two major types of sampling methods

Two Major Types of Sampling MethodsTwo Major Types of Sampling Methods

uses some form of random selection

requires that each unit have a known (often equal) probability of being selected

selection is systematic or haphazard, but not random

Probability Sampling

Non-Probability Sampling

Sampling and representativeness

Sample

Target Population

SamplingPopulation

Target Population Sampling Population Sample

Statistical Terms in SamplingStatistical Terms in Sampling

Variable

1 2 3 4 5

Statistical Terms in SamplingStatistical Terms in Sampling

Variable

responsibility

1 2 3 4 5

Statistical Terms in SamplingStatistical Terms in Sampling

Variable

Statistic

responsibility

1 2 3 4 5

Statistical Terms in SamplingStatistical Terms in Sampling

Variable

Statistic

responsibility

Average = 3.72sample

1 2 3 4 5

Statistical Terms in SamplingStatistical Terms in Sampling

Variable

Statistic

Parameter

responsibility

Average = 3.72sample

1 2 3 4 5

Statistical Terms in SamplingStatistical Terms in Sampling

Variable

Statistic

Parameter

responsibility

Average = 3.72

Average = 3.75

sample

population

Sampling ErrorSampling Error

4.54.03.53.0

150

100

50

0

responsibility

freq

uen

cyThe population has

a mean of 3.75...

Sampling ErrorSampling Error

4.54.03.53.0

150

100

50

0

responsibility

freq

uen

cyThe population has

a mean of 3.75...

...and a standard deviation

of .25

This means that...

Sampling ErrorSampling Error

4.54.03.53.0

150

100

50

0

responsibility

freq

uen

cyThe population has

a mean of 3.75...

...and a standard deviation

of .25

This means that...about 68% of cases fall between 3.5 - 4.0

Sampling ErrorSampling Error

4.54.03.53.0

150

100

50

0

responsibility

freq

uen

cyThe population has

a mean of 3.75...

...and a standard deviation

of .25

This means that...about 64% of cases fall between 3.5 - 4.0

about 95% of cases fall between 3.25 - 4.25

Sampling ErrorSampling Error

4.54.03.53.0

150

100

50

0

responsibility

freq

uen

cyThe population has

a mean of 3.75...

...and a standard deviation

of .25

This means that...about 64% of cases fall between 3.5 - 4.0

about 95% of cases fall between 3.25 - 4.25

about 99% of cases fall between 3.0 - 4.5

Types of Probability Sampling DesignsTypes of Probability Sampling Designs

• Simple Random Sampling• Stratified Sampling• Systematic Sampling• Cluster (Area) Sampling• Multistage Sampling

Simple Random SamplingSimple Random Sampling• Need a list of all eligible persons in the

population• Every person has equal chance (equal

probability) to be selected in the sample• can sample with or without replacement• Rarely used in actual surveys

• Difficult• Expensive• Excessive travel time (different location of subjects)• Excessive local introduction and organization

time

Simple Random SamplingSimple Random Sampling

• A random sample of nursing students of KUMS

• A random sample of diabetic patients registered at Bahonar clinic

Example:

Simple Random SamplingSimple Random Sampling

List of Residents

Simple Random SamplingSimple Random Sampling

List of Students

Random Subsample

Stratified Random SamplingStratified Random Sampling

• sometimes called "proportional" or "quota" random sampling

• Objective - population of N units divided into non-overlapping strata N1, N2, N3, ... Ni such that N1 + N2 + ... + Ni = N, then do simple random sample of n/N in each strata

Stratified random sample:

The population is divided into multiple strata based on common characteristics

e.g.;– Residence (Urban or rural)– Tribe, ethnicity or race– Family income (poor, moderate, or

wealthy)

Stratified Random SamplingStratified Random Sampling

List of Residents

Stratified Random SamplingStratified Random Sampling

List of students

Strata

Nursing Pharmacymedical

Stratified Random SamplingStratified Random Sampling

List of Residents

Random Subsamples

Strata

surgical Non-clinicalmedical

Systematic Random SamplingSystematic Random Sampling

• number units in population from 1 to N• decide on the n that you want or need• N/n=k the interval size• randomly select a number from 1 to k• then take every kth unit

Procedure:

Systematic Sampling:

