Chapter 5

STA 200 Summer I 2011

Explanatory and Response Variables

• Response Variable

• Explanatory Variable

• Example: An experiment might be designed to see how the explanatory variable exercise affects the response variable blood pressure.

More Terminology

• Subjects– the individuals studied in a experiment

• Treatment– any specific experimental condition applied to the

subjects

• Example: One group of subjects might be assigned a treatment of daily exercise, while another group might be assigned a treatment of no exercise.

Example• A researcher wants to measure the effect of sleep deprivation on

a person’s motor skills. The researcher takes a group of 1000 individuals and randomly divides them into four groups.

• The first group sleeps for 8 hours, the second group sleeps for 6 hours, the third group sleeps for 4 hours, and the fourth group sleeps for 2 hours.

• The next day, each individual is given a reaction time test.

• What are the explanatory and response variables?• What are the treatments?

Lurking Variables and Confounding

• Lurking Variable

• Confounding

Example• News story: “Heart patients who are happy are much more likely

to be alive 10 years down the road than unhappy heart patients.”

• “[Happiness] seems to be a factor. It has physical consequences and also attracts other people, making it easier for the patient to receive emotional support. Unhappy people, besides suffering from the biochemical effects of their sour moods, are also less likely to eat healthy, take their medicines, and exercise.”

• Eating healthy, taking medicines, and exercising are confounded with the explanatory variable, mood.

Placebo Effect

• Placebo:

• Placebo Effect:– occurs when subjects respond favorably to any

treatment, including a placebo

Example

• In a 2000 study by KHAN, the objective was to determine the effectiveness of an antidepressant in preventing suicide attempts.

• Some subjects were given the antidepressant, while others were given a placebo.

• The antidepressant group had a 40% reduction in suicide attempts.

• The placebo group had a 30% reduction in suicide attempts.

One-Track Experiment

• A one-track experiment is one where a single treatment is applied to all of the subjects.

• Example: Taking an aspirin a day is thought to reduce the risk of a heart attack. Each person in a sample is instructed to take an aspirin a day for two years. After two years, determine the proportion of people in the sample who suffered heart attacks.

Principles of Good Experimental Design

• Control the effects of lurking variables on the response by comparing two or more treatments. (For clinical trials, one treatment would be the placebo group, also known as the control group).

• Assign subjects to treatments randomly.

• Use enough subjects in each group to reduce chance variation in the results.

Logic of Experimental Design

• Randomizing produces groups that should be roughly similar.

• Comparative design (incl. placebo group) controls the effects of lurking variables, since lurking variables will affect all groups equally.

• Therefore, differences in the response variable must be due to different treatments.

• Note: An experiment set up in this manner is called a randomized comparative design.

Better Aspirin Example

• Each person in a sample of 400 is randomly assigned to one of two groups: either an aspirin group, or a placebo group.

• After two years, the proportion of heart attacks in each group is determined.

Differences in Responses

• Statistical Significance– the difference is large enough that it would rarely occur

by chance

• Practical Significance– the difference is large enough to be relevant to

individuals interested in treatment

• You can have statistical significance without practical significance.

Example

• Suppose there is an experiment comparing the effects of two drugs designed to reduce LDL cholesterol.

• If the sample size is very large, a small difference in the response variable (for example, a 1 point reduction in LDL cholesterol) may be statistically significant.

• However, such a small difference may not be practically significant. A 1 point difference in LDL cholesterol reduction probably won’t be enough to convince people to change prescriptions.