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Understanding Chi-Squared Test: Independence & Probability

Explore the Chi-Squared Test for Independence, Probability Notation, and the significance of related events in research. Learn how to determine independence using real-world examples and probability calculations.

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Understanding Chi-Squared Test: Independence & Probability

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Presentation Transcript

  1. Chi Squared Test of Independence

  2. Fundamental Question • Are two events/variables independent? (Categorical variables) • So what is independence?

  3. Coins • What would it be for two coin tosses to be independent? • What would it be for two coin tosses to be dependent

  4. Brief Probability Lesson • P(A) “The probability of (event) A” • P(Heads) probability of throwing heads • P(Tails) probability of throwing tails

  5. Some Probability Notation • P(A|B) “The probability of A given B” Ex. P(Heads-Toss 2|Heads Toss1) P(AUB) “Probability of A or B” P(AΠB) “Probability of A and B”

  6. If two events are independent • P(A|B)= P(A) Or • P(AΠB)=P(A)*P(B) • P(Heads-thow 1)=.5 • P(Heads-throw 2)=.5 • P(Heads throw one and two)=.5*.5=.25 • (Make table for example)

  7. Why does this all matter • Why would I care in research if two events are independent? • Actually- what we want to know is if things are not-independent. If they are related.

  8. Independence • Are gender and board preference related?

  9. The Real Magic • The Chi Squared Statistic

  10. Chi Squared For Anything! • Chi-squared tests how much something varies from some expectation. • Must write in the following way: df =(Rows-1)(Cols-1)

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