Transcript

Chi Square & Related Procedure

Why do we need Chi Square Procedures?

Limitation of Binomial Test

Qualitative Association

Binomial Test is for Binomial variables. If there are

multinomial variables then

1. Identical Trial2. There are k different outcomes 3. Probability of outcomes do not change from

trail to trial4. Independent trials

Measure of Correlation does not work in case of qualitative variables

Multinomial Distribution

Multinomial Distribution is

required

What is Chi Square Distribution?

Distribution Z2 = χ2(1)

Distribution ΣZ2 = Z12 + Z2

2 + Z32 + … + Zk

2 = χ2(k)

Properties

Takes only positive Value

Skewed, but becomes normal with increasing n

Mean = k, Variance = 2k

Shape of Chi Square Distribution

Uses of Chi Square & Assumptions

Goodness of Fit Test

To check whether the given data follows a given distribution or not

Test of Association

To check whether the two variables are associated or not

Assumptions

Qualitative DataData Type

E > = 1Expected

FrequencyAt most 20% Es can be less than 5

Chi Square = Σ {(O – E)2 /E}

Goodness of Fit test

Hypothesis The data follows the said distribution

Test

Chi Square Calculated > Chi Square Tabulated (df)Reject H0

The distribution of market share is as it was last year

Chi Square Calculated = Σ {(O – E)2 /E}

Significance level 1%, or 5%

E = np

Always Check the Assumptions

If Assumptions do not meet then what

P < α

Goodness of Fit test Using SPSS

How the Data Looks

IssueWhether the market share of three firms has changed or not.

Last year market share distribution was as follows (A = 25%, B = 40%, C =35%)

Sample Size = 52

Goodness of Fit test Using SPSS

Press

Goodness of Fit test Using SPSS

Brand  Observed N Expected N ResidualA 12 13.0 -1.0B 24 20.8 3.2C 16 18.2 -2.2

Total 52   

Test Statistics  BrandChi-Square .835a

df 2Asymp. Sig. .659a. 0 cells (0.0%) have expected frequencies less than 5. The minimum expected cell frequency is 13.0.

Goodness of Fit test Using SPSS

Test of Association

Hypothesis Variables are associated or dependent

Test

Chi Square Calculated > Chi Square Tabulated (df)Reject H0

Result is associated with Gender

Chi Square Calculated = Σ {(O – E)2 /E}

Significance level 1%, or 5%

E = CR/T

Always Check the Assumptions

If Assumptions do not meet then what

P < α

Test of Association Using SPSS

How the Data Looks

Issue Result is associated with Gender

Sample Size = 40

Test of Association

Test of Association

Test of Association

Test of Association

Press

 Result

TotalPass FailGender Male 12 8 20

Female 14 6 20

Total 26 14 40

Test of Association

Chi-Square Tests

  Value dfAsymp. Sig.

(2-sided)Exact Sig. (2-

sided)Exact Sig. (1-

sided)Pearson Chi-Square .440a 1 .507   a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 7.00.b. Computed only for a 2x2 table

Fisher Exact Test

Fisher Probability

If Assumptions do not meet then what

It is the substitute of Chi Square of Association when Sample size is small

McNamer Test for Dependent Association

McNamer Those who were arrested stealing will be rearrested stealing

Test of Association

changes in related or paired binomial attributes, whether changes in one direction is significantly greater than that in

the opposite direction.

Working

Compares the ratio of change with the total who changed.

Opinion AfterFavor Not Favor Total

Opion Before

Favor a b a+bNot Favor c d c+dTotal a+c b+d a+b+c+d

Opinion AfterFavor Not Favor Total

Opion Before

Favor a b a+bNot Favor c d c+dTotal a+c b+d a+b+c+d

McNamer Test Using SPSS

Issue Is there any association in the opinion before and after the speech given be a political leader?

How the Data Looks

Sample Size = 20

Opinion_bf & Opinion_after

Opinion_bfOpinion_after

Favorable UnfavorableFavorable 7 4Unfavorable 5 4

Test Statisticsa

 Opinion_bf & Opinion_after

N 20Exact Sig. (2-tailed) 1.000b

a. McNemar Testb. Binomial distribution used.

Hypothesis Testing of Categorical Data

Single Variable Two Variables

One Population

Two Population

Binary Values

Multiple Values

Goodness of Fit Test

Independent ValuesPaired Values

Chi Square Test of AssociationFisher

McNamer Test

Z Test of Proportion Binomial Test

Large Sample Normal Dist Small Sample

Chi Square Assumptions Met

YesNo

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