# SANDLERS A-TEST - Research Methodology

Joseph Sandler has developed an alternate approach based on a simplification of t-test. His approach is described as Sandler’s A-test that serves the same purpose as is accomplished by t-test relating to paired data. Researchers can as well use A-test when correlated samples are employed and hypothesised mean difference is taken as zero i.e., H0 D : m = 0 . Psychologists generally use this test in case of two groups that are matched with respect to some extraneous variable(s). While using A-test, we work out A-statistic that yields exactly the same results as Student’s t-test*. A-statistic is found as follows:

The number of degree of freedom (d.f) in A-test the same as with Student’s t-test i.e., d.f. = n – 1, n being equal to the number of pairs. The critical value of A, at a given level of significance for given d.f., can be obtained from the table of A-statistic (given in appendix at the end of the book). One has to compare the computed value of A with its corresponding table value for drawing inference concerning acceptance or rejection of null hypothesis. If the calculated value of A is equal to or less than the table value, in that case A-statistic is considered significant where upon we reject H0 and accept Ha. But if the calculated value of A is more than its table value, then A-statistic is taken as insignificant and accordingly we accept H0. This is so because the two test statistics viz., t and A are inversely related. We can write these two statistics in terms of one another in this way:

Computational work concerning A-statistic is relatively simple. As such the use of A-statistic results in considerable saving of time and labour specially when matched groups are to be compared with respect to a large number of variables. Accordingly researchers may replace Student’s t-test by Sandler’s A-test whenever correlated sets of scores are employed.
Sandler’s A-statistic can as well be used “in the one sample case as a direct substitute for the Student t-ratio.” This is so because Sandler’s A is an algebraically equivalent to the Student’s t. When we use A-test in one sample case, the following steps are involved:

1. Subtract the hypothesised mean of the population m H b g from each individual score (Xi) to obtain Di and then work out.
2. Square each Di and then obtain the sum of such squares.
3. Find A-statistic as under:
4. Read the table of A-statistic for (n – 1) degrees of freedom at a given level of significance (using one-tailed or two-tailed values depending upon Ha) to find the critical value of A.
5. Finally, draw the inference as under:
When calculated value of A is equal to or less than the table value, then reject H0 (or accept Ha) but when computed A is greater than its table value, then accept H0.