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Hairul Hafiz MahsolHairul Hafiz MahsolInstitute for Tropical Biology Institute for Tropical Biology & Conservation& ConservationSchool of Science & School of Science & TechnologyTechnology

A Brief Introduction to A Brief Introduction to SamplingSampling

Researchers usually cannot make direct Researchers usually cannot make direct observations of every individual in the observations of every individual in the population they are studying. population they are studying. – Instead, they collect data from a subset of Instead, they collect data from a subset of

individuals – a individuals – a samplesample – and use those – and use those observations to make inferences about the observations to make inferences about the entire population. entire population.

Ideally, the sample corresponds to the Ideally, the sample corresponds to the larger population on the characteristic(s) of larger population on the characteristic(s) of interest. interest.

In that case, the researcher's conclusions In that case, the researcher's conclusions from the sample are probably applicable to from the sample are probably applicable to the entire population.the entire population.

Sample & PopulationSample & Population Even though Denmark-Wahnefried Even though Denmark-Wahnefried et et

al.al. want to make conclusions about all want to make conclusions about all men in the U.S., they haven’t studied men in the U.S., they haven’t studied all those men in their research. They all those men in their research. They were forced to choose a manageable were forced to choose a manageable subset to study. subset to study. – That subset is a That subset is a samplesample, and the number , and the number

of subjects in the sample is called the of subjects in the sample is called the sample sizesample size. .

– Notation: Notation: The sample size is typically The sample size is typically denoted denoted nn, although that is not the only , although that is not the only symbol one can use, nor is it the only use symbol one can use, nor is it the only use for that symbol. for that symbol.

The group that the sample is meant to The group that the sample is meant to represent is called the represent is called the populationpopulation. . – (NOTE: The statistical concept of population (NOTE: The statistical concept of population

is distinct from the biological one.) In is distinct from the biological one.) In studying the sample, we attempt to draw studying the sample, we attempt to draw valid conclusions about the population.valid conclusions about the population.

– Notation: Notation: If the population size is both If the population size is both finite and well-defined, then we will typically finite and well-defined, then we will typically denote it denote it NN. .

– However, the population is usually not both However, the population is usually not both finite and well-defined.finite and well-defined.

Individual observationsIndividual observations– observations or measurements taken on the smallest observations or measurements taken on the smallest

sampling unitsampling unit

Sample of observationsSample of observations– a collection of individual observations selected by a a collection of individual observations selected by a

specified procedurespecified procedure

PopulationPopulation– the totality of individual observations about which the totality of individual observations about which

inferences are to be made, existing anywhere in the inferences are to be made, existing anywhere in the world or at least within a definitely specified world or at least within a definitely specified sampling area limited in space & timesampling area limited in space & time

History of samplingHistory of sampling In 1786 Pierre Simon In 1786 Pierre Simon LaplaceLaplace estimated the population of estimated the population of

France by using a sample, along with ratio estimator. He France by using a sample, along with ratio estimator. He also computed probabilistic estimates of the error. These also computed probabilistic estimates of the error. These were not expressed as modern confidence intervals but as were not expressed as modern confidence intervals but as the sample size that would be needed to achieve a the sample size that would be needed to achieve a particular upper bound on the sampling error with particular upper bound on the sampling error with probability 1000/1001. His estimates used Bayes' theorem probability 1000/1001. His estimates used Bayes' theorem with a uniform prior probability and it assumed his sample with a uniform prior probability and it assumed his sample was random.was random.

The theory of small-sample statistics developed by William The theory of small-sample statistics developed by William Sealy Gossett put the subject on a more rigorous basis in Sealy Gossett put the subject on a more rigorous basis in the 20th century. the 20th century.

However, the importance of random sampling was not However, the importance of random sampling was not universally appreciated and in the USA the 1936 universally appreciated and in the USA the 1936 Literary Literary DigestDigest prediction of a Republican win in the presidential prediction of a Republican win in the presidential election went badly awry, due to severe bias. A sample size election went badly awry, due to severe bias. A sample size of one million was obtained through magazine subscription of one million was obtained through magazine subscription lists and telephone directories. It was not appreciated that lists and telephone directories. It was not appreciated that these lists were heavily biased towards Republicans and these lists were heavily biased towards Republicans and the resulting sample, though very large, was deeply flawed.the resulting sample, though very large, was deeply flawed.

SamplingSampling

SamplingSampling is that part of statistical is that part of statistical practice concerned with the selection of practice concerned with the selection of individual observations intended to yield individual observations intended to yield some knowledge about a population of some knowledge about a population of concern, especially for the purposes of concern, especially for the purposes of statistical inference. statistical inference.

In particular, results from probability In particular, results from probability theory and statistical theory are theory and statistical theory are employed to guide practice.employed to guide practice.

Sampling is the Sampling is the process of selecting process of selecting units (e.g., people, units (e.g., people, organizations etc) organizations etc) from a population of from a population of interest so that by interest so that by studying the sample studying the sample we may fairly we may fairly generalize our results generalize our results back to the population back to the population from which they were from which they were chosen. chosen.