Similar Procedure:• List all persons in the population

• Define selection interval:

= (Sampled population)/(Sample size)

= N/n

= An integer for ease of field use

Systematic Sampling:(continued)

• Select a random starting point (first person in the sample)

• Next selection = the random start + the random interval

• And so on and so forth…

Systematic Random SamplingSystematic Random Sampling

• Assumes that the population is randomly ordered

• Advantages - easy; may be more precise than simple random sample

• Example - students study

Systematic Random SamplingSystematic Random Sampling1 26 51 762 27 52 773 28 53 784 29 54 795 30 55 806 31 56 817 32 57 828 33 58 839 34 59 8410 35 60 8511 36 61 8612 37 62 8713 38 63 8814 39 64 8915 40 65 9016 41 66 9117 42 67 9218 43 68 9319 44 69 9420 45 70 9521 46 71 9622 47 72 9723 48 73 9824 49 74 9925 50 75 100

N = 100

Systematic Random SamplingSystematic Random Sampling1 26 51 762 27 52 773 28 53 784 29 54 795 30 55 806 31 56 817 32 57 828 33 58 839 34 59 8410 35 60 8511 36 61 8612 37 62 8713 38 63 8814 39 64 8915 40 65 9016 41 66 9117 42 67 9218 43 68 9319 44 69 9420 45 70 9521 46 71 9622 47 72 9723 48 73 9824 49 74 9925 50 75 100

N = 100

want n = 20

Systematic Random SamplingSystematic Random Sampling1 26 51 762 27 52 773 28 53 784 29 54 795 30 55 806 31 56 817 32 57 828 33 58 839 34 59 8410 35 60 8511 36 61 8612 37 62 8713 38 63 8814 39 64 8915 40 65 9016 41 66 9117 42 67 9218 43 68 9319 44 69 9420 45 70 9521 46 71 9622 47 72 9723 48 73 9824 49 74 9925 50 75 100

N = 100

want n = 20

N/n = 5

Systematic Random SamplingSystematic Random Sampling1 26 51 762 27 52 773 28 53 784 29 54 795 30 55 806 31 56 817 32 57 828 33 58 839 34 59 8410 35 60 8511 36 61 8612 37 62 8713 38 63 8814 39 64 8915 40 65 9016 41 66 9117 42 67 9218 43 68 9319 44 69 9420 45 70 9521 46 71 9622 47 72 9723 48 73 9824 49 74 9925 50 75 100

N = 100

want n = 20

N/n = 5

select a random number from 1-5: chose 4

Systematic Random SamplingSystematic Random Sampling1 26 51 762 27 52 773 28 53 784 29 54 795 30 55 806 31 56 817 32 57 828 33 58 839 34 59 8410 35 60 8511 36 61 8612 37 62 8713 38 63 8814 39 64 8915 40 65 9016 41 66 9117 42 67 9218 43 68 9319 44 69 9420 45 70 9521 46 71 9622 47 72 9723 48 73 9824 49 74 9925 50 75 100

N = 100

want n = 20

N/n = 5

select a random number from 1-5: chose 4

start with #4 and take every 5th unit

Cluster Sampling

• The population is first divided into clusters• A cluster is a small-scale version of the population

(i.e. heterogeneous group reflecting the variance in the population.

• Take a simple random sample of the clusters.• All elements within each sampled (chosen) cluster

form the sample.• Generally requires a larger total sample size than

simple or stratified random sampling.

Cluster (area) Random SamplingCluster (area) Random Sampling

• Advantages - administratively useful, especially when you have a wide geographic area to cover

• Examples - randomly sample from city blocks and measure all homes in selected blocks

Example: Cluster sampling

Section 4

Section 5

Section 3

Section 2Section 1

Simple Random Sample: n = 20, N = 2000

Systematic sample: n = 20, N = 2000, k = 45

Stratified sample of 20 from 4 strata

Cluster Sample of 20 (cluster size = 4)

STATISTICAL TABLES: Table A Random Digits

SIMPLE RANDOM SAMPLING

STRATIFIED RANDOM SAMPLINGGrouped by characteristic

SYSTEMATIC SAMPLING

CLUSTER SAMPLING

TWO STAGE CLUSTER SAMPLING

(WITH RANDOM SAMPLING AT SECOND STAGE)

