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Chi Squared Test of Independence. Fundamental Question. Are two events/variables independent ? (Categorical variables) So what is independence?. Coins. What would it be for two coin tosses to be independent? What would it be for two coin tosses to be dependent. Brief Probability Lesson.

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## Chi Squared Test of Independence

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**Fundamental Question**• Are two events/variables independent? (Categorical variables) • So what is independence?**Coins**• What would it be for two coin tosses to be independent? • What would it be for two coin tosses to be dependent**Brief Probability Lesson**• P(A) “The probability of (event) A” • P(Heads) probability of throwing heads • P(Tails) probability of throwing tails**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”**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)**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.**Independence**• Are gender and board preference related?**The Real Magic**• The Chi Squared Statistic**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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