Slide 1Example to think aboutSlide 3Slide 4Slide 5Test 1Practice ProblemsAdditional Reading and ExamplesSlide 9Sampling ProceduresRepresentative SampleBiasSelection BiasNonresponse BiasResponse BiasHaphazard SamplesVolunteer Response SampleBiasRandom SamplesSimple Random SamplingSimple Random SamplingSimple Random SamplingSlide 23Table of Random DigitsSlide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Simple Random SamplesExample 3Example 3Slide 35Example 3Example 3Example 3Stratified Random SamplingStratified Random SamplingStratified Random SamplingStratified Random SamplingStratified Random SamplingStratified Random SamplingStratified Random SamplingStratified Random SamplingStratified Random SamplingStratified Random SamplingStratified Random SamplingStratified Random SamplingSlide 51Multistage Random SamplingMultistage Random SamplingMultistage Random SamplingMultistage Random SamplingMultistage Random SamplingMultistage Random SamplingMultistage Random SamplingMultistage Random SamplingMultistage Random SamplingMultistage Random SamplingSlide 62Multistage Random SamplingMultistage Random SamplingMultistage Random SamplingMultistage Random SamplingMultistage Random SamplingMultistage Random SamplingMultistage Random SamplingMultistage Random SamplingExample 4Example 4Example 4Example 4Example 4Example 4Example 4Example 4STAT 210Lecture 4SamplingSeptember 1, 2017Example to think aboutOf interest is to determine the proportion of all public buildings in Pittsburgh, Pennsylvania that have central air conditioning.What is the population of interest?What is the parameter of interest?Of interest is to determine the proportion of all public buildings in Pittsburgh, Pennsylvania that have central air conditioning.What is the population of interest?(A)All buildings(B)All public buildings(C)All public buildings in Pittsburgh, Pennsylvania(D)All public buildings in Pittsburgh, Pennsylvania with central air conditioningOf interest is to determine the proportion of all public buildings in Pittsburgh, Pennsylvania that have central air conditioning.What is the population of interest?All public buildings in Pittsburgh, PennsylvaniaWhat is the parameter of interest?Of interest is to determine the proportion of all public buildings in Pittsburgh, Pennsylvania that have central air conditioning.What is the population of interest?All public buildings in Pittsburgh, PennsylvaniaWhat is the parameter of interest?The proportion of all public buildings in Pittsburgh, Pennsylvania that have central air conditioning.Test 1Friday, September 8Questions from 1:00 to 1:10Test from 1:10 to 1:50 – papers due at 1:50!Covers chapters 1 and 2 (pages 1 – 42)Combination of multiple choice questions anda few written questions.Practice tests posted on Blackboard.Practice ProblemsPages 38 through 42Relevant problems: II.2 – II.6 Recommended problems: II.2, II.5 and II.6Additional Reading and ExamplesPages 26 through 29Top HatSampling ProceduresWe select a sample of the population and only measure (or contact) the subjects in the sample.Representative SampleThe sample should be as representative of the population as possible, meaning that the characteristics of the sample should mimic the characteristics of the population.BiasBias exists when some subjects or individuals are systematically favored over others. A sample which is representative of the population should be free of bias. If the sample is not representative, then the results will be biased in favor of the responses of those which are over-represented.Selection BiasSelection bias occurs when one or more types of subjects are systematically excluded from the sample.Nonresponse BiasWhen an individual randomly chosen to be a part of the sample cannot be contacted or fails (or refuses) to respond, then we have a nonresponse bias.Response BiasWhen respondents give inaccurate information or if the interviewer influences the subject to respond in a certain way due to the way the questions are phrased, this is response bias.Haphazard SamplesA haphazard sample involves selecting a sample by some convenient mechanism that does not involve randomization.A mall survey in which questionnaires are distributed to people as they walk through the mall, or a campus survey in which students are questioned as they walk across campus are twoexamples of haphazard samples.Volunteer Response SampleA volunteer response sample exists when subjects volunteer to be part of the study. Examples include telephone call-in polls, internet surveys, newspaper surveys, call in talk-show surveys, etc.The problem with volunteer response samples is that often those who choose to respond often have strong opinions, most often negative opinions, and hence volunteer response samplesover-represent those with strong opinions.BiasHaphazard and volunteer response samples are particularly prone to bias, particularly nonresponse bias.Random SamplesSamples in which the subjects are chosen randomly to be in the sample are often representative of the population and are, for the most part, free of bias.When each subject of the population has a positive and equal probability of being selected for the sample, then we are using a probability sampling design to select our sample. This will reduce (or eliminate) bias.Simple Random SamplingWith simple random sampling we make a list of all possible individuals in the population and randomly choose n of the subjects in such a way that every set of n subjects has an equal chance of being selected for the sample. This procedure is impartial, meaning the interviewer has no discretion as to whom is to be included in the sample.Simple Random Sampling1. Label the individuals in the population from 1 to N.Examples:1. N = 8 Label 1, 2, 3, … , 82. N = 80 Label 01, 02, 03, … , 79, 803. N = 636 Label 001, 002, 003, … , 635, 6364. N = 2198 Label 0001, 0002, 0003, … , 2197, 2198Simple Random Sampling1. Label the individuals in the population from 1 to N.2. Use a Table of Random Digits, like on page 337, to randomly select a sample of n numbers between 1 and N. These numbers correspond to the individuals who are selected to be in the sample.Table of Random DigitsLine101 03316 88692 53340 64121 93600 58636 08900 12724102 81868 52573 87151 50490 84552 49367 46816 24178103 95761 90056 04312 31893 02384 16925 90656 53372104 51025 36290 18132 02938 02150 88741 55300 12428105 11937 82853 31685 11486 59505 35119 57067
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