Analysis of Frequency Data
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What is frequency data?
Data in which all variables are categorical
How are tests for frequency data different than other tests?
The assumptions about normality and homogeneity of variance no longer apply
For a single basis of classification, which questions are we attempting to answer?
- Is the difference between observed and expected frequencies large enough to bring the null into question?
- Is the null true and the differences down to sampling error or is there a genuine difference?
For two outcomes, how could we gain the probability of a result occurring?
Using the binomial distribution
How do we use the chi square to test a hypothesis?
- Specify a model and the associated null
- Derive expected values on the basis of the model
- Calculate the residuals
- Evaluate these residuals
What is the chi square value?
A random variable with an associated probability distribution (like F etc)
What happens if more than one frequency count is used (such as in repeated measures)
Chi square cannot be used
What is the formula for chi square?
The sum of (the observed frequency - the expected frequency) squared over the expected frequency
What parameters does chi square possess?
Only one, degrees of freedom
What is the DF rule for one way chi squares?
- There are k-1 degrees of freedom
- K: number of categories
What must be used when conducting a chi square?
- Raw frequencies
- Do not use proportions or percentages
What are the degrees of freedom equal to in a chi square?
The expected values of X2
How is the formula for standardised residual values similar to chi square?
It is simply the square root of chi square
What value suggests major contribution in chi square?
- When a standardised residual is bigger than 2.0 in absolute value
- Every cell in question is said to be a major contributor to the chi square value
- Haberman said this
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