# NONPARAMETRIC TESTS

**Topics:**Non-parametric statistics, Spearman's rank correlation coefficient, Statistical tests

**Pages:**21 (1530 words)

**Published:**May 27, 2014

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 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

(c) heading.

heading.

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...

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