Chapter 1 - Sampling and Experimental Design

1 Chapter 1 - Sampling and Experimental DesignRead sections - ( and ) Sampling Plans: methods of selecting individuals from a population. We are interested in samplingplans such that results from the sample can be used to make conclusions about the Samples: Bias occurs when the sample tends to differ from the population in a systematicway. When this happens, results from the sample can not be used to make conclusions about thepopulation of Sample- An \easily available" sample of individuals which was convenient forthe researcher to collect. This is aBADsampling plan since the individuals in the conveniencesample may systematically differ from the population and therefore may not represent the Response Sample- A sample of individuals who volunteer to participate. Thisis aBADsampling plan since the individuals who volunteer may systematically differ from thepopulation and therefore may not represent the entire of Bias in Sampling : Selection Bias- The Sampling plan excludes some part of the population from the selectionprocess.

2 Those excluded from the selection process systematically differ from those :{Phone surveys exclude (1) households without a phone, (2) prisoners, and (3) homelesspeople.{Call-in polls on TV exclude (1) individuals without a TV, (2) individuals not watching theprogram, and (3) individuals who do not care to participate Measurement/Response Bias- The method of observation tends to produce measurementsthat differ from the true value of the :{uncalibrated scale{untrained or ill-trained technician{wording of a survey or interviewer in uence Non-response Bias- Data is not obtained from all individuals in the sample. This bias occurswhen those who respond systematically differ from those who do not :{Telephone and mail surveysIMPORTANT POINTS to remember: A biased sample is a biased sample, regardless of its size! Collecting more data in a biased fashionwill not correct the A biased sample still contains information about a population, but this population is not the onethat a researcher is interested in!}}}}}}

3 Information can still be gleaned from biased samples, but onemust be wary of the :{Drug trials using human volunteers{Studies on animals which have been speci cally bred for experimentsQUESTION: What type of sample and bias?A researcher is interested in the opinions of MSU students about updating gymequipment. A surveyor stands at the gym entrance door and uses the next 50 peoplewho enter as a sample and asks each their opinion about updating gym Sampling : A sample of individuals who have been chosen randomly from the samples tend to represent the population from which they are chosen since randomizationdoes not systematically favor some individuals in the population over random samples are representative of the population of interest, then inferenceis valid. In otherwords, results from a random sample can be generalized to make conclusions about the Sampling can be done: With replacement, which means that after an individual is selected to be the sample, thatindividual can potentially be selected into the sample again.}}

4 This method needs to be used whenthe sample sizenis more than 5% of the population size, 20n>N, whereNis the populationsize. Without replacement, which is much more commonly used, is where once an individual isselected to be in the sample, that individual may not be selected again. Therefore, the sampleconsists ofndistinctindividuals. This method is used when the population size is in nite; orif the population size isN, and the sample sizenis no more than 5% of the population size,20n :With or without Replacement? Sampling a 5 card hand from a standard deck of 52 playing Sampling 2000 Montanans:2 Types of Random Random Sample (SRS)- Each possible sample of sizenhas an equal chance of beingselected from the population. How to Select a SRS:{Put slips of paper in a hat, mix well, then choosenslips.{Use a computer:(a)Create asampling frame, a numbered list of all individuals in the population.}}

5 (b)Use arandom number generatorto select individuals from the ed Random Sample- Separate the population into non-overlapping homogeneousgroups, calledstrata. Take a SRS from each strata, then combine the SRSs to form the strati edrandom sample. Stratifying is bene cial if the population consists of strata that differ in regards to thevariable of interest. Usually,ni, the size of the SRS from each strata, is proportional toNi, the size of the stratawithin the :Give an example of a study for which stratifying would be Sample- If the populationnaturallyconsists of non-overlapping groups, calledclusters,where each cluster is heterogeneous ( it represents and re ects the variability in the population)then a SRS of clusters can be drawn. All individuals in the selected clusters form the :(a)There are about 20 sections of STAT 216 offered at MSU each semester. Howwould you use cluster Sampling to choose a sample from all STAT216 students?

