School

Ryerson University
Department

Quantitative Methods

Course Code

QMS 202

Professor

Jason Chin- Tiong Chan

QMS202-Business Statistics II Chapter12

Chapter 12 Chi-Square Tests

Outcomes:

1.Conduct a Chi-Square Test for the difference between two

proportions

2.Conduct a Chi-Square Test for the difference among more

than two proportions

3.Conduct a Chi-Square Test of Independence

Characteristics of the Chi-Square Distribution

1. It is denoted by the symbol

2

χ

2. It is positively skewed

3. It is always non-negative value

4. It has only one parameter, called the degrees of freedom. The

shape of a Chi-Square distribution curve is skewed to the right

for small df and becomes symmetric for large df. (There is a

family of Chi-Square distributions)

Winter2011 1

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QMS202-Business Statistics II Chapter12

Chi-Square Test

1.This test is available in which there is no assumption regarding

the shape of the population.

2.This test is for qualitative data. Examples include gender,

province of birth, or brand of peanut butter purchased.

Chi-Square Test for the difference between two proportions

(Independent Sample)

1. A two-way cross-classification table (contingency table) is

developed for comparing the count of categorical responses between

two independent groups.

2. The following contingency table has two rows and two columns

and is called a 2X2 table. The cells in the table indicate the frequency

for each row and column combination.

Column Variable (Group)

Row Variable 1 2 Totals

Items of interest X1 X2 X

Items not of interest n 1 - X 1 n 2 – X 2 n-X

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No

Yes

QMS202-Business Statistics II Chapter12

Total n1 n2 n

Where

1

X

= number of items of interest in group 1

2

X

= number of items of interest in group 2

11

Xn

−

= number of items that are not interest in group 1

22

Xn

−

= number of items that are not interest in group 2

X

=

21

XX

+

is the total number of items of interest

n - X =

)()(

2211

XnXn

−+−

, the total number of items that are

not

interest

1

n

= sample size in group 1

2

n

= sample size in group 2

21

nn

+

= total sample size

3.

2

χ

Test for the different between two proportions

( )

∑

−

=

cellsall e

e

f

ff

2

0

2

χ

where

o

f

= observed frequency in a particular cell of a contingency table

e

f

= expected frequency in a particular cell of a contingency table

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test of the equality of two proportions,

H0: 1 = 2

H1: 1 ≠ 2

≥

5

Advanced

Statistics

-test, using the test statistic

{always a right tail test}

Where

1

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