guarantees that each group is represented in the sample ADDITIONAL NOTES ABOUT STRATIFIED… STRATIFIED SAMPLING divide population into strata (homogenous layers, subpopulations) take SRS from each strata reduces overall variability (spread) guarantees that each group is represented in the sample Two key elements of stratified sampling… it does help to reduce overall variability (meaning: variability from sample to sample, in terms of the mean of each sample).

Parameters vs. Statistics (population) (sample) Means (numerical data) Proportions (categorical data) Parameter (“truth”) Statistics (“estimate”)

Sampling “error” is just sampling variation. bias ≠ error Sampling “error” is just sampling variation. “error” in statistics does not mean that you did anything wrong. It just refers to natural sampling variability.

(a) (b) (c) (d) Assuming that we were aiming for the center of each target: Which of these have a problem with BIAS? (if they struggle… remind them that bias has to do with being OFF CENTER). Which of these have a problem with high VARIABILITY? Make sure you guys understand the difference.

so if samples are prone to sampling error, why not conduct a census EVERY TIME? Taking a CENSUS of the population is (usually) time-consuming and (often) error-prone

Sources of BIAS… (still Chapter 12)

Bias A systematic error in measuring the estimate cannot do anything with bad data (“garbage in, garbage out”)

Voluntary response People chose to respond Usually only people with very strong opinions respond

Ann Landers: “If you had to do it over again, would you have children?” 10,000 parents responded… “70% of parents say kids not worth it.”

A new poll conducted by Gallup… Using a random sampling method, Gallup found that about 90% of parents were actually happy with their decision to have children.

Remember – the way to determine voluntary response is: People chose to respond Usually only people with very strong opinions respond Remember – the way to determine voluntary response is: Self-selection!!

Convenience sampling Ask people who are easy to ask

Undercoverage some groups of population are left out of the sampling process

Bias through wording of a question

Subtle differences in phrasing can make a big difference In January 2006, the New York Times asked half of the 1229 U.S. adults in their sample the following question: After 9/11, President Bush authorized government wiretaps on some phone calls in the U.S. without getting court warrants, saying this was necessary to reduce the threat of terrorism. Do you approve or disapprove of this? 53% of respondents approved.

subtle differences in phrasing can make a big difference! …but when they asked the other half of their sample a question with only slightly different wording: After 9/11, George W. Bush authorized government wiretaps on some phone calls in the U.S. without getting court warrants. Do you approve or disapprove of this? …only 46% approved Now… 53 to 46 might not sound like a HUGE difference to some of you, but based on the sample sizes, this was big enough to be considered a STATISTICALLY SIGNIFICANT difference. That’s a HUGE word, and in short, basically means that the difference likely had something to do with the question wording, and that it probably wasn’t just coincidence or chance.

subtle differences in phrasing can make a big difference! After 9/11, President Bush authorized government wiretaps on some phone calls in the U.S. without getting court warrants, saying this was necessary to reduce the threat of terrorism. Do you approve or disapprove of this? After 9/11, George W. Bush authorized government wiretaps on some phone calls in the U.S. without getting court warrants. Do you approve or disapprove of this? So… what differences do you see? (kids seem to overlook the word “President”… but that’s a big one!) If you’re trying to avoid bias, you want to avoid using words or phrases that stir up strong emotions…

BIAS through wording of question Spring, 1993, Holocaust Memorial Museum opened in Washington, DC. Survey conducted by Roper Starch Worldwide indicated that 22 percent of the American public believed it “possible that the Nazi extermination of the Jews never happened”, while another 12 percent were unsure. This is idiotic. So… if you’re a statistician, you should be asking yourself, “How was the question worded?”

Exact wording of the Roper question: Does it seem possible, or does it seem impossible to you that the Nazi extermination of the Jews never happened? Gallup question in a new poll: Does it seem possible to you that the Nazi extermination of the Jews never happened, or do you feel certain that it happened? …less than 1% responded that they thought it was possible it did not happen … and hopefully now it makes sense.

(next chapter!) Maybe take a breather. If you can get through these next few slides, it’ll make life a LOT easier next time. But if not, just manage it next time on day 4.

Experiments and Observational Studies chapter 13

observational study experimental study OBSERVATIONAL VS. EXPERIMENTAL observational study no treatment is assigned – SELF SELECTION merely observe a characteristic Prospective vs. Retrospective Prospective: Pick subjects, then follow them for some time Retrospective: Pick subjects, then look up their past records experimental study a treatment is assigned (hopefully RANDOMLY) observe the response and measure its effect RANDOM ASSIGNMENT OF SUBJECTS TO TREATMENTS IS REQUIRED TO SHOW CAUSE AND EFFECT!!!

to show CAUSE & EFFECT is with a randomized experiment!!! The ONLY way to show CAUSE & EFFECT is with a randomized experiment!!! (RANDOM ASSIGNMENT OF SUBJECTS TO TREATMENTS!!!) This is HUGE. Put stars by this in your notes packet!!!

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Experimental unit – the single individual (person, animal, plant, etc.) to which the different treatments are assigned When talking about human beings, we use the friendlier term “SUBJECTS”.

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(stop!)