Lesson 1 Designing Samples Populations Sample Then entire group of individuals about which information is wanted May be somewhat abstract The part of the population actually examined to gather information More concrete and immediate than the population Example Identify the population and the sample in the following current term Population all undergraduates at the university Sample those undergraduates surveyed A survey is carried out at a university to estimate the proportion of undergraduates living at home during the In 2005 investigators chose 400 teachers at random from the National Science Teachers Association list and polled them as to whether or not they believed in biblical creation hypothetical scenario 200 hundred of the teachers sampled responded Population National Science Teachers Association members Sample the 200 respondents A balanced coin is flipped 500 times and the number of heads is recorded Population all coin flips Sample the 500 coin flips Any sample taken should be selected at random otherwise it may be prone to bias Bias The systematic favoring of certain outcomes Ex people who volunteer for a treatment may bias results toward conclusions that the treatment offers an A sample should be selected using some probability sampling design which gives each individual or participant a improvement over a current treatment chance of being selected Four common probability sampling schemes Simple Random Sampling SRS A simple random sample of size N consists of N individuals from the population chosen in such a way that every set of N individuals has an equal chance of being selected Stratified Random Sampling The population is divided into important subgroups e g East and West Freshmen Sophomore Junior Senior which are groups of individuals or subjects that are similar in a way that may affect their response think of stratifying a university s undergraduate population by race gender or nationality Then separate simple random samples are taken from each subgroup These subgroups are called strata This is done to be sure every important subgroup is represented properly in the overall sample which will enhance the efficiency of this design Cluster Sampling The population is divided into several subgroups by geographic proximity or closeness of individuals to each other on a list These subgroups are called clusters Then some clusters are randomly picked to be in the sample There may be further random sampling of individuals within the selected clusters For instance for an on campus survey we might randomly pick a few dorms and only include some or all of the students from those dorms in the survey Cluster sampling differs from Stratified sampling in that Cluster sampling is not initially concerned with similarities among the individuals However once the clusters are created one may have to account for any possible similarities In stratified sampling we create the subgroups based on some criteria ethnicity geographic region and then random sampling of individuals or subjects is done In Cluster sampling clusters of individuals or subjects are randomly sampled Multistage Sampling Selects successively smaller groups from the population ending with clusters of individuals Most opinion polls are done in stages For example you may start by splitting your home state into regions Then stratify within each region by rural suburban and urban From these strata you would randomly select some communities from which these would be divided by some fixed area think by city blocks i e clusters Finally within these clusters all individuals would then be sampled Taking a SRS is sampling without replacement meaning that once a participant is selected this subject is not returned to the population to possibly again be selected Think of choosing sides for team You are a captain and your friend is a captain Once you choose a player that player is not returned to the pool of players to be selected again they are on your team Since we are taking samples from some population sample results can vary from sample to sample For example consider Gallup Poll conducting an election survey they run varies polls leading up to election day and the results of these polls can often differ one poll says that 48 of those registered to vote will select Person A then a follow up poll has this percentage at 45 and so on Since the people differ from sample to sample i e unlikely that the samples contain the exact same subjects we have error in sampling That is the sample result doesn t exactly match the actual real result e g on election day maybe the real percentage is 47 5 When conducting a sample survey we can calculate a conservative margin of error Conservative margin of error 1 n is size of the sample Ex Sample size of 100 n 100 1 100 1 10 0 10 or 10 This is the number in reported survey results Ex 48 of people polled said they would vote for Person A 3 This means the poll had a margin of error of 3 and that the polling agency estimates the real i e population percentage to be from 45 to 51 Confidence Interval Interval for which on can be confident contains the correct proportion of the population Ex 48 of people polled said they would vote for Person A 3 We can be confident that the actual proportion of the population that would vote for Person A is between 45 to 51 This conservative margin of error is based on a 95 level of confidence Designing Experiments Example Suppose some group claims that drinking caffeinated coffee causes hyperactivity college students ages Select some subset of college students of ages 18 to 22 and find their intake of caffeinated coffee 18 to 22 How would this group produce data to determine the validity of this statement Observational study as opposed to experiment A part of the population is sampled and examined in order to gain information about the population This is not an experiment because no treatment was imposed Unfortunately lurking variables can easily lead to unreliable results e g other dietary intake stress Give caffeinated coffee to a randomly sampled group of college students over a period of time and observe their family history behavior Experiment Treatment is imposed the caffeinated coffee This design would be an improvement over the observational study in that we can better pin down the effects of the explanatory variable intake of caffeinated coffee Experimental units The subjects on which an experiment is performed are called If they are people we call them