Page 279 - DMGT404 RESEARCH_METHODOLOGY

Unit 12: Hypothesis Testing

12.6 Non-parametric Test Notes

Non-parametric tests are used to test the hypothesis with nominal and ordinal data.
1. We do not make assumptions about the shape of population distribution.

2. The hypothesis of non-parametric test is concerned with something other than the value
of a population parameter.
3. Easy to compute. There are certain situations particularly in marketing research, where
the assumptions of parametric tests are not valid. Example: In a parametric test, we assume
that data collected follows a normal distribution. In such cases, non-parametric tests are
used. Example of non-parametric tests are Binomial test, Mann-Whitney U test, Sign test,
etc. A binomial test is used when the population has only two classes such as male, female;
buyers, non-buyers, success, failure etc. All observations made about the population must
fall into one of the two tests. The binomial test is used when the sample size is small.

Did u know? Non-parametric tests are distribution-free tests.

Advantages

1. They are quick and easy to use.
2. When data are not very accurate, these tests produce fairly good results.

Disadvantage

Non-parametric test involves the greater risk of accepting a false hypothesis and thus committing
a Type 2 error.

12.6.1 One Sample Tests

The following are the main examples of one sample non-parametric tests:

Cox and Stuart Test

This test is used to examine the presence of trends. A set of numbers is said to show upward trend
if the latter numbers in the sequence are greater than the former numbers. And similarly, one
can define a downward trend. How to examine whether a trend is noticeable in a sequence?

Example: Suppose a marketer wants to examine whether its sales are showing a trend or
just fluctuating randomly. Suppose the company has gathered the monthly sales figures during
the past one year month-wise:

Month 1 2 3 4 5 6 7 8 9 10 11 12
Sales 200 250 280 300 320 278 349 268 240 318 220 380

From the given data, analyse the sales trend.

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