Inference on discrete data is based on the binomial/multinomial distribution. It uses 2 approximate methods (z-statistic
and the chi-square) used for large samples and one exact method (Fisher's Exact Method) used for small samples. Approximate
methods are accurate for large samples and are inaccurate for small samples. There is nothing to prevent exact methods from
being used for large samples.
The first steps in the analysis is to ascertain the normal distribution of the data, equality of variances of sample
proportions being compared, and adequacy of the sample size. The data is laid out in contingency tables and is inspected manually
before application of statistical tests. The z and chi square tests give approximately the same results because chi square
is a square of z.
The z (or c ) statistic is computed as the difference between compared proportions expressed in z-score units.
The z test is used to compare one proportion against a standard or to compare two proportions.
The Pearson chi square is computed based on the observed and expected frequencies of each cell in the contingency table
and is in essence a measure of the deviation from the ‘average’. It can be used to test 2 or more proportions.
Large contingency tables are better partitioned or collapsed before applying the chi square test.
2.0 STRATIFIED and MATCHED ANALYSIS OF PROPORTIONS
The Mantel-Haenszel chi-square is used to test 2 proportions in stratified data. The MacNemar chi square is used for
pair matched data.
3.0 EXACT ANALYSIS OF PROPORTIONS
Exact methods are used instead of the chisquare test for small samples less than 20.They can be used in 2 x 2, 2 x
k, and r x c contingency tables. They involve direct computation of the p-value using factorials and probability. The p-value
is computed as the probability of results more extreme than the observed data.
4.0 ANALYSIS OF RATES and HAZARDS
Methods are available for simple and stratified analysis for incidence rates
5.0 ANALYSIS OF RATIOS
Methods are available for simple and stratified analysis of risk ratios.