Math 124: Lecture for Week 4 of 17online.sfsu.edu/meredith/statistics/S2008/Lecture_4_slides.pdfWeek...

Math 124:Week 3

Questions andAnswers

ReviewStandard Deviation

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Sampling

DesigningStudiesObservationalStudies

Experimental Studies

Surveys

Math 124: Lecture for Week 4 of 17

David MeredithDepartment of Mathematics

San Francisco State University

February 19, 2008

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Class progress

• As of 5:30PM• only 10 people had completed the Lab Exercise• only 4 people had read the complete assignment

• Passing this class is up to you.• If you do the work, you will get a good grade• An hour a day, every day, is what you need to do

• Do two 30-minute sessions if that works better

• First on-line quiz due Thursday, second on-line quizdue one week from Thursday.

• First midterm in two weeks

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What we will do tonight

1 Questions and Answers

2 Quiz

3 ReviewStandard DeviationReview Case IReview Case IIReview Case III

4 Sampling

5 Designing StudiesObservational StudiesExperimental StudiesSurveys

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2 Quiz

4 Sampling

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2 Quiz

4 Sampling

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2 Quiz

4 Sampling

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2 Quiz

4 Sampling

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Questions and Answers

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Go over quiz

www.cmu.edu/oli

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Apply the standard deviation rule

Question 1:

• Calculate the mean and standard deviation of thedataset:

5.1 6.4 6.5 8.8 8.8 9.4 9.9 10.110.2 13.1 13.5 13.5 13.6 14.4 14.6

• Is this data approximately normally distributed?• Implicit understanding for this class• Whenever you get a question like the one above, the

answer isn’t just “yes” or “no”; the answer is “yes,because . . . ” or “no, because . . . ”.

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Question 1:

5.1 6.4 6.5 8.8 8.8 9.4 9.9 10.110.2 13.1 13.5 13.5 13.6 14.4 14.6

• Is this data approximately normally distributed?

• Implicit understanding for this class• Whenever you get a question like the one above, the

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Question 1:

5.1 6.4 6.5 8.8 8.8 9.4 9.9 10.110.2 13.1 13.5 13.5 13.6 14.4 14.6

• Is this data approximately normally distributed?• Implicit understanding for this class

• Whenever you get a question like the one above, theanswer isn’t just “yes” or “no”; the answer is “yes,because . . . ” or “no, because . . . ”.

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Question 1:

5.1 6.4 6.5 8.8 8.8 9.4 9.9 10.110.2 13.1 13.5 13.5 13.6 14.4 14.6

• Is this data approximately normally distributed?• Implicit understanding for this class• Whenever you get a question like the one above, the

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Compare and contrast distributions of quantitative data from

two or more groups

Question 2: here are scores from a test I gave to Math 124last semester.

100 100 92 92 83 83 83 83 75Women 75 67 67 67 58 58 58 50 50

50 50 50 42 33 33 17100 100 100 92 92 92 92 83 83

Men 75 67 67 58 58 58 58 50 4242 33

1 How would you analyze and compare the results formen and women??

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two or more groups

Question 2: here are scores from a test I gave to Math 124last semester.

100 100 92 92 83 83 83 83 75Women 75 67 67 67 58 58 58 50 50

50 50 50 42 33 33 17100 100 100 92 92 92 92 83 83

Men 75 67 67 58 58 58 58 50 4242 33

1 How would you analyze and compare the results formen and women??

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two or more groups

Question 2 continued: here are five-number summaries forthe scores from a test I gave to Math 124 last semester.

Min. 1st Qu. Median 3rd Qu. Max.Women 17.00 50.00 67.00 83.00 100.00Men 33.0 58.0 71.0 92.0 100.0

1 Draw the boxplots.2 Would you say that the difference between men and

women was significant?

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two or more groups

1 Draw the boxplots.

2 Would you say that the difference between men andwomen was significant?

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two or more groups

1 Draw the boxplots.2 Would you say that the difference between men and

women was significant?

