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Chi-square Test of Independence

Chi-square Test of Independence. Presentation 10.2. Another Significance Test for Proportions. But this time we want to test multiple variables . With this test we can determine if two variables are independent of not. This is sometimes called inference for two-way tables.

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Chi-square Test of Independence

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  1. Chi-square Test of Independence Presentation 10.2

  2. Another Significance Test for Proportions • But this time we want to test multiple variables. • With this test we can determine if two variables are independent of not. • This is sometimes called inference for two-way tables.

  3. Chi-square Test of Independence Formulas The null and alternate hypotheses are always the same with a Test of Independence. Null Hypothesis (assumes independent) Alternate Hypothesis (not independent) Test Statistic (that symbol is called “Chi-squared”) O is the observed count for each cell in the table and E is the expected count for each cell in the table. Instead of a normal or t distribution, we now have a chi-squared distribution

  4. The Titanic • Look at the data of the passengers, their ticket, and whether or not they survived.

  5. Conditions for the Test of Independence • None of the observed counts should be less than 1 • No more than 20% of the counts should be less than 5 • Same as for the Goodness of Fit test • These are simple checks to make sure that the sample size is sufficient.

  6. The Titanic • Check the conditions • Since all counts are much greater than 5, we are ok to conduct the test • Write Hypotheses (these are always the same!) • Null: Ho: Observed = Expected • That is, what we observed should be the same as what we expected given the variables are independent • Alternate: Ha: Observed ≠ Expected • That is, the observed data is just too different from what is expected to be attributed to random chance.

  7. The TitanicCalculations • Find the expected values (assume independence) Expected Observed To find an expected count, 849 out of 1317 total passengers were rescued (64.46%), so 849/1317 or 64.46% of the 326 first class passengers should have been rescued. This logic follows for each cell in the table.

  8. The TitanicCalculations • Then, do the sum of just like with the Goodness of Fit Test • Our degrees of freedom are: • Finally, use chi-square cdf: X2cdf(99.69,99999,2)

  9. The TitanicCalculations • Using the calculator • First go to the Matrix menu (2nd x-1) • Go to edit and press enter • Enter the number of row x column • Your matrix should fit the look of your table • Enter in the data • Make the calculator match the table • Then go to your stats tests and choose chi-test

  10. The TitanicCalculations • Using the calculator • Since you entered the data into matrix [A], you can just go right to: • Calculate • Draw • Leave the expected alone as the calculator will calculate those for you (see next slide)

  11. The TitanicCalculations • Using the calculator • Let’s go check out the expected table • Go back to matrix • Edit [B] to see the values • How cool is that!

  12. The TitanicCalculations • Conclusions • The p-value represents the chance of the data occurring given the variables are independent. • For the Titanic, this was a 0.00000000000000000002% chance • REJECT THE NULL! • There is a ton of evidence to suggest that there is an association between survival rate and the type of ticket.

  13. Chi-square Goodness of Fit Test This concludes this presentation.

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