Sampling Sampling Vorasith Sornsrivichai, M.D., FETP Cert. Epidemiology Unit, Faculty of Medicine, PSU

Objectives Objectives 1. Explain the need for survey sampling 2. Define the following terms: – Reference population, study population, study sample – Internal validity, external validity – Probability sampling, equal probability selection method, disproportionate sampling – Stratification, design effect 3. Describe principles of & steps in sampling for a household survey – Simple, systematic, stratified random sampling, cluster sampling 2

Outline of Presentation Outline of Presentation • Population & sample • Validity, precision, representativeness • Non-probability VS probability sample • Proportionate VS disproportionate sampling • Sampling error, sampling variation, sampling bias • Methods in probability sampling 3

SAMPLE 4 POPULATION

Population (N) Population (N) • The whole collection of units (the “universe” ), from which a sample may be drawn • The units may be records or events, not necessarily a population of persons 5

Sample (n) Sample (n) • A selected subset of a population –Random or nonrandom –Representative or nonrepresentative • The sample is intended to give results that are representative of the whole population 6

Population (N=100) Population (N=100) Wisdom Score 100 80 60 Does wisdom y come with age? 40 20 0 7 Age (yr) 0 20 40 60 80 100 x

Sample (n=10) Sample (n=10) Wisdom Score 100 80 60 Does wisdom y come with age? 40 20 0 8 Age (yr) 0 20 40 60 80 100 x

Population (N=100) Population (N=100) Wisdom Score 100 80 60 Does wisdom y come with age? 40 20 0 9 Age (yr) 0 20 40 60 80 100 x

“ Pain makes man think. Pain makes man think. “ Thought makes man wise. Thought makes man wise. Wisdom makes life endurable." Wisdom makes life endurable." ~ John Patrick ~ ~ John Patrick ~

Why Do We Sample Populations? Why Do We Sample Populations? • Get accurate information from large populations • Efficiency of study 11

Hierarchy of Population Hierarchy of Population • Target population: The general population you want to know about • Sample: The part of target population you collect the data • We use the estimate from the sample to estimate the parameter in the target population 12

Hierarchy of Population Hierarchy of Population Reference/external External Validity population (Generalizability) Issue of population difference Study/target Internal validity population Issue of bias Actual population Statistical inference Sampling Issue of chance Study sample/population 13 (Sample)

Validity & Precision Validity & Precision Valid, Valid, and precise not precise Not valid, Not valid, but precise not precise 14

Validity & Precision Validity & Precision • Validity – Measurement reflects true value of population – Improved by good design, sampling scheme, quality assurance • Precision – The measurement results conform to themselves – Improved by increasing the sample size 15

Truth is (almost) Everything Truth is (almost) Everything • A small sample that gives a true estimate of the target population is better than a big sample that gives a precise but false estimate 16

Representativeness Representativeness • Persons • Demographic: age, sex, race • Socioeconomic: SES • Cultural • Place • Geographical: country, region • Sociological: urban VS rural • Time • Time of the day • Day of the week 17 • Seasonality

Type of Samples Type of Samples • Non-probability samples : probability of being selected is unknown – Convenience or accidental or haphazard samples e.g. Man-in-the-street surveys, grab sample • Biased – Purposive or subjective samples e.g. expert sample, quota sample • Based on knowledge • Time/resources constraints • Probability (random) samples: every unit in the population has a known probability of being selected 18

Probability Sample Probability Sample • All individuals have a known chance of selection –May have an equal chance of being selected –Or, if a stratified sampling method is used, the chance of being selected can be varied 19

Probability Sample Probability Sample • Created by –Assigning an identity (label, number) to all individuals in the population –Arranging them in alphabetical order and numbering in sequence, or simply assigning a number to each, or by grouping according to area of residence and numbering the groups 20

Probability Sample Probability Sample –Select individuals (or groups) for study by a random procedure such as use of a table of random numbers (or comparable procedure) to ensure that the chance of selection is known 21

