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Crosstabs and Chi Squares

Crosstabs and Chi Squares. Computer Applications in Psychology. When do we use these methods?. When we have categorical variables Do the percentages match up with how we thought they would? Are two (or more) categorical variables independent? Can do it with continuous variables

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Crosstabs and Chi Squares

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  1. Crosstabs and Chi Squares Computer Applications inPsychology

  2. When do we use these methods? • When we have categorical variables • Do the percentages match up with how we thought they would? • Are two (or more) categorical variables independent? • Can do it with continuous variables • If you convert them into categories • Typically don’t want to do this because you lose a lot of information, and these tests are not as “powerful” as parametric tests

  3. Example A manufacturer of watches takes a sample of 200 people. Each person is classified by age and watch type preference (digital vs. analog). The question: is there a relationship between age and watch preference?

  4. CROSSTAB

  5. CROSSTAB

  6. Chi-Squared Test for Independence • Step 1: State the hypotheses and select an alpha level • H0: Preference is independent of age • H1: Preference is related to age • We’ll set a = 0.05

  7. Chi-Squared Test for Independence • Step 2: • Compute your degrees of freedom df = (#Columns - 1) * (#Rows - 1) • Go to Chi-square statistic table and find the critical value • For this example, with df = 2, and a = 0.05 the critical chi-squared value is 5.99

  8. Chi-Squared Test for Independence • Step 3: Obtain row and column totals (sometimes called the marginals) and calculate the expected frequencies

  9. Computing Expected Frequencies

  10. For people under 30 For people over 30 Computing Expected Frequencies For digital For analog For undecided

  11. Expected Frequencies

  12. Computing the Chi-square 2 • Find the residuals (fo - fe) for each cell • Square these differences • Divide the squared differences by fe • Sum the results

  13. Computing the Chi-Square

  14. Computing the Chi-Square And finally

  15. Chi-Squared, the final step • Step 4: Compare this computed statistic (38.09) against the critical value (5.99) and make a decision about your hypotheses • here we reject the H0 and conclude that there is a relationship between age and watch preference

  16. SPSS • Okay, now let’s see how to do this in SPSS

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