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Class 11. Chi-Squared Test of Independence. EMBS Section 11.3. Chi-squared GOF test. One row (column) of Observed Counts One row (column) of Expected Counts determined based on H0 All categories are equally likely (Roulette Wheel, Soccer birth months)

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Class 11

Class 11

Chi-Squared Test of Independence

EMBS Section 11.3


Chi squared gof test
Chi-squared GOF test

  • One row (column) of Observed Counts

  • One row (column) of Expected Counts determined based on H0

    • All categories are equally likely (Roulette Wheel, Soccer birth months)

    • Categories have specified p’s (M&M colors)

    • #girls in 4 is binomial(n=4,p=.5) (Denmark Fams)

    • Expected Bin counts from NORMAL distribution (Lorex)

  • Calculated chi-squared, dof, chidist, pvalue, reject or not.


Supermarket survey
Supermarket Survey

  • A random sample of 160 employees of a national Supermarket chain were asked about a proposed wage freeze.

  • There were two categorical variables in the resulting 160-element data set.

    • JOB (Stacker, Sales, Admin)

    • RESPONSE (favorable, unfavorable, no comment)



To examine the relationship between 2 categorical variables start with a contingency table
To examine the relationship between 2 categorical variables, start with a contingency table

Response

Are RESPONSE and JOB independent?

Job


H0 response and job are independent
H0: Response and Job are independent start with a contingency table

Response

What are the expected counts given H0?

Job


H0 response and job are independent1
H0: Response and Job are independent start with a contingency table

Response

What are the expected counts given H0?

Job

(11.9)


Calculate the expected counts under h0
Calculate the Expected Counts under H0. start with a contingency table

Response

Expected Counts if independent.

Job


We know what to do now with our table of observed and expected counts
We know what to do now with our table of Observed and Expected Counts…

The calculated chi-squared statistic

The sum of the distances.


Calculate the table of distances
Calculate the table of distances.. Expected Counts…

Response

Job


Get the p value
Get the p-value Expected Counts…

Dof

=(#rows-1)(#cols-1)

=2*2

=4

Response

P-value

=Chidist(37.44,4)

=1.46E-07

Job


Chitest will do the last two steps
=CHITEST will do the last two steps Expected Counts…

  • =CHITEST(range containing the Os,

    range containing the Es)

  • Calculates the chisquared, compares it to the chidistusing the appropriate dof, and reports the p-value.

  • =CHITEST(for our data) = 1.46E-07

  • So…..You just have to calculate the Es.

CHITEST will also work for the GOF test!!


Excel demo if time

Excel Demo if time… Expected Counts…


Statistically significant
Statistically Significant? Expected Counts…

May 13, 1999

Web posted at: 11:38 a.m. EDT (1538 GMT)

(CNN) -- Young children who sleep with a light on may have a substantially higher risk of developing nearsightedness as they get older, says a new study in the journal Nature.

The collaborative study of 479 children by researchers at the University of

Pennsylvania Medical Center and The Children's Hospital of Philadelphia found 55 percent (of the 100) children who slept with a room light on before age 2 had myopia, or nearsightedness, between ages 2 and 16.

Of the (112) children who slept with a night-light before age 2, 34 percent were myopic, while just 10 percent of children who slept in darkness were nearsighted.


1 create the contingency table of observed counts
1. Create the Contingency Table of Observed Counts Expected Counts…

Earlier we would have asked P(Light│Myopic)

=55/120

Now we want to test

H0: Sleep Conditions and Subsequent Eyesight are independent

Statistically

Significant

=chidist(84.21,2) = 5.19E-19

H0: P(M) is equal for all three sleeping conditions.


Suppose we flip the contingency table
Suppose we Flip the contingency table? Expected Counts…

Calculated chi-squared = 84.21

Calculated chi-squared =

P-value = 5.19E-19

P-value =


Assignment 12
Assignment 12 Expected Counts…

  • Use the class data to test the independence of ATHLETE and HS STAT.

  • Use the Denmark Family data to test independence of “Gender Mix of first 3” and “Have 4?”


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