6 (b)What are the two main differences between a strati ed random sample and acluster sample? Sample- Select everykthindividual from the numbered population list. This workswell only if: the variable of interest is not related to the order of the list or the variable of interest is related to the list's order, but not in a cyclic : Would Systematic Sampling Work Well?(a)A Phonebook:(b)Husband/Wife Listing:1. husband 2. wife 3. husband 4. wife and Experimentation( and )Observational Study: A study which observes individuals and measures variables, but does notattempt to in uence the responses. An observational study on individuals from a random sample allows one to generalize conclusionsabout the sample to the population. An observational study cannot showcause-and-effectrelationships because there is thepossibility that the response is affected by some variable(s) other than the ones being is,confounding variablesmay be present.

7 \It ain't what you don't know that gets youinto trouble. It's what you know for sure that just ain't so." - Mark Twain Inprospectiveobservational studies, investigators choose a sample and collect new datagenerated from that sample. That is, the investigators \look forward in time." Inretrospectiveobservational studies, investigators \look backwards in time" and use datathat have already been collected. Retrospective studies are often criticized for having moreconfounding and bias compared to prospective : Prospective or Retrospective Observational Study? study that follows marijuana users in Colorado for 5 study of illegal immigrant activity last year in : A study in which treatment(s) are deliberately imposed on individuals in order toobserve their response. An experiment in which the treatments are randomly assigned to individuals can provide evidencefor acause-and-effectrelationship.

8 Furthermore, if the individuals are from a random sample,then one can generalize conclusions from the experiment to the recognize the difference between an Observational Study and an Experiment, ask yourself, \Wasthere a treatment imposed on the individuals?" In an experiment, the researcher determines (randomly)which individuals receive which treatment. In an observational study, the individuals have already self-chosen their : Observational Study or Experiment? study of the birth weight of babies and the mother's level of coffee study of lab mice whose spinal cords have been study of gender versus study of grizzly bear study of the number of 1's rolled on a weighted Variable: A variable that is related to the response variable and to the explanatoryvariable in such a way that makes it impossible to distinguish the effects of the confounding variableon the response from the effects of the explanatory variable on the : In a study of gender differences in salary, it was found that female nurses (in a certain hospital)have higher salaries, on average, than do male nurses.

9 It also was found that female nurseshave a greater number of years of experience than do male of experienceis aconfounding variable. It may be that the data give no clue as to whether the salary difference isdue to gender discrimination or due to years of experience. In a study investigating the association between the occurrence of low birth weight babies andthe mother's level of coffee consumption, it was found that an increase in the mother's coffeeconsumption is associated with an increase in the risk of having a low birth weight baby. It alsowas found that moms who smoke also consume large amounts of coffee and moms who do notsmoke consume no or small amounts of a confounding variable. Are the lowbirth weights due to the smoking or the coffee? CAN'T TELL!Principles of Experimental Design ( ) Experimental Designs: methods of assigning treatments to individuals (units or cases)Unit: an individual in an experimentSubject: a human Experimental unitFactor: a categorical explanatory variableTreatment: a combination of levels of factorsExtraneous Factor: a factor that is not of primary interest and yet affects the response variable.

10 Anextraneous factor is called a confounding variable if its effect on the response cannot be distinguishedfrom the effect of another factor on the goal of an experiment is to determine the effects of factor(s) on the response while taking intoaccount extraneous factors that also affect the Group: a group that receives no treatment (or aplacebo). The response of the treatmentgroup is compared to the response of the control group to determine effectiveness of the : a treatment that has no active ingredients (a fake treatment). A placebo is supposedto resemble the real treatment as far as appearance, taste, and feel so that subjects believe theyare receiving the true treatment. Use of a placebo mitigates \the power of suggestion." That is, atreatment, when thought to be bene cial, tends to positively affect responses (and a non-bene cialtreatment tends to negatively affect responses).