# Notes Ch13

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Published on July 15, 2009

Author: jmalpass

Source: slideshare.net

AP Statistics – Ch 13 OBSERVATIONAL STUDIES & EXPERIMENTAL DESIGN

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 variables  Level – 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  1. What are the explanatory and the production process for a new response variables. product. The chemical reaction that produces the product may have higher or lower yield, depending on the temperature  2. How many factors are there? and the stirring rate in the vessel in which the reaction takes place. The engineer decides to  3. List the treatments. investigate the effects of combinations of two temperatures (50◦ C and 60◦ C) and three stirring rates (60 rpm,  4. How many experimental units 90 rpm, and 120 rpm) on the are required for the experiment? yield of the process. She will process two batches of the product at each combination of temperature and stirring rate.

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  1. What is the factor(s) the nutritional quality of a new “instant breakfast” product by feeding it to a newly weaned male white rats. The response variable  2. There are 30 rats is a rat’s weight gain over a available for this 28 day period. A control experiment. Describe how group of rats eats a to randomly decide to standard diet but otherwise which treatment group receives exactly the same they belong. treatment as the experimental group.

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.

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