4/17/2013

Questions on chi square goodness-of-fit statistic from simulation activity

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

Which hospital would you recommend for a patient in good condition? Why?

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

Which hospital would you recommend for a patient in poor condition? Why?

Simpson's paradox refers to the reversal in the direction of a comparison when data from several groups are combined to form a single group.

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

Model 1 - Comparing c populations with separate and independent samples
Model 2 - A single sample is classified according to two categorical variables

Examples

Exercise 12.16 on p. 597
Exercise 12.17 on p. 597

Class Exercises

12.14, 12.22, 12.26, 12.30

Please read Section 12.3 for class on Friday. We will have a problem session on Chapter 12 Class Exercises from the last two days. Please come to class prepared to present these problems to your peers.