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Psychology 340 Spring 2010

Statistics for the Social Sciences. Chi-Squared Test of Independence. Psychology 340 Spring 2010. Young (under 30). Old (over 30). Chi-Squared Test for Independence. A manufacturer of watches takes a sample of 200 people. Each person is

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Psychology 340 Spring 2010

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  1. Statistics for the Social Sciences Chi-Squared Test of Independence Psychology 340 Spring 2010

  2. Young (under 30) Old (over 30) Chi-Squared Test for Independence 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?

  3. Chi-Squared Test for Independence A manufacturer of watches takes a sample of 200 people. Each person is classified by age and watch type preference (digital vs. analog). Young (under 30) Old (over 30) The question: is there a relationship between age and watch preference?

  4. Statistical analysis follows design

  5. Chi-Squared Test for Independence 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?

  6. Chi-Squared Test for Independence Chi-Squared Test for Independence 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? Step 1: State the hypotheses • H0: Preference is independent of age (“no relationship”) • HA: Preference is related to age (“there is a relationship”) Observed scores

  7. The critical chi-squared value is 5.99 Chi-Squared Test for Independence Step 2: Compute your degrees of freedom & get critical value df = (#Columns - 1) * (#Rows - 1) = (3-1) * (2-1) = 2 • Go to Chi-square statistic table and find the critical value • For this example, with df = 2, and α = 0.05

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

  9. Spot check: make sure the row totals and column totals add up to the same thing Chi-Squared Test for Independence Step 3: Collect the data.Obtain row and column totals (sometimes called the marginals) and calculate the expected frequencies Observed scores

  10. Expected scores 70 56 14 30 24 6 Digital Analog Undecided Under 30 Over 30 Chi-Squared Test for Independence Step 3: Collect the data.Obtain row and column totals (sometimes called the marginals) and calculate the expected frequencies Observed scores

  11. Expected scores 70 56 14 30 24 6 Digital Analog Undecided Under 30 Over 30 Chi-Squared Test for Independence Step 3: Collect the data.Obtain row and column totals (sometimes called the marginals) and calculate the expected frequencies Observed scores “expected frequencies” - if the null hypothesis is correct, then these are the frequencies that you would expect

  12. Chi-Squared Test for Independence Step 4: compute the χ2 • Find the residuals (fo - fe) for each cell

  13. Chi-Squared Test for Independence Step 4: compute the χ2 • Find the residuals (fo - fe) for each cell

  14. Chi-Squared Test for Independence Step 4: compute the χ2 • Square these differences • Find the residuals (fo - fe) for each cell

  15. Chi-Squared Test for Independence Step 4: compute the χ2 • Square these differences • Find the residuals (fo - fe) for each cell • Divide the squared differences by fe

  16. Chi-Squared Test for Independence Step 4: compute the χ2 • Square these differences • Find the residuals (fo - fe) for each cell • Divide the squared differences by fe • Sum the results

  17. Chi-Squared, the final step 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? Step 5: 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

  18. In SPSS • Each person gets a row • Each person has data about the variables • age & watch preference

  19. In SPSS • Analyze => Descriptives => Crosstabs • Select the two variables (usually they are nominal or ordinal) you want to examine and click the arrow to move one into the “rows” and one into the “columns” box. • Click on “statistics” button, and check the “Chi-square” box. • Click “continue.” • Click “OK.”

  20. SPSS Output Look at the “Chi-square tests” box. The top row of this box gives results for “Pearson’s Chi-Square” • “Value” is the value of the χ2 statistic, • “df” is the degrees of freedom for the test • “Asymp. Sig. (2-sided)” is the probability (p-value) associated with the test. • The chi-squared distribution, like the F-distribution, is “squared” so 1-tailed test is not possible.

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