Two Major Types of Sampling Methods
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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)
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Sample size calculation for a difference inproportions (equal sized groups)