Any questions? :-) "To conquer fear is the beginning of wisdom." "To conquer fear is the beginning of wisdom." ~ Bertrand Russell ~ ~ Bertrand Russell ~

Sampling Sampling • The process of selecting a number of subjects from all the subjects in a particular group –Conclusions based on sample results may be attributed only to the population sampled –Any extrapolation to a larger or different population is a judgment or a guess and is not part of statistical inference 23

Definition of Sampling Terms Definition of Sampling Terms • Sampling frame – Any list of all the sampling units in the population • Primary Sampling Unit (PSU) – Sample drawn from sampling frame in the first stage of sample selection • Sampling scheme – Method of selecting sampling units from sampling frame 24

EPSM EPSM • “Equal Probability of Selection Method": A sample that each final unit of selection in the population has an equal probability of selection –Simple random sampling, systematic random sampling are EPSM samples 25

Disproportionate Sampling Disproportionate Sampling • May be used for – Cost efficiency – Important small subgroup population • Stratified sampling are not EPSM, if the sampling fraction or probability of selection (n/N) is not the same for all strata 26

Sampling Error Sampling Error • That part of the total estimation error of a parameter caused by the random nature of the sample • Expressed by standard error –of mean, proportion, differences, etc • Is a function of –Sample size –Amount of variability in measuring factor of interest 27

Sampling Variation Sampling Variation • Since the inclusion of individuals in a sample is determined by chance, the result of analysis in two or more samples will differ, purely by chance 28

Sampling Bias Sampling Bias • Systematic error due to study of a nonrandom sample of a population 29

Selection Bias Selection Bias E+ E+ E+ E+ D+ D- D+ D- E- E- E- E- n D+ D- D+ D- N E+ E+ E+ E+ D+ D- D+ D- E- E- E- E- D+ D- D+ D- 30

"Mistakes are "Mistakes are the usual bridge the usual bridge between between inexperience inexperience and wisdom." and wisdom." ~ Phyllis Theroux ~ ~ Phyllis Theroux ~

Selecting a Sampling Method Selecting a Sampling Method • Population to be studied – Heterogeneity with respect to variable of interest – Size/geographical distribution • Resources available • Importance of precision of estimate or sampling error 32

Methods in Probability Sampling Methods in Probability Sampling • Simple random sampling • Systematic sampling • Stratified sampling • Cluster sampling • Multistage sampling 33

Simple Random Sampling (SRS) Sampling (SRS) Simple Random • Principle – Each person has an equal chance of being selected from the entire population • Procedure – Assign each person a number, starting with 1, 2, 3, and so on – Numbers are selected at random until the desired sample size is attained 34

Random Table Random Table Row <--------- uniform random digits --------------------------> 1 57245 39666 18545 50534 57654 25519 35477 71309 12212 98911 2 42726 58321 59267 72742 53968 63679 54095 56563 09820 86291 3 82768 32694 62828 19097 09877 32093 23518 08654 64815 19894 4 97742 58918 33317 34192 06286 39824 74264 01941 95810 26247 5 48332 38634 20510 09198 56256 04431 22753 20944 95319 29515 6 26700 40484 28341 25428 08806 98858 04816 16317 94928 05512 7 66156 16407 57395 86230 47495 13908 97015 58225 82255 01956 8 64062 10061 01923 29260 32771 71002 58132 58646 69089 63694 9 24713 95591 26970 37647 26282 89759 69034 55281 64853 50837 10 90417 18344 22436 77006 87841 94322 45526 38145 86554 42733 11 78886 86557 11295 07253 29289 44814 58898 36929 66839 81250 12 39681 54696 38482 48217 73598 93649 92705 34912 18981 74299 13 38265 45196 31143 82190 27279 79883 20219 38823 84543 22119 14 34270 41885 00079 63600 59152 10670 27951 77830 05368 58315 35 15 73869 34748 75787 88844 89522 71436 04166 06246 20952 56808 16 21732 36017 69149 70330 90500 73110 92908 55789 73450 68282

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