Statistics: Principles and Methods, 7th Edition

13

Analysis of Categorical Data

1 Formulating Testing Problems Concerning Categorical Data

2 Pearson's χ² Test for Goodness of Fit

3 Contingency Table with One Margin Fixed (Test of Homogeneity)

4 Contingency Table with Neither Margin Fixed (Test of Independence)

Are Firm Mattresses Really Best?

Although it is commonly believed that firm mattresses can help persons with low-back pain, experimental evidence is lacking. Medical researchers conducted a carefully designed experiment.¹ Of the patients admitted to the study, 158 were randomly selected to sleep on a new firm mattress and the others were given new medium-firm mattresses. The patients were not told about the firmness of their new mattresses although most perceived the correct firmness. The persons who installed the new beds and the research assistants who collected the data from patients were also kept unaware of the firmness of the mattresses.

This design includes meritable features: (1) the random assignment of treatments (mattress firmness) and (2) the double blind feature where patient and researcher are not told which treatment has been assigned.

The patients were asked to report whether or not they had low-back pain upon arising during the 90-day follow-up period.

The proportion with no low-back pain upon arising ...