NONPARAMETRIC TESTS

Nonparametric Tests

Basic Concepts
• Sampling Distribution
• Central Limit Theorem
• Parametric Tests
• Non Parametric Tests
• When to use Nonparametric Tests?

• Important Non Parametric Tests and their Parametric Alternatives
• Advantages and Disadvantages of
Nonparametric Tests.

Useful Tests
• Test of Normality.
• Chi Squared Tests
• One-Sample Runs Test
• Wilcoxon Signed-Rank Test
• Mann-Whitney Test

• Kruskal-Wallis Test
• Spearman Rank Correlation Test

Sampling Distributions
• A sampling distribution is a distribution of all of the possible values of a statistic for a given sample

population

size

selected

from

a

Central Limit Theorem the sampling
As the sample size

distribution n↑ becomes almost

gets large

normal regardless

enough…

of shape of population Parametric Tests
•

require the estimation of one or more unknown parameters •

assumptions are made about the normality of the underlying population.

•

require the use of interval- or ratio-scaled data.

•

Large sample sizes are often required to invoke the Central Limit Theorem.

Nonparametric Tests
•

Nonparametric or distribution-free tests often the only way to analyze nominal or ordinal data and draw statistical conclusions. usually focus on the sign or rank of the data rather than the exact numerical value. do not specify the shape of the parent population. can often be used in smaller samples.

When to Use Nonparametric Tests?
•

To use non-parametric methods, it must satisfy at

least

one

of

the

following

conditions:
•

The data is a nominal.

•

The data is ordinal data.

•

can be used with interval or ratio data when no assumption can be made about the population probability distribution.

Advantages and Disadvantages
(Non Parametric tests)
Advantages
1.

Disadvantages

Can often be used in
Require special tables for
1.
small