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(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' h N or N' h N or N' h
p=.05 p=.01 p=.05 p=.01 p=.05 p=.01
15 .72 .95 36 .47 .61 88 .30 .39
16 .70 .92 37 .46 .60 92 .29 .38
17 .68 .89 38 .45 .60 96 .29 .38
18 .66 .86 39 .45 .59 100 .28 .37
19 .64 .84 40 .44 .58 120 .26 .34
20 .62 .82 42 .43 .57 140 .24 .31
21 .61 .80 44 .42 .55 160 .22 .29
22 .60 .78 46 .41 .54 180 .21 .28
23 .58 .76 48 .41 .53 200 .20 .26
24 .57 .75 50 .40 .52 250 .18 .24
25 .56 .73 52 .39 .51 300 .17 .22
26 .55 .72 54 .38 .50 350 .15 .20
27 .54 .71 56 .38 .49 400 .14 .19
28 .53 .69 58 .37 .48 450 .14 .18
29 .52 .68 60 .36 .48 500 .13 .17
30 .51 .67 64 .35 .46 550 .12 .16
31 .50 .66 68 .34 .45 600 .12 .15
32 .49 .65 72 .33 .43 700 .11 .14
33 .49 .64 76 .32 .42 800 .10 .13
34 .48 .63 80 .31 .41 900 .10 .13
35 .47 .62 84 .31 .40 1000 .09 .12
Formulas used to find these h values:
For p=.05:  h =        For p=.01:  h =

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 simply 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 z 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 n1 is one sample and n2 is the other: N' = (2*n1*n2)/(n1+n2)

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.

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