Chapter 17, Problem 1P

l. Parametric tests (such as t or ANOVA) differ from nonparametric tests (such as chi-square) primarily in terms of the assumption they require and the data they use. Explain the differences.

To determine

The differences between parametric and non-parametric tests.

Answer to Problem 1P

Solution:

Non Parametric tests	Parametric tests
No information about the population is available.	Information about the population is completely known.
No assumptions are made regarding the population.	Specific assumptions are made regarding the population.
The null hypothesis is free from parameters.	The null hypothesis is made on parameters of population distribution.

Explanation of Solution

The basic difference between parametric and non-parametric tests are the assumptions associated with non-parametric tests. They are:

• The sample observations are independent.
• The variable under study is continuous.
• The probability density function is continuous.
• Lower order moments exist.
• The non-parametric tests do not require the population to have a normal distribution.

Conclusion:

These are the assumptions for non-parametric tests which are fewer and much weaker than those associated with parametric tests.

Justification:

This is why the non-parametric tests can be performed on data measured on any scale.