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Chapter 4: Designing Studies. Section 4.2 Experiments. The Practice of Statistics, 4 th edition – For AP* STARNES, YATES, MOORE. Chapter 4 Designing Studies. 4.1 Samples and Surveys 4.2 Experiments 4.3 Using Studies Wisely. Section 4.2 Experiments. Learning Objectives.
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The Practice of Statistics, 4th edition – For AP*
STARNES, YATES, MOORE
After this section, you should be able to…
A mother’s smoking during pregnancy and exposure to lead significantly increases her child’s risk for developing attention deficit hyperactivity disorder (ADHD), say researchers. In fact, as many as one third of cases of ADHD in children are linked to exposure to tobacco smoke and lead before birth, giving moms yet another reason to quit smoking during pregnancy.
For the study, researchers from Cincinnati Children’s Hospital Medical Center surveyed over 4,700 children between the ages of 4 and 15 and their parents. Over 4 percent of the children included had ADHD. The researchers found that those children whose mother smoked during pregnancy were over twice as likely to develop ADHD than a child whose mother had not smoked. In addition, a child who had been exposed to lead, giving them high lead blood levels, were four times as likely to have ADHD, as compared to a child with low lead levels in his blood.
Based on this study, should we conclude that smoking during pregnancy causes an increase in the likelihood that a child develops ADHD? Explain.
In contrast to observational studies, experiments don’t just observe individuals or ask them questions. They actively impose some treatment in order to measure the response.
An observational study observes individuals and measures variables of interest butdoes not attempt to influence the responses.
An experiment deliberately imposes some treatment on individuals to measure their responses.
When our goal is to understand cause and effect, experiments are the only source of fully convincing data.
The distinction between observational study and experiment is one of the most important in statistics.
Watch and record what happens
NO treatments applied
NO Cause and Effect can be claimed
Apply a treatment to subjects
Finding cause and effect is the GOAL
Observational studies of the effect of one variable on another often fail because of confounding between the explanatory variable and one or more lurking variables.
A lurking variable is a variable that is not among the explanatory or response variables in a study but that may influence the response variable.
Confounding occurs when two variables are associated in such a way that their effects on a response variable cannot be distinguished from each other.
Well-designed experiments take steps to avoid confounding.
Note: Each lurking variable can turn into a confounding variable if the experiment is designed poorly!!
A teacher wants to compare the effectiveness of computer software for teaching biology with that of a textbook presentation. She gives a biology pretest to a group of high school juniors, then randomly divides them into two sub-groups. One group uses the computer, and the other studies the text. At the end of the year, she tests all the students again and compares the increase in biology test scores in the two groups.
Experiment or study? Justify your answer.
One study of cell phones and the risk of brain cancer looked at a group of 469 people who have brain cancer. The investigators matched each cancer patient with a person of the same age, gender, and race who did not have brain cancer, then asked about the use of cell phones. Result: “Our data suggest that the use of handheld cellular phones is not associated with the risk of brain cancer.”
Experiment or study? Justify your answer.
An experiment is a statistical study in which we actually do something (a treatment) to people, animals, or objects (the experimental units) to observe the response. Here is the basic vocabulary of experiments.
A specific condition applied to the individuals in an experiment is called a treatment. If an experiment has several explanatory variables, a treatment is a combination of specific values of these variables.
The experimental units are the smallest collection of individuals to which treatments are applied. When the units are human beings, they often are called subjects.
Sometimes, the explanatory variables in an experiment are called factors. Many experiments study the joint effects of several factors. In such an experiment, each treatment is formed by combining a specific value (often called a level) of each of the factors.
Identify the experimental units, explanatory and response variables, and the treatments in the Careerstart experiment
Experimental Units: 14 middle schools in Forsyth County, NC
Explanatory variable: If the school used the CareerStart program with its students
Response Variable: test scores, attendance, behavior, student engagement, and graduation rates
Treatments: (1) standard middle school curriculum (2) standard curriculum plus CareerStart
Experimental Units: the 376 households
Explanatory variable: type of medication
Response Variable: if the household was lice-free
Treatments: (1) ivermectin (2) malathion
Experimental Units: 24 tomato plants
Explanatory variable: (1) if fertilizer is applied (2) amount of water
Response Variable: weight of tomatoes
Treatments: (1) fertilizer, 0.5 gallon (2) fertilizer, 1 gallon (3) fertilizer, 1.5 gallons (4) no fertilizer, 0.5 gallon (5) no fertilizer, 1 gallon (5) no fertilizer, 1.5 gallons
Does caffeine affect pulse rate?
Are there problems? Lurking variables?
Example, page 236
A high school regularly offers a review course to prepare students for the SAT. This year, budget cuts will allow the school to offer only an online version of the course. Over the past 10 years, the average SAT score of students in the classroom course was 1620. The online group gets an average score of 1780. That’s roughly 10% higher than the long- time average for those who took the classroom review course. Is the online course more effective?
Students -> Online Course -> SAT Scores
In the lab environment, simple designs often work well.
Field experiments and experiments with animals or people deal with more variable conditions.
Outside the lab, badly designed experiments often yield worthless results because of confounding.
In an experiment, random assignment means that experimental units are assigned to treatments at random, that is, using some sort of chance process.
In a completely randomized design, the treatments are assigned to all the experimental units completely by chance.
Some experiments may include a control group that receives an inactive treatment or an existing baseline treatment.
Here is a basic outline:
To implement the design, use 90 equally sized slips of paper. Label 30 of the slips “1”, 30 of the slips “2” and 30 of the slips “3”. Then, mix them up in a hat and have each subject draw a number without looking. The number that each subject chooses will be the group he or she is assigned to. At the end of the year, the amount of weight loss will be recorded for each subject and the mean weight loss will be compared for the three treatments.
Principles of Experimental Design
A placebo is a “dummy pill” or inactive treatment that is indistinguishable from the real treatment.
A response to a dummy treatment is called a placebo effect. The strength of the placebo effect is a strong argument for randomized comparative experiments.
Whenever possible, experiments with human subjects should be double-blind.
In a double-blind experiment, neither the subjects nor those who interact with them and measure the response variable know which treatment a subject received.
An observed effect so large that it would rarely occur by chance is called statistically significant.
A statistically significant association in data from a well-designed experiment does imply causation.
Is talking on a cell phone while driving more distracting than talking to a passenger? Read the Activity on page 245.
Perform 10 repetitions of your simulation and report the number of drivers in the cell phone group who failed to stop
Teacher: Right-click (control-click) on the graph to edit the counts.
In what percent of the class’ trials did 12 or more people in the cell phone group fail to stop?
Based on these results, how surprising would it be to get a result this large or larger simply due to chance involved in random assignment? Is this result statistically significant?
A block is a group of experimental units that are known before the experiment to be similar in some way that is expected to affect the response to the treatments.
In a randomized block design, the random assignment of experimental units to treatments is carried out separately within each block.
Form blocks based on the most important unavoidable sources of variability (lurking variables) among the experimental units.
Randomization will average out the effects of the remaining lurking variables and allow an unbiased comparison of the treatments.
Control what you can, block on what you can’t control, and randomize to create comparable groups.
A matched-pairs design is a randomized blocked experiment in which each block consists of a matching pair of similar experimental units.
Chance is used to determine which unit in each pair gets each treatment.
Sometimes, a “pair” in a matched-pairs design consists of a single unit that receives both treatments. Since the order of the treatments can influence the response, chance is used to determine with treatment is applied first for each unit.
This design is beneficial when you think there might be lurking variables present
Control what you can, block on what you can’t control, and randomize to create comparable groups
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