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Experiments and Sampling

by: Jacinto Carter Sr.

Experiments and Sampling STA 3313

Jacinto Carter Sr.
GPA 3.79


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This 11 page Class Notes was uploaded by Jacinto Carter Sr. on Thursday October 29, 2015. The Class Notes belongs to STA 3313 at University of Texas at San Antonio taught by Staff in Fall. Since its upload, it has received 26 views. For similar materials see /class/231435/sta-3313-university-of-texas-at-san-antonio in Statistics at University of Texas at San Antonio.

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Date Created: 10/29/15
STA 5313STA3313 Theory of Sample Surveys with Applications Summer 2007 Chapterl Introduction Lecture 1 Statistics Statistics is a branch of science that deals with collecting organizing and display of data It also deals with how to draw inference or conclusions re garding the population based on the information contained in a sample Statistics originated as an accessory to the Government The systematic study of data now has in ltrated most areas of academic and practical endeavor Examples 1 Bureau of Labor Statistics Reports unemployment rates such as 65How did the govern ment arrive at this number What does this number mean 2 Consumer Price Index CPI Over 20 surveys are conducted to come up with the CPI 3 Opinion Polls 0 Gallop Poll Predict election results 0 Harris Poll Predict election results 0 CBS New York times Poll Predict election results 0 Neilsen Rating Estimates TV ratings These opinion polls re ect the attitudes and opinions of people on various issues 4 Business and Marketing Questions such as Which products to market Where to market How to advertise There are rms which conduct surveys and information may be purchased from them on such questions Examples of such rms are l Neilsen Retail lndex Furnishes data on products such as foods cosmet ics pharmaceutucals beverages etc 2 SAMl Selling Area Marketing INC Collects information on movement of products from warehouses and Wholesalers 3 Market Research Corporation of America Provides many types of mar keting data based on surveys Applications of Sample Surveys are in Social studies Opinion polls Health Sciences etc For some interesting examples see 7 Statistics A Guide to the Unknown Three Elements of Statistical Study 1 Collecting Data Sample Surveys and Sampling 2 Describing and Presenting Data Graphical and Numerical descriptions 3 Drawing Conclusions from Data Inference estimation and test of hypoth esis Some de nitions Population The collection of all possible units of interest in any given study is called population A sample should be a scaled down version of the population mirroring every characteristic of the Whole population It should be representative of the units of the population Sample Any subset of a population is called a sample Census or Total Enumeration When data is collected on every unit of the population it is called a census Ideally we obtain the best results from a census But census may not be the best thing to do Reasons for Sampling H Cost Census can be costly specially when collecting data on every unit is expensive 3 Time Census can be very time consuming 3 Unmanagable Too much data to manage requires large body 0 f personnel 4 Impractical In some applications destructive experiments such as those involving fuses light bulbs amunitions census can be impractical Summary 1 The use of a sample reduces cost time and waste 2 Sample surveys produce summary statistics 3 Summary statistics produce estimates of population values parameters such as Mean Variance Proportions Totals etc 4 Estimation of parameters is the main goal of sample surveys Types of Samples 1 Convenience Sample Selection of easily accessible units is called a con venience sample It is not a good sample and can not be used for statistical inference 2 Probability Sample A sample is a probability sample if it is based on a planned random criterion Every possible sample has some probability 138 associates with it of being selected An Example Simple Random Sampling If N is the population size and n is the sample size then in a simple random sampling every one of the N07 samples has the probability of N10 of being selected Most Common Probability Samples Probability samples to be consid ered in this course are 1 Simple Random Sampling 2 Strati ed random Sampling 3 Systematic Sampling 4 Cluster sampling 5 Quota Sampling This Course is mainly concerned with 1 Discussion of various sampling designs 2 Use the information collected to construct estimates for the parameter such as the Mean Proportion Total etc 3 Determine the sample size needed to estimate a parameter with a pre assigned precision or accuracy and cost 4 Comparison of various sampling designs in terms of precision 5 Designing Sample surveys 6 Sampling and non sampling errors Some More De nitions Observational Unit An object on which a measurement is taken is called an observational unit This is the basic unit for observation called element Examples 1 In human studies basic units are people 2 ln census basic units are households 6 3 ln length of life studies basic units are Light Bulbs Target Population The complete collection of observations that we want to study is called the target population It should be carefully determined not easy to identify but very important For example in political polls which of the following is the target population 1 All eligible voters 2 All registered voters 3 All those who voted in the last election The choice of the target population affects the statistical results Sampled Population The population from which the sample is chosen is the sampled population It is the collection of all observational units that might have been chosen in the sample Sampling Unit The unit we actually sample such as the household light bulbs individuals departmental store hospitals etc are called sampling units Sampling Frame The list of units from which samples are selected is called sampling frame Examples 1 List of all residential phone numbers in a city 2 List all residential street addresses 3 List of all agricultural farms 4 List of all hospitals in a county Ideally the sampled population should be identical to the Target population However in reality Sampled Population Q Target Population Some Biases Selection Bias If some part of the target population is not in the sampled population a bias called Selection Bias occurs For example in a survey to estimate per capita income if transient people are ignored estimate will be biased upward Convenience samples haphazard samples and the judgement samples result in selection bias Reasons for Selection Bias 1 Mis speci cation of the target population 2 Failure to include the Target Population in the Sampling Fiame also called undercoverage 3 Substituting a convenient member of a population for a designated mem ber not readily available 4 Non Response Failure to obtain responses from all those chosen in the sample distorts the results of a survey typically non respondents differ from the respondents in some pronounced way 5 Allowing a sample to consist entirely of volunteers Radio TV or call in polls Note that large samples are generally considered good but if the sample is unrepresentative it can be quite bad it The design of the survey is far more important than the absolute size of the sample Measurement Bias Measurement bias occurs when the measuring instrument has a tendency to reord in one direction more often than the other It must be minimized in the design stage For example decide whether the plants on the boundary are to be counted Measurement biases are more common when dealing with people due to fol lowing reasons Reasons for Measurement Bias 1 People may not tell the truth 2 Lack of understanding of questions 3 Lack of proper account of events in memory 4 Variations in responses due to interviewers 5 Misreading questions or miss recording responses 6 Desire to impress the interviewer 7 Ordering and wording of questions have effects on responses Many of these problems can be avoided by proper questionnaire design Questionnaire Design This is a very important step in conducting any survey Important Steps 1 Precise statement of goals of the survey Pose precise questions consistent with the goals design questionnaire to address these aspects 2 Test Questions Test questions before sending out the questionnaire Helps in understanding various possible interpretations of the questions 10 1 3 H 0 m 51 00 0 Keep the questions Simple and Clear Questions should be neither too lengthy nor too technical They should be easily understood by non experts Questions should be speci c and not general Open versus Closed questions Closed questions with well thought and researched categories elicit more accurate responses Open Question A question is open when no speci c response cate gories are provided Closed Question A question is closed when speci c response cate gories are provided Report the actual question asked Avoid leading or loaded questions These are questions that prompt or motivate the respondent to say What investigator wants to hear Use choices rather that Agree Disagree type questions Ask only one concept in one question Pay attention to question order effect Ask general questions rst then follow with speci c questions


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