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Two Way Tables Chi Square Test PowerPoint PPT Presentation


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Two Way Tables Chi Square Test. 2 categorical variables. Data collected in a table with counts. Can test whether there is association between the 2 variables.

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Two Way Tables Chi Square Test

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Two way tables chi square test

Two Way Tables

Chi Square Test


Two way tables chi square test

2 categorical variables


Two way tables chi square test

Data collected in a table with counts.


Two way tables chi square test

Can test whether there is association between the 2 variables.


Two way tables chi square test

Market researchers think that background music can influence the mood and purchasing behavior of customers. One study compared 3 treatments: no music, French accordion music, and Italian string music. Under each condition, the researchers recorded the number of bottles of French, Italian, and other wine purchased.


Two way tables chi square test

Market researchers think that background music can influence the mood and purchasing behavior of customers. One study compared 3 treatments: no music, French accordion music, and Italian string music. Under each condition, the researchers recorded the number of bottles of French, Italian, and other wine purchased.


Music and wine data in counts

Music and wine data in counts

243 bottles total


Marginal distribution

Marginal Distribution


What percent of wine bought was italian

What percent of wine bought was Italian?


What percent of wine bought was italian1

What percent of wine bought was Italian?


Two way tables chi square test

What percent of wine was purchased from a store with no music playing


Two way tables chi square test

What percent of wine was purchased from a store with no music playing


Two way tables chi square test

Marginal Distributions

Only ask about 1 variable

Use values in “margins”


What percent of all wine bought was italian with french music playing in the store

What percent of all wine bought was Italian with French music playing in the store?


What percent of all wine bought was italian with french music playing in the store1

What percent of all wine bought was Italian with French music playing in the store?


Joint distribution

Joint distribution

Ask about both variables

Use values inside table and total


What percent of all wine bought was italian with french music playing in the store2

What percent of all wine bought was Italian with French music playing in the store?


Two way tables chi square test

Of the Italian wine purchased, what percent was from a store playing French music?


What percent of the wine purchased from french music playing stores was french

What percent of the wine purchased from French music-playing stores was French?


What percent of the wine purchased from french music playing stores was french1

What percent of the wine purchased from French music-playing stores was French?


Conditional distribution

Conditional distribution

Asks about both variables

Given one variable

Use values inside table and margins


Two way tables chi square test

Hypothesis Testing


Two way tables chi square test

  • H0

Null Hypothesis

  • Ha

Alternative Hypothesis


Two way tables chi square test

  • H0

Half of the deck is black

  • Ha

Half of the deck is notblack


Two way tables chi square test

  • Possible Outcomes

    • Reject H0

    • Fail to reject H0

  • Never

    • Prove

    • Accept


Two way tables chi square test

Standard: α = 0.05


Chi square hypothesis tests

Chi-square hypothesis tests

H0: There is NO association between music and wine in the population.

Ha: There is an association between music and wine in the population.


Two way tables chi square test

Observed Data vs. Expected Data


Two way tables chi square test

Have: Observed Counts

Want: Expected Counts if Music and Wine were Independent


Expected counts

Expected counts


Expected counts1

Expected Counts


Expected counts2

Expected Counts


Expected counts vs observed counts

Expected Counts vs Observed Counts


Chi square test statistic

Chi-square test statistic


Partial chi square values

Partial Chi-Square values


Chi square value

Chi-Square Value

χ2 = 0.52 + 2.31 + 0.52 + 0.0084 + 7.70 + 6.44 + 0.39 + 0.00029 + 0.43

χ2 = 18.31


Chi square table

Chi-Square Table


Degrees of freedom

Degrees of Freedom

DF = (r-1)(c-1)

r = 3

c = 3

DF= (3-1)*(3-1)= 2x2 =4


Chi square table1

Chi-Square Table

Test statistic = 9.49


Two way tables chi square test

Test Statistic

If table value < χ2 then reject H0

If table value > χ2 then fail to reject H0


Chi square hypothesis tests1

Chi-square hypothesis tests

X2 = 18.31 > 9.49

Reject H0.

We have evidence there is an association between music and wine in the population.


Two way tables chi square test

Is table value < χ2

Yes

No

reject H0

Fail to reject H0

We have evidence Ha

We do not have evidence Ha


Two way tables chi square test

When is chi-square test appropriate?


Two way tables chi square test

Tables larger than 2x2:

  • the smallest expected count ≥ 1

  • <20% of cells have expected counts < 5.

    2x2 tables:

  • all 4 expected cell counts ≥ 5


Two way tables chi square test

Psychological and social factors can influence the survival of patients with serious diseases. One study examined the relationship between survival of patients with coronary heart disease and pet ownership. Each of 92 patients was classified as having a pet or not and by whether they survived for one year. The researchers suspect that having a pet might be connected to the patient status.


Pet ownership and heart disease data counts

Pet ownership and heart disease data (counts)


Assuming a patient is still alive what is the probability he owns a pet

Assuming a patient is still alive, what is the probability he owns a pet?


Assuming a patient is still alive what is the probability he owns a pet1

Assuming a patient is still alive, what is the probability he owns a pet?


Two way tables chi square test

What is the probability a patient is still alive and owns a pet? (J,M,C)


Two way tables chi square test

What is the probability a patient is still alive and owns a pet? (J,M,C)


Two way tables chi square test

What is the probability a patient owns a pet?

(J,M,C)


Two way tables chi square test

What is the probability a patient owns a pet?

(J,M,C)


Two way tables chi square test

Steps for ALL Chi-Square Tests

Write Hypothesis

Find Expected Counts (check if test is appropriate)

Find value by adding all partial chi-square values

Find DF

Find “test statistic” (table value use )

Write Conclusion


Chi square test for pet ownership and patient status

Chi-square test for pet ownership and patient status

H0: There is NO association between pet ownership

and patient status in the population.

Ha: There is an association between pet ownership and patient status in the population.


Expected counts3

Expected Counts


Partial chi square values1

Partial Chi-Square Values

χ2 = 0.786 + 0.579 + 4.408 + 3.211

χ2 = 8.984


Two way tables chi square test

df = (2-1)(2-1) = 1

Critical value from table for α = 0.05 is 3.84.

Since 8.984 > 3.84, we can reject H0and conclude that we have evidence that owning a pet and survival are not independent.


Two way tables chi square test

M&Ms and Two-way Tables


Full class m ms data in counts large sample size necessary for test

Full-class M&Ms data in counts(large sample size necessary for test)


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