NON-PARAMETRIC TEST - Test for Randomness

 

Procedure testing of hypothesis

1.      Setting up of hypothesis – Null hypothesis and Alternative hypothesis.

2.      Defining the level of significance (α)

3.      Computation of test statistic

 The test statistics is a statistic based on appropriate probability distribution. It is used to test                     whether the null hypothesis set up should be accepted or rejected.

Z – Distribution: Use z- distribution under normal curve for large sample (i.e., if the sample size n≥    30). The Z – statistic is defined as

4.      Critical region or critical value.

The rejection region or critical region is the region of the standard normal curve corresponding to a predetermined level of significance (α).

The value of the sample statistics defines the region of acceptance and rejection is called the critical value.

5.      Decision :

The last step is the decision about the null hypothesis is whether to accept it or reject it. In this regard, compare the computed value of Z with critical value or significant value or table value Z_tab at a given level of significance  and decide as under:

(i)                 If |Z _calculated| < |Z _tabulated|, then we accept the null hypothesis H₀ at 5% or 1% level of significance & conclude that there is no significant difference.

(ii)              If |Z _calculated| > |Z _tabulated|, then we reject the null hypothesis H₀ at 5% or 1% level of significance & conclude that there is a significant difference.