STAT 203 Observational Studies and Experiments Dr. Bruce Dunham Department of Statistics UBC Lecture 20

Introduction There are various ways data can be obtained for a study. Broadly, we have observational studies and designed experiments. The latter have advantages in terms of reducing bias and the impact of confounding and lurking variables.

Collecting Data We must remember questions we posed earlier when considering the results of a study: What is the motivation for the study? What type of individuals/objects were investigated? What variables were measured, and how? Where and when?

Observational Studies A (subset of the) target population is observed without deliberate intervention. E.g., A German study compared 118 eye cancer patients to 475 patients who did not have cancer. All patients were questioned about their cell phone usage. The eye cancer patients used cell phones more often, on average. The subjects determined their use of cell phones, and hence their exposure to the related radiation.

Retrospective and Prospective Studies The previous example was a retrospective study: the researchers found the subjects first then found their cell-phone habits. Such studies use historical records that may be inaccurate. (Can you recall your cell-phone usage from last year?) In a prospective study, subjects are obtained in advance of collecting data on them.

Problems with Observational Studies Although prospective studies are usually better than retrospective ones, neither can conclusively prove causation. E.g., Is there a relationship between violent crime rate and gun laws? The "country effect" can never be removed here.

Designed Experiments The researcher assigns subjects to certain experimental conditions, usually called treatments. Assignment of subjects (if people, more generally experimental units) to treatment is at random. Outcomes are measured via a response variable.

Example A study on 200 mice split the mice into two groups of 100. One group were exposed to microwaves for two half-hour periods per day, the other group were not exposed. After 18 months, incidences of brain tumours were twice as high in the microwave- exposed group as in the group who were not exposed to microwaves. Mice were the subjects, and exposure/non-exposure to microwaves was the treatment. The group not exposed were the control group. The response variable was incidence of brain cancer.

Factors An explanatory variable in an experiment is called a factor. Factors have levels. A combination of factor levels applied to an experimental unit is called a treatment. E.g., an agricultural experiment involved measuring the yield obtained in each of three areas in three consecutive years. There are two factors here, each with three levels, and so nine treatments.

Four Principles of Design Control: Other than the treatments, conditions for subjects in each treatment group should be identical (or nearly so). Randomization: Allocation of subjects to treatments should be at random. Replication: Multiple responses under different treatments helps assess variability. Blocking: We may need to control for variables that are not of direct interest in the study.

Example A study wished to assess the effect of using clickers in an intro stats course. Two instructors, Prof X and Dr Y would teach with and without clickers. Two factors, each with two levels means four treatments. But only two sections could be taught each term. “Term” is a confounding variable. By blocking we can assign treatments across the two terms: term 1 Prof X no clickers, Dr. Y clickers, term 2 Prof X clickers, Dr. Y no clickers.

1. The study in Q1 is A.An observational study. B.A designed experiment. C.A sample survey.

2. For the experiment in Q1, the number of treatments is A.2 B.3 C.4 D.9 E.36

3. The study in Q2 is A.An observational study. B.A designed experiment. C.A sample survey.

Visit Review today’s activity. Read chapter 13 of text. Don’t forget midterm test next week! Before the next class :