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Chi-Square Test of Independence

Chi-Square Test of Independence. Purpose: Test whether two nominal variables are related Design: Individuals categorized in two ways. Assumptions. Mutually exclusive groups Expected frequencies at least 5 per cell. Formula for Chi-Square. Example.

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Chi-Square Test of Independence

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  1. Chi-Square Test of Independence • Purpose: Test whether two nominal variables are related • Design: Individuals categorized in two ways

  2. Assumptions • Mutually exclusive groups • Expected frequencies at least 5 per cell

  3. Formula for Chi-Square

  4. Example Males and females were categorized on whether they were right or left-handed. Is there a significant relationship between handedness and gender?

  5. Observed Frequencies FEMALE MALE LEFT 10 10 RIGHT 25 20

  6. FEMALE MALE R LEFT 10 10 20 RIGHT 25 20 45 C 35 30 STEP 1: Find Row and Column totals.

  7. STEP 2: Find fe for each group.

  8. LEFT, FEMALE RIGHT, FEMALE LEFT, MALE RIGHT, MALE

  9. STEP 3: For each group, compute (fo-fe)2 and divide by fe.

  10. LEFT, FEMALE RIGHT, FEMALE LEFT, MALE RIGHT, MALE

  11. STEP 4: Add up the results across all groups to get the chi-square. 2 = .06+.02+.06+.03 = .17

  12. STEP 5: Look up 2crit in table, using df = (rows-1)(columns-1). df = (2-1)(2-1)=1 2crit = 3.84

  13. STEP 6: Compare your c2 to the critical value. 2 = .17 2crit = 3.84

  14. APA Format Sentence A chi-square test of independence showed no significant relationship between handedness and gender, 2 (1, N = 65) = 0.17, p > .05.

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