introduction to sampling - gtk.uni-miskolc.hugtk.uni-miskolc.hu/files/12114/s4_sampling.pdf ·...

• Faculty of Economics• Gazdaságelméleti és Módszertani Intézet

Introduction to Sampling

Petra Petrovics

4th seminar


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


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.


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


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


= 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


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).


Sample statistic Sample size

Mean

Proportion

2

22tn

2

2pqtn

Sample Size in case of SRS

If the population size is unknown.


• 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


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.


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


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


Estimation from Stratified Sample

where

xstx

ii x

N

Nx

2

2

2

ixi

x sN

Ns


Thank You for Your Attention

introduction to sampling - gtk.uni-miskolc.hugtk.uni-miskolc.hu/files/12114/s4_sampling.pdf ·...

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