Contingency Table Analysis
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What is the main question we are posing when using contingency tables?
Is there any relationship or contingency between the two bases of classification?
What do we do when there is no obvious predictor variable?
Assess the degree of association or correlation instead of contingency
What do we do when the predictor variable is known?
We can assess the relative frequencies, proportions or probabilities of data?
Draw a 2 x 2 contingency table
When would we say that two variables are independent of each other?
If the correlation between them is 0
How can two events be said to be independent?
- Probability of their joint occurrence is the product of the probability of their separate occurrences
- This is known as the multiplication rule
What does the multiplication rule provide?
The expected probabilities under the null hypothesis
What does the multiplication rule generate to test independence?
- The expected frequencies
- This test does not work for probabilities
For the example: (Original|Self), what does the vertical line mean?
- Original is conditional upon self
- This is an example of a conditional probability
How might one use chi square to test for contingency?
- Use marginal totals to form marginal proportions
- Under the null for independence use these proportions to calculate the expected proportions
- Multiply by the total number of cases to get the expected frequencies
- Subtract expected frequencies from observed frequencies in each cell to find the residuals
- Calculate the degrees of freedom
- Calculate the chi square value
How are degrees of freedom calculated for chi square?
- R: Number of rows
- C: Number of columns
How do we calculate the expected frequency for a given cell?
Multiply the marginal frequencies (totals) for the row and column of that cell and divide by the grand total (N)
What would you like to do?
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