CHAPTER 9: Producing Data: Experiments, Exercises of Design

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CHAPTER 9:

Producing Data: Experiments

Lecture PowerPoint Slides

The Basic Practice of Statistics

6 th^ Edition

Moore / Notz / Fligner

Chapter 9 Concepts

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 Observation vs. Experiment

 Subjects, Factors, Treatments

 How to Experiment Badly

 Randomized Comparative Experiments

 Cautions About Experimentation

 Matched Pairs and Other Block Designs

 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.

Observation vs. Experiment

An observational study observes individuals and measures variables of interest but does not attempt to influence the responses. The purpose is to describe some group or situation.

An experiment deliberately imposes some treatment on individuals to measure their responses. The purpose is to study whether the treatment causes a change in the response.

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.

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Confounding

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.

How to Experiment Badly

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Experiments are the preferred method for examining the effect of one variable on another. By imposing the specific treatment of interest and controlling other influences, we can pin down cause and effect. Good designs are essential for effective experiments, just as they are for sampling.

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.

Students  Online Course  SAT Scores

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?

How to Experiment Badly

Experimental Units

In the laboratory environment, simple designs often work well.

Field experiments and experiments with animals or people deal with more variable conditions.

Outside the laboratory, badly designed experiments often yield worthless results because of confounding.

Many laboratory experiments use a design like the one in the online SAT course example:

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Randomized Comparative

Experiments

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.

Experimental Units

Random Assignment

Group 1

Group 2

The Logic of Randomized

Comparative Designs 11

Randomized comparative experiments are designed to give good evidence that differences in the treatments actually cause the differences we see in the response.

1. Control for lurking variables that might affect the response, most simply by comparing two or more treatments. 2. Randomize: Use chance to assign experimental units to treatments. 3. Replication: Use enough experimental units in each group to reduce chance variation in the results.

Principles of Experimental Design

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.

Blocked Designs

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Completely randomized designs are the simplest statistical designs for experiments. But just as with sampling, there are times when the simplest method doesn’t yield the most precise results.

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 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.

Matched Pairs

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A common type of randomized block design for comparing two treatments is a matched pairs design. The idea is to create blocks by matching pairs of similar experimental units.

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 which treatment is applied first for each unit.