�Preliminaries��Introduction to Statistical Investigations

Three threads

• Six Step Statistical Investigation Method
• Variability
• Probability

Statistics vs. Anecdotal Evidence

Smoking causes cancer.

Seat belts save lives.

Statistics

• Scientific conclusions cannot be based on anecdotal evidence. We need evidence from data.
• Statistics is the science of producing useful data to address a research question, analyzing the resulting data, and drawing appropriate conclusions from the data.

Six-Step Statistical Investigation Method

Example: Organ Donations

• While 90-95% of US adults approve of organ donation in principle, far less than that actually sign up (a little over 50%) when getting a driver’s license.
• Different states have different recruiting methods.
• Do these different methods result in different sign-up rates?

Recruiting Organ Donors

Step 1. Ask a Research Question

• In general: Is there a method that will increase the likelihood that a person agrees to become an organ donor.
• More specifically: Does the default option presented to driver’s license applicants influence the likelihood of someone becoming an organ donor?

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Recruiting Organ Donors

Step 2: Design a study and collect data

• The researchers decided to recruit various participants and ask them to pretend to apply for a new driver’s license.
• The participants did not know in advance that different options were given for the donor question, or even that this issue was the main focus of the study.
• They offered an incentive of $4.00 for completing an online survey. After the results were collected, the researchers removed data arising from multiple responses from the same IP address, surveys completed in less than five seconds, and respondents whose residential address could not be verified.

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Recruiting Organ Donors

Step 2: Design a study and collect data

• Some of the participants were forced to make a choice of becoming a donor or not, without being given a default option (the “neutral” group).
• Other participants were told that the default option was not to be a donor but that they could choose to become a donor if they wished (the “opt-in” group).
• The remaining participants were told that the default option was to be a donor but that they could choose not to become a donor if they wished (the “opt-out” group).

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Recruiting Organ Donors

Step 3: Explore the data.

• 44 of the 56 (78.6%) participants in the neutral group agreed to become organ donors,
• 23 of 55 (41.8%) participants in the opt-in group agreed to become organ donors, and
• 41 of 50 (82.0%) participants in the opt-out group agreed to become organ donors.

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Recruiting Organ Donors

Step 4: Draw inferences beyond the data.

• Researchers found strong evidence that the neutral and opt-out versions do lead to a higher chance of agreeing to become a donor, as compared to the opt-in version currently used in many states.
• In fact, they could be quite confident that the neutral version would increase the chances that a person agree to become a donor by between 20 and 54 percentage points, a difference large enough to save thousands of lives per year in the United States.

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Recruiting Organ Donors

Step 5: Formulate conclusions.

• Based on the analysis of the data and the design of the study, it is reasonable for these researchers to conclude that the neutral and opt-out versions cause an increase in the proportion who agree to become donors.
• But because the participants in the study were volunteers recruited from internet bulletin boards, generalizing conclusions beyond these participants is only legitimate if they are representative of a larger group of people.

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Recruiting Organ Donors

Step 6: Look back and ahead.

• One limitation of the study is that participants were asked to imagine how they would respond, which might not mirror how people would actually respond in such a situation.
• A new study might look at people’s actual responses to questions about organ donation or could monitor donor rates for states that adopt a new policy.
• Researchers could also examine whether presenting educational material on organ donation might increase people’s willingness to donate.
• Another improvement would be to include participants from wider demographic groups than these volunteers.

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Michigan has a neutral default … with advertising while you wait!

Variability:Old Faithful

Old Faithful

• Researchers collected data on 222 eruptions taken over a number of days in the summers of 1978 and 1979.
• The results are shown in a dotplot.

Old Faithful

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• We can see from the dotplot that Old Faithful is not perfectly predictable.
• The time until the next eruption varies from eruption to eruption.
• This variability is the most fundamental property in studying Statistics.  Without variability, we wouldn’t need statistics.

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Old Faithful

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Basic Terminology

• Some aspects to look for in a distribution of a quantitative variable are:
• Shape: Is the distribution symmetric? Mound-shaped? Are there several peaks or clusters?
• Center: Where is the distribution centered? What is a typical value?
• Variability: How spread out are the data? Are most within a certain range of values?
• Unusual observations: Are there outliers that deviate markedly from the overall pattern of the other data values? Are there other unusual features in the distribution?

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Old Faithful

• Let’s take another look at the dotplot and describe the distribution.

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• What could be some explanations for the variability?

Old Faithful

• One explanation could be the duration of previous eruption (short: < 3.5 min. or long > 3.5 min.)

Probability Exploration: Cars or Goats