Multi-Stage SamplingMulti-Stage Sampling

• Cluster (area) random sampling can be multi-stage

• Any combinations of single-stage methods

Types of Probability Sampling DesignsTypes of Probability Sampling Designs

• Simple Random Sampling• Stratified Sampling• Systematic Sampling• Cluster (Area) Sampling• Multistage Sampling

Nonprobability Sampling DesignsNonprobability Sampling Designs

Major IssuesMajor Issues

• Likely to misrepresent the population• May be difficult or impossible to detect

this misrepresentation

Types of Nonprobability SamplesTypes of Nonprobability Samples

• Accidental, haphazard, convenience• Modal Instance• Purposive• Expert• Quota• Snowball• Heterogeneity sampling

Accidental or Haphazard SamplingAccidental or Haphazard Sampling

• “Man on the street”• Medical student in the library• available or accessible clients• volunteer samples

• Problem: we have no evidence

for representativeness

Modal Instance SamplingModal Instance Sampling

• Sample for the typical case• Typical medical students age?• Typical socioeconomic class?• Problem: may not represent the modal

group proportionately

Purposive SamplingPurposive Sampling

• Might sample several pre-defined groups (e.g., patients who does not attend at follow up visits)

• Deliberately sampling an extreme group• Problem: Proportionality

Expert SamplingExpert Sampling

• have a panel of experts make a judgment about the representativeness of your sample

• Advantage: at least you can say that expert judgment supports the sampling

• Problem: the “experts” may be wrong

Quota SamplingQuota Sampling

• select people nonrandomly according to some quotas

• Proportional Quota Sampling• Nonproportional Quota Sampling

Snowball SamplingSnowball Sampling

• one person recommends another, who recommends another, who recommends another, etc.

• good way to identify hard-to-reach populations

• for example, adolescents who abuse recreational drugs

Heterogeneity SamplingHeterogeneity Sampling

• make sure you include all sectors - at least several of everything - don't worry about proportions (like in quota sampling)

• use when one or more people are a good proxy for the group

• for instance, when brainstorming issues across stakeholder groups

Convenience Sampling

• The sample is identified primarily by convenience.

• It is a nonprobability sampling technique. Items are included in the sample without known probabilities of being selected.

• Example: A professor conducting research might use student volunteers to constitute a sample.

Convenience Sampling

• Advantage: Relatively easy, fast, often, but not always, cheap

• Disadvantage: It is impossible to determine how representative of the population the sample is. – Try to offset this by collecting large sample size.

Sampling

Random Non Random

Simple

Systematic

Cluster

Multi Stage

Stratified

Proportionate Disproportionate

Haphazard

Convenience

Modal Instance

Purposive

Expert

Snowball

Heterogeneity

Quota

Sampling summary

• Random sampling seldom done in practice.

• Stratified sampling yields better results with smaller samples.

• Systematic sampling is easy to manage.

Sample size determination

A question?

Are Females more intelligent than Males?

• H0 Null hypothesis: Women and Men have the same mean IQ

• Ha Alternative hypothesis: The mean IQ of Women is greater than the Men

Type 1 and 2 errors

Truth

Decision H0 true H0 false

Reject H0 Type I error Correct decision

Accept H0 Correct Type II error

decision

Power

• The easiest ways to increase power are to:– increase sample size

– increase desired difference (or effect size)

Steps in estimating sample size for descriptive survey

• Identify major study variable• Determine type of estimate (%, mean,

ratio,...) • Indicate expected frequency of factor of

interest• Decide on desired precision of the

estimate • Decide on acceptable risk that estimate

will fall outside its real population value• Adjust for estimated design effect• Adjust for expected response rate

Sample size fordescriptive survey

z: alpha risk expressed in z-score

p: expected prevalence

q: 1 - p

d: absolute precision

g: design effect

z² * p * q 1.96²*0.15*0.85n = -------------- ---------------------- = 544

d² 0.03²

Cluster sampling

z² * p * q 2*1.96²*0.15*0.85n = g* -------------- ------------------------ = 1088d² 0.03²

Simple random / systematic sampling

Sample size calculation for a difference inmeans (equal sized groups)

69

Sample size calculation for a difference inproportions (equal sized groups)