Sampling

Ewnetu Firdawek

Outline

• Basic Sampling concepts– The need for sampling– The concept of inference – Internal and External validity

• Sampling Methods – Probability and Non-Probability

• Details on Sampling Methods• Sampling in different setups and conditions

– Multiple sampling

• How large is a sample?

Sampling

• Sampling involves selecting a number of units from a defined population.

Definition:

• Sampling is the process of selecting a smaller number of elements from a larger defined target group of elements such that the information gathered from the smaller group will allow judgments to be made about the larger group.

• Or: it is the procedure by which some members of a given population are selected as representative of the entire population.

Population Vs Sample

• Population is the larger set of objects/ people we wish to study.– E.g. the number of kebeles– The number of population– The number of health centers

• Sample is a set of “representative” objects/ people we choose in order to estimate the characteristics of the larger set of population.– E.g. 100 of the kebeles– 3500 of the population– 200 of the health centers

Basic Sampling Concepts

• Most researches involve the observation of sample from a predefined population of interest.

• A sample of people or objects are observed for exposure to various risk factors, health outcomes and other related variables.

• The conclusion drawn from the study are often based on generalizing the results observed in the sample to the entire population from which the sample was drawn.

• Therefore the accuracy of conclusion will depend on how well the samples have been identified and their representativeness to the study population.

The need for sampling

• Sampling is a process of selection of a section of population for an observation or study.

• Among the reasons why samples are chosen– To minimize cost and resources; related to data collection, data

processing and dissemination.– For urgency of the information; or to reduce field time– To increase accuracy with enhanced methods

• Take examples:– An information required for urgent decision making, – The time and resources required to conduct a complete enumeration,

Census.

The concept of Inference

• Inference is a generalization made about a source population from a sample of that population.

• Statistical Inference makes use of information from a sample to draw conclusions (inferences) about the population from which the sample was taken.

• The basic concept is drawn from Central Limit Theorem.

“The mean of means is equal to population mean.”

Parameter

Population

Sample

Statistic

Inference

Internal and External Validity

• Internal Validity: – Internal validity addresses the "true" causes of the outcomes that you

observed in your study. – An experiment is internally valid to the extent that it shows a cause-

effect relationship between the independent and dependent variables.– At the same time, you are able to rule out extraneous variables, often

unanticipated, causes for your dependent variables.– In short, it is the measure of how your study reflects the truth in the

sampled population.

• External Validity:– It is the degree of generalizability of the findings to the source

population.

Definitions and Sampling Process

• Concerns in appropriate sampling– The sample should be representative of the population– Every variable of interest should have the same distribution

in the sample as in the population from which the sample is drawn.

• Source Population: /Reference, Target/– It is the population of interest.– E.g. women. Children. Adolescents,

• Study population:– Population from which the sample are actually drawn and

about which a conclusion can be made.– The study population is limited than source population.– In some cases the source population and study population

may be similar. – The population to whom generalization is made.– E.g. married women, Under 5 children attending U5 OPD,..

• Sampling frame:– A list of elements or units of the population from which the

sample is to be selected.– Sampling frame is not a requirement for every sampling

design.

• Sampling unit: – The unit of selection. E.g. individual, household, institution

• Study unit:– The unit where the observation is made or the information is

collected.

• Sampling Fraction:– The ratio of the sample size to the study population in %.

• Sampling Design or Scheme– The scheme for selecting the sampling units from the study

population.– E.g. SRS,Cluster Sampling. Stratified, Systematic…..

• Sampling procedure:– It is the schematic representation of the sampling design

showing the way to reach to each sampling and study unit.

Figure showing sampling procedure

eg. Zone x

↓ Purposive sampling town Y K1 K2 k3 k4 k5 k6 k7 k8 k9 k10 k11

↓SRS 4 kebeles will be selected

↓cluster sampling 776 no of HH with eligible women

Study subjectsThe actual

participants in the study

SampleSubjects who are

selected

Sampling FrameThe list of potential subjects

from which the sample is drawn

Study populationThe Population from whom the study

subjects would be obtained

Source or Target populationThe population to whom the results would be

applied

• Eg.: In a study of the prevalence of HIV among orphan children in Addis Ababa, a random sample of orphan children in Lideta Sub City ‐were included

• Target popn-all orphan children in Addis Ababa• Study population: All orphan children in Lideta

Sub City‐• Sample: Orphan children included in the actual

study from Lideta Sub City‐

Sampling Process:

1. Identify the Source Population

2. Identify the Study Population

3. Identify the Sampling Unit and Study Unit

4. Develop the Sampling Frame

5. Identify the Sampling Design

6. Develop the sampling procedure

Example

A national Study is planned to be conducted on Public Health Institutions

• Source Population: Health Institutions in Ethiopia• Study population: District Hospitals and Health Centers• Sampling Unit: Health Institution• Study Units: ART Clinics• Sampling Frame: List of District Hospitals and Health Centers• Sampling Design: Random, Systematic, Stratified, Cluster,…

Sampling Methods

Broad categories• Probability Sampling Methods

– Random selection procedure, each unit of the sample is chosen on the bases of chance

– All units in the study pop has a known equal non-zero chance of selection

– A sampling plan with known statistical properties– Random, Systematic, Stratified, Multi-stage, Cluster,

• Non-Probability Sampling– There is no equal chance of selection for study units– It is a deliberate sampling method,– There no known chance of selection to every trait– No guarantee to assure representativeness – Quota, Purposive, Convenience,

Simple Random Sampling

• The simplest form of probability sampling

• Ensure highest level of probability• It is selection by random selection and

chance• Each element has equal chance of

selection• Selection can be made by lottery, TRN

or using computer programs.• Requirements: Sampling frame and

Sample size

Systematic Random Sampling

• Individuals are sampled at regular interval, every kth interval from the sampling frame.

• We randomly select a number to start from the sampling frame.

• It is less time consuming and easy to perform than SRS.

• The sampling interval K is calculated as ; Population Size N is divided by the desired sample size n K= N/n

• Then we randomly select a number j between 1 and K, the sample element j then we select every Kth element thereafter, which is, j, j+k, j+2k, j+3k, …

Stratified Sampling

• It is the sampling method by which all groups in the source population are represented.

• The sampling frame is then divided into small groups or called STRATA according to a characteristic.

• Then random or systematic sampling will be used to obtain the pre-determined sample size.

• It is possible when the proportion to each strata is known.• Example: strata can be formed based on ethnic group, age

groups,…..

• For a given sample size it reduces errors compared to simple random sampling IF groups are different from each other.

• Probabilities of selection may be different for different groups.

Random Cluster Sampling

• It is done when a list of study groups are available.• The population is divided into groups, usually

Geographic or organizational basis.• These groups are then called CLUSTER.• In pure cluster sampling the whole cluster is selected

and each members of the cluster are included in the study unit.

• Clusters are usually assumed to be similar.

• Cluster sampling has very high error if the clusters are different from each other.

• Cluster sampling will not be effective for such a case.

• The possibility of omitting some kind of subjects tend to increase with cluster sampling.

WHAT IF DIFFERENT CLUSTERS?

The solution!!!STRATIFIED CLUSTER SAMPLING

• Reduces the error in cluster sampling by creating strata of clusters

• Sample one cluster from each stratum

Stratification Vs. Clustering

STRATIFICATION

• Divides population into different groups from each other; sex, race, age

• Sample randomly from each group

• Less error than SRS• Expensive to form

stratification

CLUSTERING

• Divides population into comparable groups; schools, geography,

• Randomly sample some of the groups or clusters

• More error compared to SRS

• Reduces cost to sample only some areas or organizations

Multi-stage Sampling

• It is don in a very large and diverse population.• The population may be divided in different stages,.• Usually done in community based national studies.• Typical example; suppose a national study is planned,

– Then interested to represent each kebele– A multi-stage sampling is applied– The stages are Regions, Zones, Woredas and Kebeles– The larger the clusters selected the greater the

representativeness.

• Then systematic or random sampling can be applied.

Non-Probability samplingAssignment 3 Reading on:

– Quota Sampling– Convenience Sampling– Purposeful Sampling

• Qualitative methods of sampling– Extreme case sampling– Maximum variation sampling– Homogenous sampling– Typical Case sampling– Critical Case Sampling– Snow ball sampling/ Chain Sampling

• Bias in Sampling

How large is a sample?

• In planning any investigation we must decide how many people need to be studied in order to answer the study objectives.

• If the SS is too small we may fail to detect important effects, or may estimate effects too imprecisely. If the SS is too large then we will waste resources.

• The SS is usually a compromise between what is desirable and what is feasible.

• The feasible sample size is determined by the availability of resources for data collection and analysis.

What we need to know to determine sample size?

• Proportion of the interest variable• Margin of error• Confidence Intervals 95% = X± 1.96(SE)• Statistical Significance (Type I error)= α

• Where – n is the desired sample size– Z is the confidence level at a certain value of Significance– P is the proportion of the interest variable– W is the margin of error , expressed in proportion

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wp)p(1Z

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Thank you