Sampling and Sample Size Determination

Please download to get full document.

View again

of 42
4 views
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.

Download

Document Related
Document Description
Sampling and Sample Size Determination. Terms . Sample Population Population element Census. Why use a sample?. Cost Speed Accuracy Destruction of test units. Steps. Definition of target population Selection of a sampling frame (list) Probability or Nonprobability sampling
Document Share
Document Transcript
Sampling and Sample Size DeterminationTerms
  • Sample
  • Population
  • Population element
  • Census
  • Why use a sample?
  • Cost
  • Speed
  • Accuracy
  • Destruction of test units
  • Steps
  • Definition of target population
  • Selection of a sampling frame (list)
  • Probability or Nonprobability sampling
  • Sampling Unit
  • Error
  • – Random sampling error (chance fluctuations)
  • Nonsampling error (design errors)
  • Target Population (step 1)
  • Who has the information/data you need?
  • How do you define your target population?
  • - Geography - Demographics - Use - AwarenessOperational Definition
  • A definition that gives meaning to a concept by specifying the activities necessary to measure it.
  • Eg. Student, employee, user, area, major news paper.
  • What variables need further definition?(Items per construct)Sampling Frame (step 2)
  • List of elements
  • Sampling Frame error
  • Error that occurs when certain sample elements are not listed or available and are not represented in the sampling frame
  • Probability or Nonprobability (step 3)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
  • There are NO statistical techniques for measuring random sampling error in a non-probability sample. Therefore, generalizability is never statistically appropriate.
  • Classification of Sampling MethodsSamplingMethodsProbabilitySamplesNon-probabilitySystematicStratifiedConvenienceSnowballClusterSimpleRandomQuotaJudgmentProbability Sampling Methods
  • Simple Random Sampling
  • the purest form of probability sampling.
  • Assures each element in the population has an equal chance of being included in the sample
  • Random number generators
  • Sample SizeProbability of Selection = Population SizeAdvantages
  • minimal knowledge of population needed
  • External validity high; internal validity high; statistical estimation of error
  • Easy to analyze data
  • Disadvantages
  • High cost; low frequency of use
  • Requires sampling frame
  • Does not use researchers’ expertise
  • Larger risk of random error than stratified
  • Systematic Sampling
  • An initial starting point is selected by a random process, and then every nth number on the list is selected
  • n=sampling interval
  • The number of population elements between the units selected for the sample
  • Error: periodicity- the original list has a systematic pattern
  • ?? Is the list of elements randomized??
  • Advantages
  • Moderate cost; moderate usage
  • External validity high; internal validity high; statistical estimation of error
  • Simple to draw sample; easy to verify
  • Disadvantages
  • Periodic ordering
  • Requires sampling frame
  • Stratified Sampling
  • Sub-samples are randomly drawn from samples within different strata that are more or less equal on some characteristic
  • Why?
  • Can reduce random error
  • More accurately reflect the population by more proportional representation
  • Advantages
  • minimal knowledge of population needed
  • External validity high; internal validity high; statistical estimation of error
  • Easy to analyze data
  • Disadvantages
  • High cost; low frequency of use
  • Requires sampling frame
  • Does not use researchers’ expertise
  • Larger risk of random error than stratified
  • Systematic Sampling
  • An initial starting point is selected by a random process, and then every nth number on the list is selected
  • n=sampling interval
  • The number of population elements between the units selected for the sample
  • Error: periodicity- the original list has a systematic pattern
  • ?? Is the list of elements randomized??
  • Advantages
  • Moderate cost; moderate usage
  • External validity high; internal validity high; statistical estimation of error
  • Simple to draw sample; easy to verify
  • Disadvantages
  • Periodic ordering
  • Requires sampling frame
  • Stratified Sampling
  • Sub-samples are randomly drawn from samples within different strata that are more or less equal on some characteristic
  • Why?
  • Can reduce random error
  • More accurately reflect the population by more proportional representation
  • How?1.Identify variable(s) as an efficient basis for stratification. Must be known to be related to dependent variable. Usually a categorical variable2.Complete list of population elements must be obtained3.Use randomization to take a simple random sample from each stratumTypes of Stratified Samples
  • Proportional Stratified Sample:
  • The number of sampling units drawn from each stratum is in proportion to the relative population size of that stratum
  • Disproportional Stratified Sample:
  • The number of sampling units drawn from each stratum is allocated according to analytical considerations e.g. as variability increases sample size of stratum should increase
  • Types of Stratified Samples…
  • Optimal allocation stratified sample:
  • The number of sampling units drawn from each stratum is determined on the basis of both size and variation.
  • Calculated statistically
  • Advantages
  • Assures representation of all groups in sample population needed
  • Characteristics of each stratum can be estimated and comparisons made
