Linearity Concept Of Significance &

Chi Square Test

SUBMITTED TO:

PROF. YASMIN SULTANA SUBMTTED BY:

DEPARTMENT – PHARMACEUTICS SANIYA TAKKAR

SCHOOL OF PHARMACEUTICAL EDUCATION

AND RESEARCH M.PHARM,1ST SEM, DEPARTMENT OF

PHARMACEUTICS

JAMIA HAMDARD

TABLE OF CONTENTS

HISTORY

BASIS OF STATISTICAL INFERENCE

HYPOTHESIS

ZONE OF ACCEPTANCE AND REJECTION

TYPE 1 AND TYPE 2 ERROR

POWER OF TEST

CONFIDENCE LEVEL

EFFECT OF SAMPLE SIZE ON TEST

TEST OF SIGNIFICANCE

PARAMETRIC VS. NON PARAMETRIC TESTS

CHI SQUARE TEST

History

THE TERM STATISTICAL

SIGNIFICANCE WAS COINED BY

RONALD FISHER

Chi Square Test

Two non-parametric hypothesis tests

using the chi-square statistic: the chi-

square test for goodness of fit and the

chi-square test for independence.

Relation of Chi square test to

parametric and non parametric tests

• THE TERM “NON-PARAMETRIC” REFERS TO THE FACT THAT

THE CHI-SQUARE TESTS DO NOT REQUIRE ASSUMPTIONS

ABOUT POPULATION PARAMETERS NOR DO THEY TEST

HYPOTHESES ABOUT POPULATION PARAMETERS.

• PREVIOUS EXAMPLES OF HYPOTHESIS TESTS, SUCH AS THE T

TESTS AND ANALYSIS OF VARIANCE, ARE PARAMETRIC

TESTS AND THEY DO INCLUDE ASSUMPTIONS ABOUT

PARAMETERS AND HYPOTHESES ABOUT PARAMETERS.

Relation of Chi square test to parametric

and non parametric tests (Contd)

• THE DIFFERENCE BETWEEN THE CHI-SQUARE

TESTS AND THE OTHER HYPOTHESIS TESTS WE

HAVE CONSIDERED (T AND ANOVA) IS THE

NATURE OF THE DATA.

• FOR CHI-SQUARE, THE DATA ARE

FREQUENCIES RATHER THAN NUMERICAL

SCORES.

The Chi-Square Test for Goodness-

of-Fit

• THE CHI-SQUARE TEST FOR GOODNESS-OF-FIT USES

FREQUENCY DATA FROM A SAMPLE TO TEST HYPOTHESES

ABOUT THE SHAPE OR PROPORTIONS OF A POPULATION.

• EACH INDIVIDUAL IN THE SAMPLE IS CLASSIFIED INTO ONE

CATEGORY ON THE SCALE OF MEASUREMENT.

• THE DATA, CALLED OBSERVED FREQUENCIES, SIMPLY

COUNT HOW MANY INDIVIDUALS FROM THE SAMPLE ARE

IN EACH CATEGORY.

The Chi-Square Test for Goodness-of-Fit

(contd)

• THE NULL HYPOTHESIS SPECIFIES THE PROPORTION

OF THE POPULATION THAT SHOULD BE IN EACH

CATEGORY.

• THE PROPORTIONS FROM THE NULL HYPOTHESIS

ARE USED TO COMPUTE EXPECTED FREQUENCIES

THAT DESCRIBE HOW THE SAMPLE WOULD

APPEAR IF IT WERE IN PERFECT AGREEMENT WITH

THE NULL HYPOTHESIS.

The Chi-Square Test for Independence

The second chi-square test, the chi-square test for

independence, can be used and interpreted in two

different ways:

1. Testing hypotheses about the relationship

between two variables in a population, or

2. Testing hypotheses about differences between

proportions for two or more populations.

The Chi-Square Test for Independence

(Cont)

Although the two versions of the test for

independence appear to be different, they are

equivalent and they are interchangeable.

The first version of the test emphasizes the

relationship between chi-square and a correlation,

because both procedures examine the relationship

between two variables.

The Chi-Square Test for Independence

(Cont)

The second version of the test emphasizes

the relationship between chi-square and an

independent-measures t test (or ANOVA)

because both tests use data from two (or

more) samples to test hypotheses about the

difference between two (or more) populations.

The Chi-Square Test for Independence

(Cont)

For the goodness of fit test, the expected frequency for each category is

obtained by

expected frequency = fe = pn

(p is the proportion from the null hypothesis and n is the size of the sample)

For the test for independence, the expected frequency for each cell in the

matrix is obtained by

(row total)(column total)

expected frequency = fe = ─────────────────

n

The Chi-Square Test for Independence

(Cont)

A chi-square statistic is computed to measure the amount of

discrepancy between the ideal sample (expected frequencies

from H0) and the actual sample data (the observed

frequencies = fo).

A large discrepancy results in a large value for chi-square

and indicates that the data do not fit the null hypothesis and

the hypothesis should be rejected.

The Chi-Square Test for Independence

(Cont)

The calculation of chi-square is the same for all chi-square tests:

(fo – fe)

2

chi-square = χ2 = Σ ─────

fe

The fact that chi-square tests do not require scores from an interval or

ratio scale makes these tests a valuable alternative to the t tests, ANOVA,

or correlation, because they can be used with data measured on a

nominal or an ordinal scale.

Measuring Effect Size for the Chi-

Square Test for Independence

When both variables in the chi-square test for

independence consist of exactly two

categories (the data form a 2×2 matrix), it is

possible to re-code the categories as 0 and 1

for each variable and then compute a

correlation known as a phi-coefficient that

measures the strength of the relationship.