OBSERVATIONAL STUDIES&

EXPERIMENTAL DESIGN

AP Statistics – Ch 13

Definitions

Observational Study – researchers simply observe or question the participants about opinions, behaviors, or outcomes. No treatment is imposed

Experiment – researchers manipulate something and measure the effect of the manipulation on some outcome of interest.

Confounding variable or lurking variable- a variable that both affects the response variable and is also related to the explanatory variable. Occurs more often in observational studies

Examples of Observational Studies

Suppose that an observational study finds that people who take at least 500 mg of vitamin C every day get fewer colds than other people do.

Another observational study found that attending church services extends the life span about as much as moderate exercise or not smoking.

Another study found that a greater percentage of Southerners have high blood pressure than do people in any other region of the United States.

Observational Studies

Observational studies can not determine a cause and effect relationship. They can only demonstrate an association.

Randomized Experiments

Experimental Units – animals, plants, things. People are called subjects or participants

Factors – explanatory variablesLevel – combining specific value of each of

the factors (ex. Higher dosages of the same drug)

Example 1

Researchers studying the absorption of a drug into the bloodstream inject the drug (the treatment) into 25 people. The response variable is the concentration of the drug in a subject’s blood, measured 30 minutes after the injection.

This experiment has a single factor with one level.

If three different doses of the drug are injected, there is still a single factor (dosage of the drug), now with three levels.

Example 2

A chemical engineer is designing the production process for a new product. The chemical reaction that produces the product may have higher or lower yield, depending on the temperature and the stirring rate in the vessel in which the reaction takes place. The engineer decides to investigate the effects of combinations of two temperatures (50◦ C and 60◦ C) and three stirring rates (60 rpm, 90 rpm, and 120 rpm) on the yield of the process. She will process two batches of the product at each combination of temperature and stirring rate.

1. What are the explanatory and response variables.

2. How many factors are there?

3. List the treatments.

4. How many experimental units are required for the experiment?

Placebo Effect

A placebo is a dummy treatment that can have no physical effect. A response without actual treatment is called the placebo effect.

Placebo Pills, Placebo Surgeries

Three principles of a controlled experiment

Control – control the effects of lurking variables such as the placebo effect.

Randomization – randomly place participants in groups, all experimental units are allocated at random among all treatments.

Replication – repeat treatment on several subjects (30 participants means treatment is repeated 30 times)

Example 3

A food company assesses the nutritional quality of a new “instant breakfast” product by feeding it to a newly weaned male white rats. The response variable is a rat’s weight gain over a 28 day period. A control group of rats eats a standard diet but otherwise receives exactly the same treatment as the experimental group.

1. What is the factor(s)

2. There are 30 rats available for this experiment. Describe how to randomly decide to which treatment group they belong.

Statistically Significant

An observed effect is statistically significant when the effect is too large to attribute plausibly to chance variation.

Cautions

Hidden bias – remember that bias is systematically favoring a certain outcome.

Lack of realism – experiment in a lab setting may not be the same when implemented in the real world.

Double Blind Experiment

Neither the participant nor the person measuring or evaluating the response is aware who receives the treatment/placebo.

Block Experiment

A group of volunteers are sorted by some characteristic before being placed randomly into treatment groups.

Blocking helps to reduce the chances of that characteristic from becoming a lurking variable

If we block by gender, then we suspect that men and women may respond to treatment differently, therefore we split them up separately to begin with.

Randomizing within blocks further reduces the effects of lurking variables.

Blocking continued

When we block we are creating groups that are similar.

This reduces variation…meaning the standard deviation of the measurements will be smaller.

It will be easier for us to tell if our results are significant because of the reduced variation.

Matched Pairs Design

1 – Two units are closely matched. A coin is flipped to see which unit receives the treatment and which one receives the placebo or standard treatment.

2 – One subject receives both treatments. A coin is flipped to determine which treatment is tried first.