Crosstabs and Chi Squares Computer Applications in Psychology

When do we use these methods? When we have categorical variables 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 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

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?

CROSSTAB

CROSSTAB

Chi-Squared Test for Independence  Step 1: State the hypotheses and select an alpha level –H 0 : Preference is independent of age –H 1 : Preference is related to age –We’ll set  = 0.05

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  = 0.05 the critical chi-squared value is 5.99

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

Computing Expected Frequencies

For people under 30 For people under 30 For people over 30 For people over 30 For digital For analog For undecided

Expected Frequencies

Computing the Chi-square Find the residuals (f o - f e ) for each cell Find the residuals (f o - f e ) for each cell Square these differences Square these differences Divide the squared differences by f e Divide the squared differences by f e Sum the results Sum the results 2

Computing the Chi-Square

And finally

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 H 0 and conclude that there is a relationship between age and watch preference

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