Kathleen Z. Rooney
Sampling Methods and Experimental Design
Whether in an AP course or in an introductory high school course in Statistics, production of data is an important component. Students need to understand what samples are and how samples can be used to make inferences about a population. Sampling methodologies are an important subject, each type should be understood along with along with their potential sources of bias. Random selection is a core principle in the creation of a statistically useful sample.
The importance of randomization extends to treatment assignments in experimental design. Random assignment avoids bias that can be a fatal flaw in drawing conclusions from a study or experiment. The correct design of an experiment in clinical practice requires a statistician. While scientists and medical doctors are often carrying out the experiment, without the correct underlining design, analysis is not meaningful. Therefore the topic of experimental design is essential to learning statistics and to understanding the process of how a drug gets to market.
Students will follow a topic outline similar to College Board's suggested syllabus
21
where students spend about two weeks looking at randomization, sampling and experiments. The following are three examples of lessons that incorporate pharmaceutical industry applications with the development of proficiency in analysis and design of experiments.
LESSON 1
The history and use of Sampling Methods
Resources
The First Measured Century (Book and Video)
http://www.pbs.org/fmc/lessons/lesson4.htm
22
Random Rectangles
23
Teachers can adapt the lesson plan from the one on the PBS website. In my class I will use the video segment and worksheet and then use random rectangles activity to draw samples. This is an excellent overview of the concepts of sampling. It introduces samples, populations and bias in sampling through a 20th century example of the failure of a biased sample to predict accurately.
OBJECTIVE
Students will identify samples and populations. Students will compare sampling methodologies and analyze sampling methods for bias.
ASSESSMENT/PRODUCT
Worksheet analysis of video segment. Dot Plots of random rectangles. Written analysis of sampling methods.
OPENER
Discussion: How do we decide what products to buy? What is safe and effective? What do statistics in the news tell us? Who do you trust?
PROCEDURE
Watch Gallup segment from "The First Measured Century."
Students will take notes and complete the accompanying worksheet. Class discussion on bias will follow. Give examples in sampling methodologies (SRS, cluster, stratified, systematic). Create a class list of potential for bias in sampling methodologies.
Using "Random rectangles" from "Activity Based Statistics."
Students will use their judgment to select five rectangles that best represent the scope of the rectangles on the page. Students average their rectangles and add their mean to the class dotplot on the board.
Students will use randomization to select five rectangles on the page.
Teacher demonstrate randint command on TI-84 (MTH>PRB #5 randint)
Using randint, students select 5 rectangles and find their mean and add to second class dotplot.
Class will verbally analyze, discuss, compare/contrast the two dot plots looking for center and spread.
LESSON 2
Elements of an experiment
OBJECTIVE
Students will correctly identify the elements of a well-designed experiment and know how to describe and diagram an experiment.
ASSESSMENT/PRODUCT
Students will read a prose description of an experiment and sketch the design.
OPENER
Discussion of confounding factors, causation, controlling treatments in a study. There are many examples to use. I use the example of gastric freezing from "Statistics through Applications"
24
This example couples two experiments, one with a faulty design and a reworking of the experiment with a significantly different outcome. The first design did not use a placebo-controlled group and so did not have a comparison group with which to measure placebo effect. It was difficult to determine if the positive reports of pain relief were due to placebo or actual relief. In the second trial 160 ulcer patients received a balloon treatment for pain relief; 82 received a freezing solution in the balloon, 78 received a body-temperature balloon. The first treatment group reported a 34% rate of improvement, the second showed a 38% rate of improvement. The placebo worked even better than the treatment.
There is lots to discuss here: placebo effect, placebo-control groups, placebos that are not "sugar pills". In terms of consumer awareness, we can discuss the potential benefits and dangers to the consumer, the role of the individual's right to choose treatments, informed consent of subjects, methods of blinding, and the medical profession's decision on how best to treat based on financial or ethical reasons.
PROCEDURE
Working in groups, students should read the study. Students should have index cards with the titles:
Experimental Question
Subjects
Response variable
Students should arrange the cards logically and write information from the study prose on the correct index card.
Using the Gastric Freezing example we can repeat this by adding the secondary study, which used a placebo-controlled group. We will add these index cards into the set.
Factors
Levels
Once the students have arranged and discussed the design, the class should work to draw these designs, with each student producing their own, which includes indications of randomizing, indications of factors and levels. Students should read a follow-up experiment and analyze it in a prose segment as an assessment.
LESSON 3
Bringing a drug to the market: Need, treatment, safety, efficacy
OBJECTIVE
Students will look at the history of clinical trials and look at a study involving a specific drug.
ASSESSMENT/PRODUCT
Students will research a current drug and describe the protocol for clinical trials. Students may also read and respond to excerpts from "The Treatment."
25
OPENER
Discussion: How do we treat disease? Where do treatments come from? How do we know that they are safe? What are the ways in which drugs are tested and sale of drugs controlled?
Listen to excerpts from CBC program on Thalidomide.
Discussion on Safety and efficacy (What experimental designs are needed to study each?)
Discussion of Phase 1, Phase 2, Phase 3, Phase 4 trials.
PROCEDURE
Students will use clinicaltrials.gov website to investigate clinical trials ongoing or completed.
An excellent starting point is to look at the clinical trials search for trials: http://clinicaltrials.gov/ct2/search
The top right hand side of each page gives a link to the glossary, which can be helpful when interpreting the information.
Students can input their city name (works well for New Haven) or a disease of interest.
Once a study is chosen, students can look at it in tabular view (use tabs at top of page)
This view lays out the WHO, WHAT, WHEN, WHERE, HOW of a study.
Students can scroll down below the study description to find the Study Phase, type, design, condition and treatment.
Alternately teacher can give out fact sheets about a trial accessed from the website: http://clinicaltrials.gov/