  • Reduces variability from systematic
  • Disadvantages
  • Requires accurate information on proportions of each stratum
  • Stratified lists costly to prepare
  • Cluster Sampling
  • The primary sampling unit is not the individual element, but a large cluster of elements. Either the cluster is randomly selected or the elements within are randomly selected
  • Why?
  • Frequently used when no list of population available or because of cost
  • Ask: is the cluster as heterogeneous as the population? Can we assume it is representative?
  • Cluster Sampling example
  • You are asked to create a sample of all Management students who are working in Lethbridge during the summer term
  • There is no such list available
  • Using stratified sampling, compile a list of businesses in Lethbridge to identify clusters
  • Individual workers within these clusters are selected to take part in study
  • Types of Cluster Samples
  • Area sample:
  • Primary sampling unit is a geographical area
  • Multistage area sample:
  • Involves a combination of two or more types of probability sampling techniques. Typically, progressively smaller geographical areas are randomly selected in a series of steps
  • Advantages
  • Low cost/high frequency of use
  • Requires list of all clusters, but only of individuals within chosen clusters
  • Can estimate characteristics of both cluster and population
  • For multistage, has strengths of used methods
  • Disadvantages
  • Larger error for comparable size than other probability methods
  • Multistage very expensive and validity depends on other methods used
  • Classification of Sampling MethodsSamplingMethodsProbabilitySamplesNon-probabilitySystematicStratifiedConvenienceSnowballClusterSimpleRandomQuotaJudgmentNon-Probability Sampling Methods
  • Convenience Sample
  • The sampling procedure used to obtain those units or people most conveniently available
  • Why: speed and cost
  • External validity?
  • Internal validity
  • Is it ever justified?
  • Advantages
  • Very low cost
  • Extensively used/understood
  • No need for list of population elements
  • Disadvantages
  • Variability and bias cannot be measured or controlled
  • Projecting data beyond sample not justified.
  • Judgment or Purposive Sample
  • The sampling procedure in which an experienced research selects the sample based on some appropriate characteristic of sample members… to serve a purpose
  • Advantages
  • Moderate cost
  • Commonly used/understood
  • Sample will meet a specific objective
  • Disadvantages
  • Bias!
  • Projecting data beyond sample not justified.
  • Quota Sample
  • The sampling procedure that ensure that a certain characteristic of a population sample will be represented to the exact extent that the investigator desires
  • Advantages
  • moderate cost
  • Very extensively used/understood
  • No need for list of population elements
  • Introduces some elements of stratification
  • Disadvantages
  • Variability and bias cannot be measured or controlled (classification of subjects0
  • Projecting data beyond sample not justified.
  • Snowball sampling
  • The 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 respondents
  • Advantages
  • low cost
  • Useful in specific circumstances
  • Useful for locating rare populations
  • Disadvantages
  • Bias because sampling units not independent
  • Projecting data beyond sample not justified.
  • Determining Sample Size
  • What data do you need to consider
  • Variance or heterogeneity of population
  • The degree of acceptable error (confidence interval)
  • Confidence level
  • Generally, we need to make judgments on all these variables
  • Determining Sample Size
  • Variance or heterogeneity of population
  • Previous studies? Industry expectations? Pilot study?
  • Sequential sampling
  • Rule of thumb: the value of standard deviation is expected to be 1/6 of the range.
  • Determining Sample SizeFormulas:Means n = (ZS/E) 2Proportions n = Z2 pq/ E2Percentiles n = pc (100 – pc) Z2/ E2Z at 95% confidence = 1.96Z at 99% confidence = 2.58Sample Size (Mean)Exercise 1
  • We are about to go on a recruitment drive to hire some auditors at the entry level. We need to decide on a competitive salary offer for these new auditors. From talking to some HR professionals, I’ve made a rough estimate that most new hires are getting starting salaries in the $38-42,000 range and the average (mean) is around $39,000. The standard deviation seems to be around $3000.
  • I want to be 95% confident about the average salary and I’m willing to tolerate an estimate that is within $500 (plus or minus) of the true estimate. If we’re off, we can always adjust salaries at the end of the probation period.
  • What sample size should we use?
  • Sample Size (Proportion)Exercise 2
  • We’ve just started a new educational TV program that teaches viewers all about research methods!!
  • We know from past educational TV programs that such a program would likely capture 2 out of 10 viewers on a typical night.
  • Let’s say we want to be 99% confident that our obtained sample proportion of viewers will differ from the true population proportions by not more than 5%.
  • What sample size do we need?
  • Sample size (Percentage)Exercise 3
  • We wish to determine the required sample size with 95% confidence and 5% error tolerance that the percentage of Canadians preferring the federal Liberal party.
  • A recent poll showed that 40% of Canadians questioned preferred the Liberals.
  • What is the required sample size?
  • Search Related
    We Need Your Support
    Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

    Thanks to everyone for your continued support.

    No, Thanks