# NONPARAMETRIC TESTS

Topics: Non-parametric statistics, Spearman's rank correlation coefficient, Statistical tests Pages: 21 (1530 words) Published: May 27, 2014
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
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

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
the population probability distribution.

(Non Parametric tests)
1.

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

Generally more powerful
If
normality
can
be
than parametric tests
assumed, parametric tests
2.
2.
when normality cannot
are
generally
more
be assumed.
powerful.
Can be used for ordinal
3.
data.

Important Non Parametric Tests
and their
Parametric Alternatives

Test of Normality
• Use Box Plot
• Use Histogram

Chi – Squared Test of
Independence
• Contingency Tables

A contingency table is a cross-tabulation of n paired
crossobservations into categories.

Each cell shows the count of observations that fall
into the category defined by its row (r) and column

Occupation
Newspaper

Public Sector Private Sector
Self
Employee
Employee
Employed

Grand
Total

Hindustan Times

43

18

51

112

Indian Express

21

38

22

81

The Hindu

15

37

20

72

Times of India

29

27

33

89

Grand Total

108

120

126

354

In a test of independence for an r x c contingency table,
the hypotheses are
H0: Variable A is independent of variable B
H1: Variable A is not independent of variable B

Use the chi-square test for independence to test these
hypotheses.

This non-parametric test is based on frequencies.

Decision Rule

Calculate n = (r – 1)(c – 1)

Calculate expected frequency for each cell ejk = RjCk/n

For a given α, look up the right-tail critical value.

Calculate

Reject Ho if Calculated value is more than critical value.

One-Sample Runs Test
• Wald-Wolfowitz Runs Test

The one-sample runs test (Wald-Wolfowitz test) detects
oneWaldtest)
nonrandomness.
nonrandomness.

Ask – Is each observation in a sequence of binary events
independent of its predecessor?

A nonrandom pattern suggests that the observations are not
independent.
independent.

The hypotheses are
H0: Events follow a random pattern
H1: Events do not follow a...