SPSS: Expected frequencies, chi-squared test. In-depth example, Schemes and Mind Maps of Statistics

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SPSS: Expected frequencies, chi-squared test.

In-depth example: Age groups and radio choices.

Dealing with small frequencies.

Quick Example: Handedness and Careers

Last time we tested whether one nominal variable was independent of another.

We did this by looking at the cross tabs and seeing how far the observed frequencies were from the frequencies we would expect if the two variables were independent.

Get chi-squared is also heavy in math, so in the real world, SPSS and other software can handle most of it for us.

Most important things to know:

• How to get the expected frequency from a particular cell.
• Chi-squared is a measure of how far the observed frequencies are from the expected frequencies.
• Large chi-squared values mean large deviations from the expected frequencies.
• The df for chi-squared is (rows – 1) x (columns – 1)

SPSS: Expected frequencies

Start with a crosstab.

Analyze  Descriptive Stats  Crosstabs

The cells button brings up the menu of what you want the cells

to show. Uncheck observed and check expected.

Then click Continue, then OK. This will produce a crosstab of the expected values.

If father figure type and parenting style were independent, there would be 9.4 moderate style stepfathers in our sample on average.

Checking both observed and expected produces a table that has both the observed and expected values in the same table.

It allows cell-to-cell comparison but it’s more cluttered.

The null hypothesis of independence fits the moderates and stepfathers.

But live-in partners appear to be more permissive and less authoritarian than other types of father figure.

Bats: Observing frequencies you wouldn’t expect.

SPSS: Full crosstab analysis. Consider the following data on a sample of people’s ages and radio preference.

We want to know if a person’s radio preference depends on what generation they belong to.

We have the data from 72 people in total in three nominal categories of radio choice and three ordinal categories of age.

Should we do an odds ratio or a chi-squared?

Chi-squared. Because we have 3x3 table.

Odds Ratio only works for 2x2 tables.

SPSS: Chi-Squared is also in the crosstabs section.

Analyze  Descriptive Statistics  Crosstabs.

Click on the Statistics button.

Checking Chi-Squared produces the following table.

We want the Pearson Chi-Square. (yeah, Pearson is a big deal)

χ^2 = 10.

df = 4. We could have got this from

(rows – 1) x (cols. – 1) = 2 x 2 = 4.

We also know that the p-value = .036.

So if we were testing for independence at alpha =0.05, we would reject the null hypothesis of independence.

For interest: Asymp. Sig. stands for Asymptotic Significance. Asymptotic in statistics means “As n  infinity.”