3Sample vs PopulationA population includes all individuals or objects of interestA sample is all the cases that we have collected data on, usually a subset of the populationStatistical inference is the process of using data from a sample to gain information about the population
4The Big PicturePopulationSamplingSampleStatistical Inference
5Most Important to You Which of the following is most important to you? AthleticsAcademicsSocial LifeCommunity ServiceOther
6Most Important to YouSuppose researchers studying student life at Duke use the results of our clicker question to investigate what Duke students find importantWhat is the sample?What is the population?Can the sample data be generalized to make inferences about the population? Why or why not?
7Sampling Population Sample Sampling GOAL: Select a sample that is similar to the population, only smaller
9Dewey Defeats Truman?The paper was published before the conclusion of the 1948 presidential election, and was based on the results of a large telephone poll which showed Dewey sweeping TrumanHowever, Harry S. Truman won the electionWhat went wrong?
10Sampling BiasSampling bias occurs when the method of selecting a sample causes the sample to differ from the population in some relevant wayIf sampling bias exists, we cannot trust generalizations from the sample to the population
12Can you avoid sampling bias? The next slide shows Lincoln’s Gettysburg Address. The entire population, all words in his address, will be shown to you.Your task: Select a sample of 10 words that resemble the overall address. Write them down.Calculate the average number of letters for the words in your samplePlace a dot above your sample average on the board
13Lincoln’s Gettysburg Address “Four score and seven years ago our fathers brought forth, on this continent, a new nation, conceived in Liberty, and dedicated to the proposition that all men are created equal. Now we are engaged in a great civil war, testing whether that nation, or any nation so conceived and so dedicated, can long endure. We are met on a great battle-field of that war. We have come to dedicate a portion of that field, as a final resting place for those who here gave their lives that that nation might live. It is altogether fitting and proper that we should do this. But, in a larger sense, we can not dedicate—we can not consecrate—we can not hallow—this ground. The brave men, living and dead, who struggled here, have consecrated it, far above our poor power to add or detract. The world will little note, nor long remember what we say here, but it can never forget what they did here. It is for us the living, rather, to be dedicated here to the unfinished work which they who fought here have thus far so nobly advanced. It is rather for us to be here dedicated to the great task remaining before us—that from these honored dead we take increased devotion to that cause for which they here gave the last full measure of devotion—that we here highly resolve that these dead shall not have died in vain—that this nation, under God, shall have a new birth of freedom—and that government of the people, by the people, for the people, shall not perish from the earth.”
14Can you avoid sampling bias? Actual average: 4.29 lettersPeople are TERRIBLE at selecting a good sample, even when explicitly trying to avoid sampling bias!We need a better way…
15Take a RANDOM sample! Random Sampling How can we make sure to avoid sampling bias?Imagine putting the names of all the units of the population into a hat, and drawing out names at random to be in the sampleTake a RANDOM sample!
16Random SamplingBefore the 2008 election, the Gallup Poll took a random sample of 2,847 Americans. 52% of those sampled supported ObamaIn the actual election, 53% voted for ObamaRandom sampling is a very powerful tool!!!
17Selecting a Random Sample Option 1: Actually draw names out of a hatOption 2: Number all units in the population, and generate random numbersOnline:RStudio: To generate n random numbers between 1 and max, usesample(1:max, n)> sample(1:100,5)
18Selecting a Random Sample Option 3: Use RStudio to randomly sample directly from a vector of population unitspopulation = vector of population unitsn = sample sizesample(population, n)
19“Random” NumbersPick 10 “random” numbers between 1 and 268. Write these numbers down.(Note: When choosing a real sample, you should use technology to generate random numbers. This is simply for illustrative purposes in class.)Using the next slide, calculate the average number of letters in the words corresponding to your random numbersPlace a dot above this average on the board
21Random vs Non-Random Sampling Random samples have averages that are centered around the correct numberNon-random samples may suffer from sampling bias, and averages may not be centered around the correct numberOnly random samples can truly be trusted when making generalizations to the population!
