An investigator wishes to determine how well cardiac output (in liters per minute) before aortic valve replacement for aortic stenosis estimates subsequent cardiac function. Cardiac function is assessed as class I through IV. The investigator measures the cardiac output on 100 randomly selected patients presenting for aortic valve surgery for aortic stenosis at a major cardiac surgery center.

Patients are classified into cardiac functional classes after surgery. This is done without knowledge of any patient's presurgical cardiac output. The investigator hopes to determine how strongly cardiac functional class after surgery is associated with cardiac output before surgery.

Let us use the flowchart of statistics to address two basic questions of analysis.

1. Estimation: What measurement should be used to summarize the data which have been found in this investigation?

2. Inference: How can we use the study data to investigate whether there is a real association between cardiac output before surgery and subsequent cardiac functional class among patients in the population from which the investigator's sample was selected?