Z TEST ANDLIMITATIONS OF TEST OF SIGNIFICANCE

Z Test

Fisher has also given a method of testing the significance of the correlation in small samples. In this method the co-efficient of correlation in the sample of r is transformed into Z. The value of Z is calculated by the formula

Z= ½ loge* 1+r

1-r

The standard error of Z is

SEZ = 1

n-3

Similarly the co-efficient of correlation in the universe or P can be transformed into . The value of is calculated in the same value of Z here the co-efficient of correlation of the universe is taken into account.

To test the significance of a co-efficient of correlation the difference between the Z and is calculated and the difference of relationship and then the standard error of Z is then found out. If the difference is more than thrice or twice the standard error is supposed to be significant.

Significance of the difference between two sample co- efficients of correlation

Z test can be used to test of significance of the difference of two sample co- efficients of correlation. The co- efficients of correlation are first transformed into Z by the formula and then the standard error of the difference of the two Z’s is calculated by the formula

Standard Error= Z1- Z2 = 1 + 1 n1-3 n2-3

If actual difference between the two Z’s is more than thrice or twice

the standard error of the difference it is said to be significant

otherwise not.

Limitations Of Test 0f Significance

There are issues with relying on significance testing for evaluating

Significance test should be used when generalising from the sample to population. Significance test should be used only in attempts to generalise the sample’s results to a population.

Significance tests conducted with low power can be misleading

Program evaluation studies with less than approximately 50 participants tend to lack sufficient statistical power. Significance tests conducted with high power can be misleading

For studies involving large sample sizes (e.g., > ~ 400), a different problem occurs with significance testing because even small effects are likely to become significant, although these effects may be trivial. In these situations, more attention should be paid to effect sizes than to statistical significance testing.

When examining effects using small sample size, significant testing can be misleading because its subject to type II errors. Contrary to population opinion, statistical significance is not a direct indicator of size of effect, but rather it is a function of sample size, effect size and p level.

When examining effects using large samples, significant test can be misleading because even small or trival effects are likely to produce statistically significant results. This can be dealt with by reporting and significance test results.