(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 Z-score 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.

Go back to the Statistics page.