22Bowl of Soup Analogy Think of tasting a bowl of soup… Population = entire bowl of soupSample = whatever is in your tasting bitesIf you take bites non-randomly from the soup (if you stab with a fork, or prefer noodles to vegetables), you may not get a very accurate representation of the soupIf you take bites at random, only a few bites can give you a very good idea for the overall taste of the soup
23Simple Random Sample These methods generate a simple random sample In a simple random sample, each unit of the population has the same chance of being selected, regardless of the other units chosen for the sampleMore complicated random sampling schemes exist, but will not be covered in this course
24Realities of SamplingWhile a random sample is ideal, often it isn’t feasible. A list of the entire population may not be available, or it may be impossible or too difficult to contact all members of the population.Sometimes, your population of interest has to be altered to something more feasible to sample from. Generalization of results are limited to the population that was actually sampled from.In practice, think hard about potential sources of sampling bias, and try your best to avoid them
25Non-Random SamplesSuppose you want to estimate the average number of hours that Duke students spend studying each week. Which of the following is the best method of sampling?Go to the library and ask all the students there how much they studyall Duke students asking how much they study, and use all the data you getGive a clicker question in STAT 101 and force every student to respondStand outside the Bryan Center and ask everyone going in how much they study
26Bad Methods of Sampling Sampling units based on something obviously related to the variable(s) you are studyingSampling only students in the library when asking how much they study, or sampling only students taking a statistics class“Today’s Poll” on fitnessmagazine.com asked “Have you ever hired a personal trainer?”. 27% of respondents said “yes” – can we infer that 27% of all humans have hired a personal trainer?
27Bad Methods of Sampling Letting your sample be comprised of whoever chooses to participate (volunteer bias)ing or mailing the entire population, and then making conclusions about the population based on whoever chooses to respondExample: An airline s all of it’s customers asking them to rate their satisfaction with their recent travel
28Road SafetyThe Federal Office of Road Safety in Australia conducted a study on the effects of alcohol and marijuana on performanceParticipants were volunteers who responded to advertisements for the study on rock radio stationsVolunteers were given a random combination of the two drugs, then their performance was observedWhat is the sample? What is the population?Is there sampling bias?Will the results be informative and/or do you think the study is worth conducting?
29Data Collection and Bias Sampling Bias?PopulationSampleOther forms of bias?DATA
30Other Forms of BiasEven with a random sample, data can still be biased, especially when collected on humansOther forms of bias to watch out for in data collection:Question wordingContextInaccurate responsesMany other possibilities – examine the specifics of each study!
31Question Wording“Do you think the US should allow public speeches against democracy?”“Do you think the US should not forbid public speeches against democracy?”Source: Rugg, D. (1941). “Experiments in wording questions,” Public Opinion Quarterly, 5,21% said speeches should be allowed39% said speeches should be not be forbidden
32Question WordingA random sample was asked: “Should there be a tax cut, or should money be used to fund new government programs?”A different random sample was asked: “Should there be a tax cut, or should money be spent on programs for education, the environment, health care, crime-fighting, and military defense?”Tax Cut: 60% Programs: 40%Tax Cut: 22% Programs: 78%
33Context “If you had it to do over again, would you have children? Ann Landers column asked readers“If you had it to do over again, would you have children?The first request for data contained a letter from a young couple which listed worries about parenting and various reasons not to have kids=> 30% said “yes”The second request for data was in response to this number, in which Ann wrote how she was “stunned, disturbed, and just plain flummoxed”95% said “yes”
34Having ChildrenIf we were to run the question all by itself in the newspaper with a request for responses, could we trust the results?YesNo
35Having ChildrenNewsday conducted a random sample of all US adults, and asked them the same question, without any additional leading material91% said “yes”Do you think the true proportion of parents who are happy they had children is close to 91%?(a) Yes(b) No
36Inaccurate ResponsesIn a study on US students, 93% of the sample said they were in the top half of the sample regarding driving skillSvenson, O. (February 1981). "Are we all less risky and more skillful than our fellow drivers?". Acta Psychologica 47 (2): 143–148.From random sample of all US college students, 22.7% reported using illicit drugs. Do you think this number is accurate?Substance Abuse and Mental Health Services Administration (2010). “Results from the 2009 National Survey on Drug Use and Health: Volume 1.” Summary of National Findings (Office of Applied Studies, NSDUH Series H-38A, HHS Publication No. SMA Findings). Rockville, MD, heeps://nsduhweb.rti.org/
37SummaryData is collected on a sample, and we would like to use the data to make inferences to the larger populationSampling bias can occur when the sample does not resemble the populationSampling bias can be avoided by random samplingBias exists when the sample data do not accurately reflect the true population data, and bias can occur in many waysWhen making conclusions based on data, STOP AND THINK ABOUT HOW THE DATA WERE COLLECTED!
38SummaryAlways think critically about how the data were collected, and recognize that not all forms of data collection lead to valid inferences
39To Do Complete the class survey on Sakai (due Monday, 1/23) me if you still need a textbookme with your gmail adress if you still need an RStudio accountBuy a clicker (grading starts 1/30)(go to this google doc if you want to buy one used from a previous student)