Binomial Distributions
Normal Distribution
t-Distributions
F Distributions
Chi Square Distributions
Microsoft Excel
|
z |
Area |
|
-
|
.000 |
|
-3.00 |
.001 |
|
-2.33 |
.01 |
|
-2.00 |
.02 |
|
-1.64 |
.05 |
|
-1.28 |
.10 |
|
-1.00 |
.16 |
|
-.84 |
.20 |
|
-.52 |
.30 |
|
-.25 |
.40 |
|
.00 |
.50 |
|
.25 |
.60 |
|
.52 |
.70 |
|
.84 |
.80 |
|
1.00 |
.84 |
|
1.28 |
.90 |
|
1.64 |
.95 |
|
2.00 |
.98 |
|
2.33 |
.99 |
|
3.00 |
.999 |
|
+ |
1.00 |
Areas corresponding to selected z scores in normal distribution.
The critical values for t and z one-tailed tests at the .05 significance level, for different degrees of freedom, are shown in the table below.
|
|
t |
t2 |
|
1 |
6.31 |
39.87 |
|
2 |
2.92 |
8.53 |
|
3 |
2.35 |
5.54 |
|
4 |
2.13 |
4.54 |
|
5 |
2.02 |
4.06 |
|
6 |
1.94 |
3.78 |
|
7 |
1.90 |
3.59 |
|
8 |
1.86 |
3.46 |
|
9 |
1.83 |
3.36 |
|
10 |
1.81 |
3.28 |
|
15 |
1.75 |
3.07 |
|
20 |
1.72 |
2.97 |
|
30 |
1.70 |
2.88 |
|
40 |
1.68 |
2.84 |
|
60 |
1.67 |
2.79 |
|
120 |
1.66 |
2.75 |
|
|
1.64 |
2.71 |
Values of the t and t2 corresponding to the five percent area of the t-distribution for selected degrees of freedom (one-tailed test). The degrees of freedom equal to n - 2. The t2 equals F for 1 degree of freedom. For infinitely large degrees of freedom, t equals z.
Using the t distribution for estimation of probability associated with the strength of a relationship in lieu of the normal distribution increases the threshold of the significance criterion and thus makes results less likely to be significant when a small number of subjects is used for analysis. For groups of subjects larger than 60, the z-test and t-tests can be used interchangeably.
The F Distribution
|
|
1 |
2 |
3 |
|
|
1 |
39.87 |
49.5 |
53.6 |
63.3 |
|
2 |
8.53 |
9.00 |
9.16 |
9.49 |
|
3 |
5.54 |
5.46 |
5.39 |
5.13 |
|
4 |
4.54 |
4.32 |
4.19 |
3.76 |
|
5 |
4.06 |
3.78 |
3.62 |
3.11 |
|
6 |
3.78 |
3.46 |
3.29 |
2.72 |
|
7 |
3.59 |
3.26 |
3.07 |
2.47 |
|
8 |
3.46 |
3.11 |
2.92 |
2.29 |
|
9 |
3.36 |
3.01 |
2.81 |
2.16 |
|
10 |
3.28 |
2.92 |
2.73 |
2.06 |
|
15 |
3.07 |
2.70 |
2.49 |
1.76 |
|
20 |
2.97 |
2.59 |
2.38 |
1.61 |
|
30 |
2.88 |
2.49 |
2.28 |
1.49 |
|
40 |
2.84 |
2.44 |
2.23 |
1.38 |
|
60 |
2.79 |
2.39 |
2.18 |
1.29 |
|
120 |
2.75 |
2.35 |
2.13 |
1.19 |
|
|
2.71 |
2.30 |
2.08 |
1.00 |
Values of F for selected degrees of freedom at the five percent level of significance (one-tailed test). For one degree of freedom, F equals t2. F(1, ¥) equals z2. Critical values in the F distribution and their equivalence with the other distributions are summarized below.
|
|
|
|
1 |
2.71 |
|
3 |
6.25 |
|
5 |
9.24 |
|
10 |
15.99 |
|
20 |
28.41 |
|
30 |
40.26 |
|
40 |
51.81 |
|
50 |
63.17 |
|
100 |
118.5 |
|
|
|
For one degree of freedom, chi-square equals z-square. For infinite number of degrees of freedom, chi-square, divided by the degrees of freedom, equals F with both of its degrees of freedom equal to infinity.