Chi Square - Statistics - Lecture Slides, Slides of Statistics

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Chi Square

Use of CHI SQUARE

• Testing the equality of more than two proportion
• If we classify population into several categories

with respect to two attributes, Chi Square can be

used to determine whether the two attributes

are independent of each other (age and job

performance)

• Help us to know whether the difference they

observe among several samples proportions are

significant or only due to chance

Contingency Table

• Suppose that in four region, the National

Health Care Company samples its hospital

employees attitude towards job performance

reviews. Respondents are given a choice

between the present method (2 reviews a

year) and a proposed method (quarterly

reviews).

• Table which illustrates these responses is

called contingency table.

Contingency Table

NW SE Central W Coast Total

No. who prefer present method

68 75 57 79 279

Number who prefer new method

32 45 33 31 141

Total 100 120 90 110 420

Test Statistic

All Cells e

e

f

f f

2 (^20)

f 0 = Observed Frequency in a cell

f e = Theoretical or Expected Frequency

Decision Rule

χ^2

χ^2 U

Decision Rule: If χ^2 > χ^2 U, reject H 0 , otherwise, do not reject H 0

The χ^2 test statistic approximately follows a chi-square distribution with one degree of freedom

0

Do notreject H 0 Reject H 0

χ2 Goodness-of-Fit Test

The χ^2 goodness-of-fit test compares

expected (theoretical) frequencies

of categories from a population distribution

to the observed (actual) frequencies

from a distribution to determine whether

there is a difference between what was

expected and what was observed.

Example

• The Gordon Company requires that college

seniors who are seeking position with it be

interviewed by three executives. This enables

the company to obtain a consensus evaluation

of each candidate. Each executive gives the

candidate either a positive or negative rating.

Table contains the result of the last 100

candidates.

Hypothesis

H0: A binomial distribution with p=0.40 is a

good description of the interview process

H1: A binomial distribution with p=0.40 is not a

good description of the interview process

Example:

• Use chi square goodness of fit test to

determine if the following observed data are

normally distributed. Let alfa=0.05. What are

your estimated mean and standard deviation?

Category Observed 10- under 20 6 20 under 30 14 30 under 40 29 40 under 50 38 50 under 60 25 60 under 70 10 70 under 80 7