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 k1 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 X^{2}

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