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Key Issues of Survey Sampling

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Questions: 1. What is survey? 2. Do you believe in survey? (why) 3. What is population (collection of interest of objects) 4. What is difference in finite and infinite population? 5. Relation between sample and population. 6. Criteria for representative sample 7. What is sample statistic and sampling distribution? 8. What is standard error? 9. What is effect of sample size? 10. How to determine sample size? 11. How you can improve quality of estimates? Important points
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  Questions: 1.   What is survey? 2.   Do you believe in survey? (why) 3.   What is population (collection of interest of objects) 4.   What is difference in finite and infinite population? 5.   Relation between sample and population. 6.   Criteria for representative sample 7.   What is sample statistic and sampling distribution? 8.   What is standard error? 9.   What is effect of sample size? 10.   How to determine sample size? 11.   How you can improve quality of estimates? Important points for survey sampling 1.   Survey is a technique of observing a population for getting knowledge about population. Other technique is to perform experiment. 2.   Variation in any characteristic may be represented through distribution 3.   Histogram is simplest tool to understand distribution 4.   Histogram can be summarized in terms of parameters like mean, variance etc. In other words parameters help in determining distribution. Parameters are characteristics of population and supposed to be constant. 5.   Statistic (function of sample value like sample mean) of representative sample can give estimate of population. In other words, Statistic is numerical quantity which can be calculated on the basis of sample. 6.   The observed value of statistic depends on the particular sample; hence it varies from sample to sample. Such variability is called sampling variability. 7.   Mechanism to draw sample is called sampling. Samples may be drawn by using mechanism based on probability or based on convenience or based on purpose. Sample drawn through mechanism based on probability is called probability sampling. In probability sampling, every unit of population has definite probability to be included (may not be equal) in sample. 8.   Variation in sample trial can be measured by variation in sample statistic. 9.   Variation in sample statistic can be estimated through distribution of statistic (Sampling Distribution). 10.   More representative sample should have lesser bias and variance 11.   Mean of sample statistic gives information about sampling bias while variance of statistic gives information regarding quality of the estimate. 12.   Mathematical formula of sampling distribution of particular statistic is important for understanding logical nature of sampling bias and variance.  13.   Central limit theorem provides mathematical formula for sampling distribution of sample mean and proportion. 14.   The Central Limit Theorem describes the characteristics of the population of the means which has been created from the means of an infinite number of random population samples of size (n), all of them drawn from a given parent population . The Central Limit Theorem predicts that regardless of the distribution of the parent population:    The mean of the population of means (or sample mean) is always equal to the mean of the parent population from which the population samples were drawn.    The standard deviation of the population of means is always equal to the standard deviation of the parent population divided by the square root of the sample size (n).    The distribution of means will increasingly approximate a normal distribution as the size (n) of samples increases. 15.   Standard error is standard deviation of sampling statistic. 16.   There are many type of sampling technique. The most basic sampling technique is simple random sampling (SRS) (with or without replacement). 17.   Systematic sampling is a statistical method involving the selection of elements from an ordered sampling frame. The most common form of systematic sampling is an equal-probability method. 18.   A stratified sample can provide greater precision than a simple random sample of the same size. 19.   The main disadvantage of a stratified sample is that it may require more administrative effort than a simple random sample. 20.   All stratified sampling designs fall into one of two categories, each of which has strengths and weaknesses as described below.    Proportionate stratification:  With proportionate stratification, the sample size of each stratum is proportionate to the population size of the stratum. This means that each stratum has the same sampling fraction. Proportionate stratification provides equal or better precision than a simple random sample of the same size. Gains in precision are greatest when values within strata are homogeneous. Proportionate stratification provide estimate for population but not for stratum.    Disproportionate stratification . With disproportionate stratification, the sampling fraction may vary from one stratum to the next. If variances differ across strata, disproportionate stratification can provide better precision than proportionate stratification. Explain following statements (1)   Standard deviation of sample median is larger than standard deviation of sample mean (1.3 times) for normal distribution. (2)   It is difficult to derive mathematical formula for sampling distribution of median for non-normal distribution. (3)   Proportion can be treated as mean with certain restriction. (4)   (.43, .53) is interval such that we may be reasonably confident that there is 95% chance that population proportion is in that interval. Exercises  1.   Arrange following activities in Survey Design in sequence i)Data collection, ii) Questionnaire design, iii) Objectives, iv) Framing Questions, ii) Sampling design, iv) Preparation of data processing system v) Pilot test of questionnaire (1 mark) 2.   What is the Difference between survey and experiment? (2 Marks) 3.   Which are the part of metadata? ( 1 mark) i)age of respondent, ii) Questionnaire ID, iii) Investigator name iv) Land possessed by the household 4.   What is the concept of Hung question in a questionnaire? ( 1 mark) 5.   What is drawback of proportionate stratification? (2 marks) 6.   What is standard error of sample statistic? How standard error of sample mean is related with population variance and sample size. (2 marks) 7.   From population containing 1000 people, a sample of 5 people has been drawn by using Simple Random Sample (SRS) with replacement for estimating the average age of population. Age of person in sample has been given as (21,25,31,24,26). calculate 95% confidence interval for the estimate. (Hint calculate sample mean, SD, SE. Marks will be given on each step). (6 marks) Ans: sample mean: 25.4 Sample SD: 13.3 St. error: 1.6 CI: (22.2,28.6) References 1.   Sampling distributions 2.   Simple random sample vs Stratified sample 3.   Sample design 4.   Online book on statistics 
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