(See the bottom of the page for an example of the use of this table.)
Critical h values for confidence levels of 5% and 1%
N or N'  critical h 
p=.05  p=.01 
15  .716  .941 
16  .693  .911 
17  .672  .884 
18  .653  .859 
19  .636  .836 
20  .620  .815 
21  .605  .795 
22  .591  .777 
23  .578  .760 
24  .566  .744 
25  .554  .729 
26  .544  .714 
27  .533  .701 
28  .524  .688 
29  .515  .676 
30  .506  .665 
31  .498  .654 
32  .490  .644 
33  .483  .634 
34  .475  .625 
35  .469  .616 

N or N'  critical h 
p=.05  p=.01 
36  .462  .607 
37  .456  .599 
38  .450  .591 
39  .444  .583 
40  .438  .576 
42  .428  .562 
44  .418  .549 
46  .409  .537 
48  .400  .526 
50  .392  .515 
52  .384  .505 
54  .377  .496 
56  .370  .487 
58  .364  .478 
60  .358  .470 
64  .346  .455 
68  .336  .442 
72  .327  .429 
76  .318  .418 
80  .310  .407 
84  .302  .397 

N or N'  critical h 
p=.05  p=.01 
88  .295  .388 
92  .289  .380 
96  .283  .372 
100  .277  .364 
120  .253  .333 
140  .234  .308 
160  .219  .288 
180  .207  .272 
200  .196  .258 
250  .175  .230 
300  .160  .210 
350  .148  .195 
400  .139  .182 
450  .131  .172 
500  .124  .163 
550  .118  .155 
600  .113  .149 
700  .105  .138 
800  .098  .129 
900  .092  .121 
1000  .088  .115 

Formulas used to find these h values:
For p=.05:
For p=.01:
To illustrate the use of this table, let us assume that we are comparing two samples each having 140 observations in them and an h difference of .32. Since the N in both samples is the same, we look down the column marked N or N' until we come to 140. We look to our right and see that an h of .23 or above is significant at the .05 level of confidence and an h of .31 is significant at the .01 level. Since the h in this hypothetical example is .32, the difference between the two samples is statistically significant at the .01 level of confidence, meaning there is less than one chance in a hundred that the difference we have found is not a real difference.
Since it is widely known that a Zscore of 1.96 is significant at the .05 level of confidence and one of 2.58 significant at the .01 level, some researchers might want to display the significance finding in terms of a Z score. There is an easy formula for finding Z from h: Z is h times the square root of n/2.
In the above example, the N for both samples was the same. In many cases, however, the samples will be of different sizes. Then N' must be determined with the following straightforward formula, where n_{1} is one sample and n_{2} is the other: N' = (2*n_{1}*n_{2})/(n_{1}+n_{2})
Once N' is determined, it also can be used in the formula to convert h to Z: Z is h times the square root of N'/2.
As can be seen by a casual inspection of the above table, it does not take a very large h for statistical significance when sample sizes are in the hundreds. Since, as noted, our sample sizes are usually large, the question of statistical significance is not a primary one for us. Perhaps this table makes it even more clear why we are concerned with effect sizes rather than statistical significance.
Go back to the Statistics page.
