Crosstabs and Chi Squares

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Crosstabs and Chi Squares

• Computer Applications in Psychology

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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 dont want to do this because you lose
  a lot of information, and these tests are not as
  powerful as parametric tests

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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?
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CROSSTAB
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CROSSTAB
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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
• Well set a 0.05

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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

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Chi-Squared Test for Independence

• Step 3 Obtain row and column totals (sometimes
  called the marginals) and calculate the expected
  frequencies

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Computing Expected Frequencies
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Computing Expected Frequencies

• For people under 30

• For people over 30

For digital
For analog
For undecided
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Expected Frequencies
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Computing the Chi-square
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• Find the residuals (fo - fe) for each cell
• Square these differences
• Divide the squared differences by fe
• Sum the results

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Computing the Chi-Square
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Computing the Chi-Square
And finally
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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

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SPSS

• Okay, now lets see how to do this in SPSS