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Produce a two-way table and compare conditional

percentages

Question 3: Here’s some imaginary data.

Explanatory A B A A A B B A B AResponse X Z Z Z X Y X X X X

Explanatory A B B A B A B B A AResponse X X Z Y Z X Y Z X X

• How would you analyze and summarize these datanumerically and graphically?

• Do it.

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percentages

Question 3: Here’s some imaginary data.Explanatory A B A A A B B A B A

Response X Z Z Z X Y X X X X

• Do it.

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percentages

• Do it.

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percentages

• Do it.

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Interpret the value of the correlation coefficient

• This question is taken from a sample CSET test. CSETis a test that qualifies potential high school mathteachers as competent in mathematics.

• Question 4: Suppose the equation for the regressionline through some data is Y = 4.5 + 2.3X . Then thecorrelation coefficient for the data could be:

1 2.42 0.63 -0.74 -1.3

• If the regression equation was Y = 4.5− 2.3X , whatcould the correlation coefficient be?

• Explain your reasons.

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• This question is taken from a sample CSET test. CSETis a test that qualifies potential high school mathteachers as competent in mathematics.

• Question 4: Suppose the equation for the regressionline through some data is Y = 4.5 + 2.3X . Then thecorrelation coefficient for the data could be:

1 2.42 0.63 -0.74 -1.3

• If the regression equation was Y = 4.5− 2.3X , whatcould the correlation coefficient be?

• Explain your reasons.

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Question 5: Here’s the data from the text relating thelongevity of animals to their gestation period.

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• Is the correlation coefficient for these data positive ornegative?

• Does including the outlier increase or decrease thecorrelation coefficient?

• The correlation with the outlier is 0.66; without theoutlier the correlation is 0.52.

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• Does including the outlier increase or decrease thecorrelation coefficient?

• The correlation with the outlier is 0.66; without theoutlier the correlation is 0.52.

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In the special case of linear relationship, use the least

squares regression line

Question 6: Here’s a subset of the data from the textrelating the longevity of animals to their gestation period.

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• Is the correlation coefficient:

1 -0.632 -0.283 0.414 0.755 0.96

• The correlation coefficient is 0.75

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• Is the correlation coefficient:

1 -0.632 -0.283 0.414 0.755 0.96

• The correlation coefficient is 0.75

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The regression equation for these data is Y = 12.9 + 10.3X

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Question 7:

1 Can you estimate the gestation period for an animalthat lives for 15 years?

3 Can you estimate the life span of an animal with agestation period of 150 days?

167 days; no, that would require extrapolation; 13.3 years

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Question 7:

3 Can you estimate the life span of an animal with agestation period of 150 days?

167 days; no, that would require extrapolation; 13.3 years

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Recognize and explain the phenomenon of Simpson’s

Paradox

• Simpson’s paradox occurs when data indicates oneconclusion, but when divided into two parts each partindicates the opposite conclusion, or when divided intomany parts most parts indicate the opposite conclusion

• Obviously this cannot happen, but it does• example from UC Bekeley (Wikipedia–Simpson’s

Paradox)http://en.wikipedia.org/wiki/Simpson’s_paradox

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Let’s take a fifteen minute break.

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Identify the sampling method used in a study

• A statistical study usually begins with a sample of somesort

• Sample of people from the population you want to study• Sample of rocks from the area you want to study• Sample of blood from the person you want to study

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• Good types of samples• a simple random sample (selected at random and

without replacement) is, as the name suggests, thesimplest probability sampling plan.

• in cluster sampling we randomly choose whole orentire groups (clusters) of individuals belongingtogether in one way or another, such as taking a simplerandom sample of households and studying allindividuals in each sampled household.

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In stratified sampling we first divide the population intogroups of individuals that are similar to each other in animportant way with respect to the variable of interest (forexample, by gender, or year in college), and then choose asimple random sample from within each group. The groupsare called strata and hence the name "stratified sampling".Using this (a bit more cumbersome) method may help toobtain a representative sample more efficiently.

