Chi Squared Tests for Contingency Tables (Edexcel A-Level Further Mathematics): Flashcards

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Chi Squared Tests for Contingency Tables
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Statistically independent events definition

One's occurrence doesn't affect other's probability

Independence formula: P(A and B)=?P(A \text{ and } B) = ?

P(A)×P(B)P(A) \times P(B)

Chi-squared test for contingency tables tests what?

Whether two events are statistically independent

H0H_0 in chi-squared independence test

The two events are statistically independent

Minimum expected frequency requirement

All entries must be 5\geq 5

Action when expected frequencies <5< 5

Combine columns to eliminate small values

Contribution formula in χ2\chi^2 test

(OE)2E\frac{(O - E)^2}{E}

Degrees of freedom formula

(rows1)×(columns1)(rows - 1) \times (columns - 1)

When to use Yates' correction

When ν=1\nu = 1 (1 degree of freedom)

Yates' correction formula

(OE0.5)2E\frac{(|O - E| - 0.5)^2}{E}

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