must be less than 1.18, or 4 − V must be less than 1.18.
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