Hypothesis Testing & Contingency Tables

FOLLOWING TOPIC PASTED FROM YAHOO GROUPS

ORIGINATOR: Vicky R

DATE: Sat Nov 22, 2008

Hi All

Can anyone explain me the following :

1) What are parametric & nonparametric tests used in hypothesis testing. Brief about parametric & nonparametric tests ?

2) Please explain hypothesis test for proportion - 1 & proportion - 2. What is proportion - 1 & proportion - 2 ?

3) Please explain contingency Table. An example how the table is used for testing the assumptions ?

Can anyone explain this to me ?

Regards

Vijay

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FOLLOWING RESPONSE WAS PASTED TO YAHOO GROUPS

Vicky,

Let me take a stab at your first question:

a) In hypothesis testing, let's say we are comparing the means of two samples A and B with

Ho : Mean (A) = Mean (B.)

Ha: Mean (A) > Mean (B.)

If we know that data A and B are normally distributed, we would usually use the 2-Sample t Test. This is called a parametric test because we are relying on the assumption that A and B are normal and hence they have some parameters (mean & standard deviation) that are used to describe the underlying distribution.

For non-parametric tests, we DO NOT assume any specific shape for the underlying distribution for A and B. If we know that A and/or B is not normal, we can use other tests to compare the samples. An example of a test that does not use any specific distribution is the Mann-Whitney test. We may use other methods to compare these samples such as the sum of the ranks of the ordered pairs.

Of course, even though we can use non-parametric tests for all applications, we would prefer to use the parametric cousins if we can because they are more powerful, in the sense that they can detect

differences with fewer samples. However, the parametric tests are also restrictive in the sense that we need to make sure the underlying distribution assumptions are met otherwise we will be drawing the wrong conclusions.

Hope this helps.

SJ.

FYI: We were not covering non-parametric tests in the past Black Belt programs due to lack of time but this is now included in the new 6-day program version.