Analysis of Frequency Data

Data in which all variables are categorical

The assumptions about normality and homogeneity of variance no longer apply

• 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?

Using the binomial distribution

• Specify a model and the associated null 
• Derive expected values on the basis of the model
• Calculate the residuals
• Evaluate these residuals

A random variable with an associated probability distribution (like F etc)

Chi square cannot be used

The sum of (the observed frequency - the expected frequency) squared over the expected frequency

Only one, degrees of freedom

• There are k-1 degrees of freedom 
• K: number of categories

• Raw frequencies 
• Do not use proportions or percentages

The expected values of X²

It is simply the square root of 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