11/18/2009

Questions on chi square goodness-of-fit statistic

Relations in Categorical Data

The relationship between two categorical variables is described by a two-way table of counts or percents.
Consider survival data at two hospitals after surgery

	Hospital A	Hospital B
Died	63	16
Survived (6+ weeks after surgery)	2037	784

The marginal distribution of each variable in a two-way table is calculated by looking at the row sums or column sums.
The conditional distribution of one variable given a specific level of the other variable is obtained by considering table entries as proportions of their row or column sums.
Which hospital would you recommend? Why?

Now, consider the Condition of the Patient

GOOD CONDITION	Hospital A	Hospital B
Died	6	8
Survived (6+ weeks after surgery)	594	592

POOR CONDITION	Hospital A	Hospital B
Died	57	8
Survived (6+ weeks after surgery)	1443	192

There is no single graph or statistic which detects the relationship between categorical variables.

Bar graphs may be helpful.

Formal Inference for two-way tables

Examples

Class Exercises

Quiz #3 will be on Friday. You may use one sheet (8.5" x 11") of notes during the quiz.