Two Sample Tests

In some  situation the researchers may be taking  statistical decisions based on two samples. Each  of the  two  samples may  represent a particular under consideration. For  example one  may be interested to study the effectiveness of teaching methods like  unstructured teaching and  structured teaching. Suppose college have changed their method of teaching from  unstructured  teaching to structured teaching recently. Then the researcher has to take a random sample of students of a particular programme from  different colleges and collect their performances before introducing the structured methods of teaching  and after introducing the structured method of teaching. The respective observation will  form  two  samples .

There are many  more examples which  are as listed below:

a.Number of defects found in the daily  lots  of items produced by a set of similar machines  before  and after  installing a costly  automatic inspection systems in them.

b. Monthly  sales revenues of a product in different regions before launching  an advertisement  campaign and after launching the advertisement campaign.

c.Number of daily transaction in a bank  before and after introducing computers.

d. Number of outpatients treated in a government hospital before and after providing modern infrastructure.

There  are various non parametric tests  but we will  discuss only a few  of the  better  known and more widely used ones.

a.The sign test

1. One samples  test

2.Two sample sign test ( sing test for  paired data)

3.A rank  sum test ( Mann Whitney u test)

4. The one  sample  runs  test

5.Rank  correlation ( described in chapter 10 )