RM Session 5.ppt

SAMPLING DESIGNSampling Techniques,Central Limit TheoremandSample SizeCompiled by Dr Rajesh Devasia

Compiled by Dr Rajesh Devasia

Basic Concepts

Population: entire group of objects or persons of interest Sample: a portion, a part, or a subset of the population Population element: An individual member of a population



ConceptsCensus: an investigation of all individual elements that make up a population

Sampling frame: a list of elements from which a sample may be drawn also called working population.Compiled by Dr Rajesh Devasia


Reasons for Sampling

TimeCostAdequacy of sample resultsDestructive nature of certain tests Physical impossibility



Types

Probability Sample: A sampling technique in which every member of the population will have a known, nonzero probability of being selected

Non-Probability Sample: Units of the sample are chosen on the basis of personal judgment or convenience



Pictorial ClassificationCompiled by Dr Rajesh Devasia


Probability Sampling methodsSimple random sample :A sample selected so that each item or person in the population has the same chance of being included. Each item is numbered and a table of random numbers, is used to select the members of the sample.There are many software programs, such as MINITAB and Excel that have routines that will randomly select a given number of items from the population.



Simple random sampleAdvantages minimal knowledge of population neededEasy to analyze data

DisadvantagesHigh cost; low frequency of useDoes not use researchers expertiseLarger risk of random error than stratifiedCompiled by Dr Rajesh Devasia


Systematic random sample A random starting point is selected and then every kth member of the population is selected.

In a systematic random sample, you might take all the items in the population and number them 1, 2, 3,.... Next, a random starting point is selected, let's say 39. Every kth item thereafter, such as every 100th, is selected for the sample. This means that 39, 139, 239, 339, and so on would be a part of the sample.Compiled by Dr Rajesh Devasia


Systematic random sampleAdvantages Moderate cost; moderate usageSimple to draw sample; easy to verify

DisadvantagesPeriodic orderingRequires sampling frameCompiled by Dr Rajesh Devasia


Stratified random sample A population is divided into groups, called strata, and a sample is randomly selected from each stratum For example, if our study involved Army personnel, we might decide to stratify the population (all Army personnel) into generals, other officers, and enlisted personnel Compiled by Dr Rajesh Devasia


Stratified random sampleAdvantages Assures representation of all groups in sample population neededCharacteristics of each stratum can be estimated and comparisons madeReduces variability from systematic DisadvantagesRequires accurate information on proportions of each stratumStratified lists costly to prepareCompiled by Dr Rajesh Devasia


Cluster sampling A population is divided into clusters using naturally occurring geographic or other boundaries. Then, clusters are randomly selected and a sample is collected by randomly selecting from each cluster Cluster sampling is often used to reduce the cost of sampling when the population is scattered over a large geographic area Compiled by Dr Rajesh Devasia


Cluster samplingAdvantagesLow cost/high frequency of useCan estimate characteristics of both cluster and population

DisadvantagesLarger error for comparable size than other probability methodsCompiled by Dr Rajesh Devasia


Non Probability Sampling methodsConvenience Sample: The sampling procedure used to obtain those units or people most conveniently available

DisadvantagesVariability and bias cannot be measured or controlledProjecting data beyond sample not justified.Compiled by Dr Rajesh Devasia


Judgment or Purposive SampleThe sampling procedure in which an experienced research selects the sample based on some appropriate characteristic of sample member to serve a purposeDisadvantagesBias because sampling units not independentProjecting data beyond sample not justified.Compiled by Dr Rajesh Devasia


Quota SampleThe sampling procedure that ensure that a certain characteristic of a population sample will be represented to the exact extent that the investigator desiresDisadvantagesVariability and bias cannot be measured or controlled (classification of subjects0Projecting data beyond sample not justified.Compiled by Dr Rajesh Devasia


Snowball samplingThe sampling procedure in which the initial respondents are chosen by probability or non-probability methods, and then additional respondents are obtained by information provided by the initial respondentsDisadvantagesBias because sampling units not independent

Projecting data beyond sample not justified.Compiled by Dr Rajesh Devasia


Sampling Error The difference between a sample statistic and its corresponding population parameter.For example, it is unlikely that the mean welfare payment for a sample of 50 recipients is exactly the same as the mean for all 4,000 welfare recipients. We expect a difference between a sample statistic and its corresponding population parameter. The difference is called sampling error.Compiled by Dr Rajesh Devasia


Sampling distribution of the sample meanA probability distribution of all possible sample means of a given sample size.The mean of all the sample means will be exactly equal to the population mean.If the population from which the samples are drawn is normal, the distribution of sample means is also normally distributed.If the population from which the samples are drawn is not normal, the sampling distribution is approximately normal, provided the samples are sufficiently large (usually accepted to include at least 30 observations).



The Central Limit Theorem If all samples of a specified size are selected from any population, the sampling distribution of the sample means is approximately a normal distribution. This approximation improves with larger samplesCompiled by Dr Rajesh Devasia


Standard Error of the Mean

The Central Limit Theorem does not address the dispersion of the sampling distribution of sample means nor does it address the comparison of the sampling distribution of sample means to the mean of the populationIt can be shown that the mean of the sampling distribution is the population mean, and if the dispersion in the population is , the dispersion of the means is /nCompiled by Dr Rajesh Devasia


Sample Size3 factors to be consideredVariance or heterogeneity of population (S)The magnitude of acceptable error (E)Confidence level (Z)

Means :n = (ZS/E) 2Proportions :n = Z2 pq/ E2



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RM Session 5.ppt