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Question 8: What kind of study might cluster sampling

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Whatever kind of sampling you use, a larger sample isusually more accurate than a smaller sample.• Later in this course we study how much improvement a

larger sample can give you• There’s always a trade-off between cost and accuracy.

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• Bad sorts of samples• volunteer sample• convenience sample• wrong sampling frame• systematic sampling

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• [X ]press’ own unscientific, on-campus exit pollsurveyed 409 people who voted on campus. Sixty-ninepercent of the people polled said they voted for BarackObama while only 20 percent voted for Hillary Clinton.

• Question 10• What kind of sample was this?• How many people voted Republican?

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Identify the design of a study (controlled experiment vs.

observational study)

• There are three kinds of statistical studies

• Observational• Experimental• Survey

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• There are three kinds of statistical studies• Observational

• Experimental• Survey

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• There are three kinds of statistical studies• Observational• Experimental

• Survey

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• There are three kinds of statistical studies• Observational• Experimental• Survey

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Identify the design and other features of a study

• Observational studies observe variables as theynaturally occur

• Advantage: ecological validity—subjects behavenaturally

• May be negated by subjects’ knowledge that they arebeing observed (Hawthorne effect)

• Hawthorne works of the Western Electric Company inChicago 1924-32

• Disadvantage: difficult to control for lurking variables• For example, if quit-smoking programs are studied by

allowing people to choose one or another quit-smokingmethod spontaneously, then those more determined toquit may tend to choose a different method than thosewho aren’t really trying.

• This will make the method selected by the quitters lookgood

• You overcome this difficulty by conducting an experimentin which people who want to quit smoking are randomlyassigned to different treatments.

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• Disadvantage: difficult to control for lurking variables

• For example, if quit-smoking programs are studied byallowing people to choose one or another quit-smokingmethod spontaneously, then those more determined toquit may tend to choose a different method than thosewho aren’t really trying.

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• On a test, please don’t limit yourself to saying: “Adisadvantage of observational studies is that they mayfail to uncover lurking variables”.

• Always add: “For example, ...”• Your answer should demonstrate an understanding of

the terms “observational study” and “lurking variable”.

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• Always add: “For example, ...”

• Your answer should demonstrate an understanding ofthe terms “observational study” and “lurking variable”.

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• Always add: “For example, ...”• Your answer should demonstrate an understanding of

the terms “observational study” and “lurking variable”.

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Explain how the study design impacts the type of

conclusions that can be drawn

• Experimental studies put subjects in artificial situationsto observe behavior

• Advantage: can control for lurking variables bycontrolling situation

• Example: studying smoking

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• Experimental studies put subjects in artificial situationsto observe behavior

• Advantage: can control for lurking variables bycontrolling situation

• Example: studying smoking

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Disadvantages of experimental studies

• subjects may not behave naturally (lack of ecologicalvalidity)

• Yale University psychologist Stanley Milgram 1963conducted experiment where subjects supposedlyadministered shocks to help learners (who were reallyactors). Learners simulated pain, but subject, on ordersof experimenter kept inflicting greater and greatershocks.

• What did this experiment prove?• Question 11: can you see any ethical problems with this

experiment

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Disadvantages of experimental studies• subjects may not behave naturally (lack of ecological

validity)

• Yale University psychologist Stanley Milgram 1963conducted experiment where subjects supposedlyadministered shocks to help learners (who were reallyactors). Learners simulated pain, but subject, on ordersof experimenter kept inflicting greater and greatershocks.

experiment

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validity)• Yale University psychologist Stanley Milgram 1963

conducted experiment where subjects supposedlyadministered shocks to help learners (who were reallyactors). Learners simulated pain, but subject, on ordersof experimenter kept inflicting greater and greatershocks.

experiment

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• What did this experiment prove?

• Question 11: can you see any ethical problems with thisexperiment

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experiment

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experiment

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Blind and double-blind studies, use of placebos areattempts to improve ecological validity of studies

• An experiment is blind if the subject doesn’t know whichtreatment they are receiving

• An experiment is double blind if the subject and thoseadministering the treatments don’t know whichtreatment they are using

• A placebo is a treatment that has no effect. It is used sothat subjects and those administering treatments don’tknow who is in the “no treatment” group.

