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2. 2. • The tendency of the casual mind is to pick out or stumble upon a sample which supports or defies its prejudices, and then to make it the representative of a whole class. –Walter Lippmann
3. 3. Sampling • A population is the aggregate of all the members of a defined group that is being studied. • A census involves collection of from every member of the population being studied
4. 4. • A sample is a group of people, objects, or items taken from a larger population as a representative of the population for measurement and generalizing the findings to the population as a whole
5. 5. Sampling Design Process
6. 6. Select a Sampling Technique • Bayesian Versus Traditional approach • Sampling with or without replacement • Nonprobability Versus probability sampling
7. 7. Sampling Techniques Convenience Sampling Non-Probability Sampling Purposive Sampling QuotaSampling Sampling Techniques Snowball Sampling Simple Random Sampling Probability Sampling Systematic Sampling Stratified Sampling Area Sampling Cluster Sampling Double Stage Sampling Sampling With Probability Proportional To Size
8. 8. Convenience: • Convenience sampling is done based on ease of selection of sample. The samples are chosen simply because they were the most convenient to choose.
9. 9. Purposive Sampling • For purposive sampling, the researcher chooses the sample based on who they think would be appropriate for the study.
10. 10. Quota Sampling • Under quota sampling the samples are selected in quotas from different strata.
11. 11. Snowball Sampling • Snowball sampling is non-probability sampling technique where existing samples elements recruit future sample elements from among their acquaintances
12. 12. Simple Random Sampling • Simple random sampling is defined by two properties. First, each member of the population has an equal and known probability of being selected in the sample. Second, each combination of members of the population has an equal chance of forming the sample.
13. 13. Systematic Sampling • Systematic sampling is also called as Interval sampling. The sample is chosen by selecting a random starting point and then picking every ith element in succession from the sampling frame.
14. 14. stratified sampling • For stratified sampling, the population is divided into homogeneous groups called Strata. The strata should be mutually exclusive and collectively exhaustive. Independent samples are selected from each stratum
15. 15. Cluster Sampling • In cluster sampling the target population is first divided into subpopulations called clusters. The clusters are mutually exclusive and collectively exhaustive subpopulations. A random sample of clusters is selected, using probability sampling techniques.
16. 16. • If clusters are geographic subdivisions, then the cluster sampling is also referred to as area sampling. In case the cluster sampling units do not have the same or approximately same number of elements, then each cluster being included in the sample is selected randomly such that the probability of selection is proportional to the size of the cluster. This type of cluster sampling is called Sampling with probability proportional to size.
17. 17. Selection of Non-probability versus probability sampling Selection of non-probabilityversus probability samplingtechnique depends on many factors. Some key conditionsin favor of probabilityand non- probability samplingare discussed in below table: Selection Criteria Favor Non-Probability Sampling Favor Probability Sampling Type of Research QualitativeResearch Quantitative Research Relativemagnitudeof Sampling and Non sampling error Non sampling error is larger Samplingerror is larger Population Homogeneity High Low Statistical Considerations Unfavorable Favorable Operational Considerations Favorable Unfavorable Time Availability Low High Budget Low High
18. 18. Question for Discussion • In order to survey the opinions of its customers, a restaurant chain obtained a random sample of 30 customers from each restaurant in the chain. Each selected customer was asked to fill out a survey. Which one of the following sampling plans was used in this survey? – Cluster sampling – Stratified sampling
19. 19. Online Sampling Techniques • Internet surveys provide an easy and cost effective method of survey. The online survey can also provide a much better user experience while answering the questions than printed questionnaires.
20. 20. • BREAK
21. 21. Important terms and symbols • Sample Statistic: A sample statistic is a summary description of a characteristic or measure of the sample. The sample statistic is used as an estimate of the population parameter. • Population Parameter: A population parameter is a summary description of a fixed characteristic or measure of the entire target population. A population parameter indicates the true value which would be obtained if a census was done instead of a sample survey.
22. 22. • Descriptive statistics: The statistics that describe basic characteristics and summarize the data in a straightforward and understandable manner. • Inferential statistics: The statistics which is used to make inferences or generalize results from a sample to an entire population
23. 23. • Proportions: A proportion denotes the percentage of population elements that successfully meet some criteria related to a particular characteristic. A proportion may be expressed as a percentage (20%), a fraction (1/5), or a decimal value (0.20) • Mean: The mean is the arithmetic average. Researchers generally wish to know the population mean µ
24. 24. Sampling Distribution • The sampling distribution is a distribution of a sample statistic calculated for each sample that can be possibly drawn from the target population
25. 25. For infinite population, sample size for means is calculated as: For finite population sample size for means is calculated as:
26. 26. Sample Size • A researcher wants to estimate the population mean of P/E ratio for all stocks listed on National Stock Exchange with 99 per cent confidence. Suppose the sample standard deviation of P/E ratios for stocks listed on the NSE is s = 6.5. How many stocks should be included in the sample if margin of error of 2 is desired?
27. 27. For infinite population, sample size for proportions is calculated as: For finite population sample size for proportions is calculated as: For finite population, sample size for means for a stratified sample is calculated as:
28. 28. • A warehouse received a shipment of returned glass bottles. These bottles are to be sampled to estimate the proportion that is unusable. From past experience, the proportion of unusable bottles is estimated to be 10 per cent. How large a random 2 2 2 =(2.576) (6.5) /(2) =70.09 sample should be taken to estimate the true proportion of unusable bottles to within 7% with 90 per cent confidence?
29. 29. It is given that e= 0.07, 0.10, Confidence level= 90% α/2 = 1.645 at 90 per cent confidence level Using the formula for n and substituting the given values, we have 2(0.10*0.90) / (0.07)2 = 49.7025 n= (1.645)
30. 30. Question • For a population of 900, what should be the sampling size necessary to estimate the populatin mean at 95 per cent confidence with a sampling error of 5 and the standard deviation equal to 15?
31. 31. Discussion Question • A survey is carried out at a university to estimate the percentage of undergraduates interested in hostel accommodation during the current year. The university's registrar keeps an alphabetical list of all undergraduates, undergraduates registered in the year during which this research is conducted. Someone proposes to choose a number at random between one and one hundred, count that far down the list, then take that name and every hundredth name after it for the sample.
32. 32. – What will the sample size be? – Is this a probability method? Is it the same as simple random sampling – Assume now that the registrar's list is not alphabetical, but rather ordered by their percentage score in previous semester. Would this method of sampling be adequate? – Someone else proposes to go out and take the first hundred undergraduates she sees as the sample. Is this a probability method? Is it the same as simple random sampling? – Assume that many students in the university who are from other cities would have a higher chance of needing hostel. What sampling method would you recommend?