PSYC30013 Lecture Notes - Lecture 4: Test Statistic, Contingency Table, Statistic
Lecture 4
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- Two types of frequencies we can observe in four cells: data [observed frequencies],
and values that would have been observed if there was no association between row
variable and column variable making it up
- Expected frequency of a cell = (cell row frequency x cell column frequency) / total
sample size
- The expected marginal frequencies always equal the observed marginal frequencies
in both the rows and the columns
- The total sum of all expected cell frequencies always equals the total sum of all
observed cell frequencies (which each equal the total n).
- So. . .
- → Greater discrepancy between the observed and the expected cell frequencies
indicates a greater degree of dependency.
- → Greater dependency reflects a stronger association between the two categorical
variables.
- → Stronger association correspond to a larger observed χ 2 test statistic value
- . . . . all other things being equal.
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Document Summary
Two types of frequencies we can observe in four cells: data [observed frequencies], and values that would have been observed if there was no association between row variable and column variable making it up. Expected frequency of a cell = (cell row frequency x cell column frequency) / total sample size. The expected marginal frequencies always equal the observed marginal frequencies in both the rows and the columns. The total sum of all expected cell frequencies always equals the total sum of all observed cell frequencies (which each equal the total n). Greater discrepancy between the observed and the expected cell frequencies indicates a greater degree of dependency. Greater dependency reflects a stronger association between the two categorical variables. Stronger association correspond to a larger observed 2 test statistic value all other things being equal. Margins and sample sizes are the same expected frequencies are the same for each table.