Stat 512

Day 2: Designing Experiments

Leftovers from Tuesday

Questions on syllabus? Repeating the question Blackboard problems?

Sooner turn in, sooner get feedback?

Last Time

Microwave popcorn factory Two categorical variables

level of exposure, whether airway obstruction Graphical summary: segmented bar graph Numerical summary: difference in conditional

proportions Not able to draw cause-and-effect conclusions

Other differences between the two groups that might explain the higher airway obstruction rates in high exposure group?

Not able to generalize to all microwave plant workers “Healthy worker effect”

Figure 1: Comparison of Airway Obstruction from Level of Exposure

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Last Time

Smoking and lung cancer Two categorical variables (amount of smoking

and with or without disease) Graphical summary: segmented bar graph Numerical summary: difference in conditional

proportions Can’t draw cause and effect conclusion

Could be some other difference (diet) between the EV groups that explains higher lung cancer rates with more smoking

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Lung cancer patient

Last Time

Generalizing from sample to population? Reasonable to conclude 605/(605+780), or 44%,

of all males of similar ages and economic status have lung cancer?

Measurement issues Relying on recall… Know they are sick…

Second famous smoking study Hammond and Horn (1958) Find 12,000 healthy men, complete a

questionnaire on smoking habits, had 22,000 American Cancer Society volunteers follow them for 44 months to see whether they die from lung cancer Advantages? Disadvantages?

Practice Problems

Identifying variables Supreme Court Justices:

Qualitative: gender, party Quantitative: age, number of yes votes

Not OK: number of republicans

Practice Problems

Victims of violence OU: people (not “number of victims”) EV: whether abused RV: whether commit crime Not ok in defining variables:

Those who… Number abused… Whether abuse leads to violent crime…

(c) Mostly to spur discussion… Which variable was “controlled” by the researchers…

More practice:

The book Day Hikes in San Luis Obispo County by Robert Stone gives information on 72 different hikes that one can take in the county. For each of the 72 hikes, Stone reports the distance of the hike (in miles), the anticipated hiking time (in minutes), the elevation gain (in feet), and the region of the county in which the hike can be found (North County, South County, Morro Bay, and so on, for a total of eight regions). Observational units? Types of variables

More Practice: Hiking in SLO

Are these legitimate variables? Longest hike in the book Those hikes in the North County region Proportion of hikes with an elevation gain of more

than 500 feet Is hiking time related to elevation gain?

Example 1: Near-sightedness and Night Lights “Myopia and ambient lighting at night,”

Quinn, G.E., Shin, C.H., Maguire, M.G. and Stone, R.A.

Nature, 399:113-114, 1999.

Example 1: Myopia and Night Lights

Room light Night light Darkness

Far-sighted 12 39 40

Normal 22 115 114

Near-sighted 41 78 18

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Example 1: Myopia and Night Lights Base rate: .286 Conditional Proportions

Room light: .55 myopia, .16 hyperopia Night light: .336 myopia, .168 hyperopia Darkness: .105 myopia, .232 hyperopia

Convincing evidence that using more light in the child’s room causes a higher rate of myopia?

Terminology: Confounding variable Has an influence on the response, but its

effects cannot be separated from those of the explanatory variable

room light

parents with bad eyes

darkness

parents with good eyes

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eye-sight

Example 2: Have a Nice Trip

Can instruction in a recovery strategy improve an older person’s ability to recover from a loss of balance? 12 subjects have agreed to participate in the study Assign 6 people to use the lowering strategy and 6

people to use the elevating strategy Similar amounts of men in both groups?

Proportion of group 1 that are male – proportion of group 2 that are male

What would we like to be true about these proportions?

Investigation 1-7: Have a Nice Trip Take 12 index cards Put one of the 12 names on each card Shuffle the cards and deal out 6 to learn the

lowering strategy and the other 6 to learn the elevating strategy

What is the number of males in each group? The male proportion in each (out of 6)? What is the difference in these 2 proportions?

Pool Results

Quantitative variable Different type of graph…

What are the observational units and variable in this graph?

Long-term pattern?

Use applet to repeat the process a large number of times

Open IE, double click on “Dr. Beth Chance” > “Statistical Methods” > “Stat 512 Java Applets” > “Randomizing Subjects

The applet mimics exactly what you did with the index cards.

Effect of randomization

If you randomly assign subjects to the groups, what is generally true about the groups?

If after imposing the treatment, you later observe a difference between the groups, to what can you attribute that difference?

Moral

Randomization equalizes variables between groups Should not have potentially confounding variables If later (after treatments) observe a difference

between groups, feel comfortable attributing that difference to the explanatory variable

Remaining question Will always be some difference, by chance How big does this difference have to be?

Example: Friendly Observers

“The trouble with friendly faces: Skilled performance with a supportive audience,” Butler, J. L., and Baumeister, R. F. Journal of Personality and Social Psychology, 75:

1213-1230, (1998).

To do

By Friday, noon Turn in HW 1 (4 problems)

By Tuesday Preview the Friendly Observers example

(complete questions (a)-(e)) Submit PP 2 in Blackboard Pick and start reading one of the 3 articles