• Many but not all experiments benefit from the use ofblind and double-blind protocols and the use ofplacebos.

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Blind and double-blind studies, use of placebos areattempts to improve ecological validity of studies• An experiment is blind if the subject doesn’t know which

treatment they are receiving

• An experiment is double blind if the subject and thoseadministering the treatments don’t know whichtreatment they are using

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treatment they are receiving• An experiment is double blind if the subject and those

administering the treatments don’t know whichtreatment they are using

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treatment they are receiving• An experiment is double blind if the subject and those

administering the treatments don’t know whichtreatment they are using

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More disadvantages of experimental studies

• Subjects may not follow protocols or report inaccurately• Some experiments may be immoral.

• Could you ask a random group of drivers not to useseatbelts?

• Medical experiments are sometimes stoppedmidstream when dangers become clear

• On March 2, 2004, NIH announced that it had stoppedthe estrogen-alone study in the interest of safety aftercareful consideration of preliminary data and an averagefollow-up of nearly 7 years http://www.nhlbi.nih.gov/whi/estro_alone.htm

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More disadvantages of experimental studies• Subjects may not follow protocols or report inaccurately

• Some experiments may be immoral.• Could you ask a random group of drivers not to use

seatbelts?• Medical experiments are sometimes stopped

midstream when dangers become clear• On March 2, 2004, NIH announced that it had stopped

the estrogen-alone study in the interest of safety aftercareful consideration of preliminary data and an averagefollow-up of nearly 7 years http://www.nhlbi.nih.gov/whi/estro_alone.htm

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More disadvantages of experimental studies• Subjects may not follow protocols or report inaccurately• Some experiments may be immoral.

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Determine how features of a survey impact the collected

data and its accuracy

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• Advantage: Cheap, easy to perform• Disadvantage: must be carefully constructed

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• Advantage: Cheap, easy to perform

• Disadvantage: must be carefully constructed

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• Advantage: Cheap, easy to perform• Disadvantage: must be carefully constructed

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Problematic survey questions

• limited response options• unbalanced response options• leading questions

• Here’s a real question taken from a political survey:"Some people say (your Democratic incumbent) is astrong supporter of Hillary Clinton and will support herliberal agenda of big government and higher taxes ifshe becomes President. Do you plan to vote for thisperson in November?" (Washington Post, Letter to theEditor, 9/29/07)

• Political surveys like this are called push polls

• planting ideas with questions• complicated questions• sensitive questions

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• limited response options

• unbalanced response options• leading questions

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• limited response options• unbalanced response options

• leading questions• Here’s a real question taken from a political survey:

"Some people say (your Democratic incumbent) is astrong supporter of Hillary Clinton and will support herliberal agenda of big government and higher taxes ifshe becomes President. Do you plan to vote for thisperson in November?" (Washington Post, Letter to theEditor, 9/29/07)

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• planting ideas with questions

• complicated questions• sensitive questions

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• planting ideas with questions• complicated questions

• sensitive questions

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“Randomized responses” to deal with sensitive questions

• Want to ask people if they have done something bad(fill in your own example)

• Tell them to flip a coin and not show it to you• If heads, answer truthfully• If tails, answer “yes”

• At end of study, remove a number of yes answers equalto half the subjects used

• Question 12: Would this method work if the instructionsread: If tails, answer “no”

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“Randomized responses” to deal with sensitive questions• Want to ask people if they have done something bad

(fill in your own example)

• Tell them to flip a coin and not show it to you• If heads, answer truthfully• If tails, answer “yes”

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(fill in your own example)• Tell them to flip a coin and not show it to you

• If heads, answer truthfully• If tails, answer “yes”

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Math 124: Lecture for Week 4 of 17online.sfsu.edu/meredith/statistics/S2008/Lecture_4_slides.pdfWeek...

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