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• Faculty of Economics• Gazdaságelméleti és Módszertani Intézet
Introduction to Sampling
Petra Petrovics
4th seminar
• Faculty of Economics• Gazdaságelméleti és Módszertani Intézet
StatisticsDescriptive Inferential
- it is concerned only withcollecting and describing data
- it is used when tentativeconclusions about a populationare drawn on the basis of asample
- set of elements- set of all possible measurements- the number of elements: N or
- the portion of the population- about which information is gathered- representative- the number of elements: n
Population Sample
• Faculty of Economics• Gazdaságelméleti és Módszertani Intézet
Basic Definitions
• The total set of observations that can be made iscalled the population.
• A sample is a subset of a population.
• A parameter is a measurable characteristic of apopulation, such as a mean or standard deviation.
• A statistic is a measurable characteristic of asample, such as a mean or standard deviation.
• Faculty of Economics• Gazdaságelméleti és Módszertani Intézet
Sampling
• The process of obtaining a sample
• Obtaining information on a population
• Reason:
o the population is dynamic we cannot possiblyexamine every member of a population
o economically more efficient
Saving us time & money
• Faculty of Economics• Gazdaságelméleti és Módszertani Intézet
Sampling MethodsRandom / Probability sampling Non-random /
Non-probability sampling
• every unit in the population hasa chance (greater than zero) ofbeing selected in the sample
• this probability can be accuratelydetermined
= known probability of occurring, butthese probabilities are notnecessarily equal
• the sampling error can becomputed
• some elements of the populationhave no chance of selection
• the probability of selection can'tbe accurately determined
• Information about therelationship between sample andpopulation is limited
• Faculty of Economics• Gazdaságelméleti és Módszertani Intézet
= a procedure for selecting sample elements from a population
representative sample
I. Probability sampling
– Simple random sampling
– Stratified sampling
– Cluster sampling
– Multistage sampling
II. Non-probability sampling
– Convenience sampling
– Quota sampling
– Snowball sampling
– Systematic sampling
Sampling Methods
• Faculty of Economics• Gazdaságelméleti és Módszertani Intézet
Simple Random Sampling
• Each element of a population has an equal probabilityof being selected to the subset.
• Homogenous, finite population; sampling withoutreplacement
• + It guarantees that the sample chosen isrepresentative of the population
• - We need to know the sampling frame
• We need a method that ensures randomness – use ofrandom numbers (number determined totally bychance, with no predictable relationship to any othernumber).
• Faculty of Economics• Gazdaságelméleti és Módszertani Intézet
Sample statistic Sample size
Mean
Proportion
2
22tn
2
2pqtn
Sample Size in case of SRS
If the population size is unknown.
• Faculty of Economics• Gazdaságelméleti és Módszertani Intézet
• The population is divided into H groups, called strata.
• Each element of the population can be assigned to one, and onlyone, stratum.
• The number of observations within each stratum Nh is known,and N = N1 + N2 + N3 + ... + NH-1 + NH .
• The researcher obtains a probability sample from each stratumseparately, producing a stratified sample.
• Use:– to ensure that particular groups within a population are adequately
represented in the sample– to improve efficiency by gaining greater control on the composition
of the sample.
Stratified Sampling
• Faculty of Economics• Gazdaságelméleti és Módszertani Intézet
Advantages and Disadvantages of StratifiedSampling
Advantages Disadvantages
• Greater precision than a simple randomsample of the same size.
• More administrative effort
• Requires a smaller sample, which savesmoney
• Guard against an "unrepresentative"sample (e.g., an all-male sample from amixed-gender population).
• We obtain sufficient sample points tosupport a separate analysis of anysubgroup.
• Faculty of Economics• Gazdaságelméleti és Módszertani Intézet
Types of Stratified Sampling
• Uniform stratification: the samples selected fromeach strata are equal
• Proportional stratification: the sample size isproportional to the relative size of the strata
• Optimum stratification (Neyman): sample sizes isproportional to the stratum standard deviation
nN
Nn
ii
iii
• Faculty of Economics• Gazdaságelméleti és Módszertani Intézet
Proportional Startification
• Each stratum has the same sampling fraction.
• Provides equal or better precision than SRS.
• Gains in precision are greatest when values within strataare homogeneous.
• Gains in precision accrue to all survey measures.
• If costs and variances are about equal across strata,choose proportionate stratification over disproportionatestratification .
N
N
n
n ii
• Faculty of Economics• Gazdaságelméleti és Módszertani Intézet
Estimation from Stratified Sample
where
xstx
ii x
N
Nx
2
2
2
ixi
x sN
Ns
• Faculty of Economics• Gazdaságelméleti és Módszertani Intézet
Thank You for Your Attention