The sampling process consists of 5 The sampling process consists of 5 stages:stages:– Definition of population of concern Definition of population of concern – Specification of a sampling frame, a set of Specification of a sampling frame, a set of

items or events that it is possible to measure items or events that it is possible to measure – Specification of sampling method for Specification of sampling method for

selecting items or events from the frame selecting items or events from the frame – Determine the sample size Determine the sample size – Implement the sampling plan Implement the sampling plan – Sampling and data collecting Sampling and data collecting – Review of sampling process Review of sampling process

Sampling frameSampling frame In the most straightforward case, such In the most straightforward case, such

as the sentencing of a batch of material as the sentencing of a batch of material from production (acceptance sampling from production (acceptance sampling by lots), it is possible to identify and by lots), it is possible to identify and measure every single item in the measure every single item in the population and to include any one of population and to include any one of them in our sample. them in our sample.

However, in the more general case this However, in the more general case this is not possible. is not possible. – There is no way to identify all rats in the set There is no way to identify all rats in the set

of all rats. of all rats. – There is no way to identify every voter at a There is no way to identify every voter at a

forthcoming election (in advance of the forthcoming election (in advance of the election).election).

Having established the frame, there Having established the frame, there are a number of ways of organizing it are a number of ways of organizing it to improve efficiency and to improve efficiency and effectiveness.effectiveness.

Simple samplingSimple sampling– In this case, all elements of the frame are In this case, all elements of the frame are

treated equally and it is not subdivided or treated equally and it is not subdivided or partitioned. partitioned.

Stratified samplingStratified sampling– Where the population embraces a Where the population embraces a

number of distinct categories, the number of distinct categories, the frame can be organized by these frame can be organized by these categories into separate categories into separate stratastrata or or demographics. demographics.

– Typically, strata should be chosen to:Typically, strata should be chosen to: have means which differ substantially from have means which differ substantially from

one another one another minimise variance within strata and minimise variance within strata and

maximise variance between strata. maximise variance between strata.

Cluster samplingCluster sampling– Sometimes it is cheaper to 'cluster' the Sometimes it is cheaper to 'cluster' the

sample in some way e.g. by selecting sample in some way e.g. by selecting respondents from certain areas only, or respondents from certain areas only, or certain time-periods only. (Nearly all certain time-periods only. (Nearly all samples are in some sense 'clustered' in samples are in some sense 'clustered' in time - although this is rarely taken into time - although this is rarely taken into account in the analysis.)account in the analysis.)

– Cluster sampling is an example of 'two-Cluster sampling is an example of 'two-stage sampling' or 'multi-stage sampling': in stage sampling' or 'multi-stage sampling': in the first stage a sample of areas is chosen; the first stage a sample of areas is chosen; in the second stage a sample of respondent in the second stage a sample of respondent withinwithin those areas is selected. those areas is selected.

Quota samplingQuota sampling– In In quota samplingquota sampling, the population is first , the population is first

segmented into mutually exclusive sub-segmented into mutually exclusive sub-groups, just as in stratified sampling. groups, just as in stratified sampling.

– Then judgement is used to select the Then judgement is used to select the subjects or units from each segment based subjects or units from each segment based on a specified proportion. on a specified proportion.

– In quota sampling the selection of the In quota sampling the selection of the sample is non-random. sample is non-random.

– This non-random element is its greatest This non-random element is its greatest weakness and quota versus probability has weakness and quota versus probability has been a matter of controversy for many been a matter of controversy for many years.years.

Sampling methodSampling method Within any of the types of frame identified Within any of the types of frame identified

above, a variety of sampling methods can above, a variety of sampling methods can be employed, individually or in be employed, individually or in combination.combination.

Random samplingRandom sampling– In random sampling, also known as probability In random sampling, also known as probability

sampling, every combination of items from the sampling, every combination of items from the frame, or stratum, has a known probability of frame, or stratum, has a known probability of occurring, but these probabilities are not occurring, but these probabilities are not necessarily equal. necessarily equal.

– With any form of sampling there is a risk that With any form of sampling there is a risk that the sample may not adequately represent the the sample may not adequately represent the population but with random sampling there is population but with random sampling there is a large body of statistical theory which a large body of statistical theory which quantifies the risk and thus enables an quantifies the risk and thus enables an appropriate sample size to be chosen. appropriate sample size to be chosen.

– The simplest form of random sampling is The simplest form of random sampling is called called simple random samplingsimple random sampling. Pretty . Pretty tricky, huh? Here's the quick description of tricky, huh? Here's the quick description of simple random sampling: simple random sampling:

– ObjectiveObjective: To select : To select nn units out of units out of NN such such that each that each NCnNCn has an equal chance of being has an equal chance of being selected. selected.

– ProcedureProcedure: Use a table of random : Use a table of random numbers, a computer random number numbers, a computer random number generator, or a mechanical device to select generator, or a mechanical device to select the sample.the sample.

Matched Random SamplingMatched Random Sampling– A method of assigning participants to A method of assigning participants to

groups in which pairs of participants groups in which pairs of participants are first matched on some are first matched on some characteristic and then individually characteristic and then individually assigned randomly to groups. assigned randomly to groups.

– (Brown, Cozby, Kee, & Worden, 1999, (Brown, Cozby, Kee, & Worden, 1999, p.371).p.371).

Stratified Random SamplingStratified Random Sampling– Stratified Random SamplingStratified Random Sampling, also , also

sometimes called sometimes called proportionalproportional or or quotaquota random sampling, involves dividing your random sampling, involves dividing your population into homogeneous subgroups population into homogeneous subgroups and then taking a simple random sample in and then taking a simple random sample in each subgroup. each subgroup.

– In more formal terms: In more formal terms: Objective: Divide the population into non-Objective: Divide the population into non-

overlapping groups (i.e., overlapping groups (i.e., stratastrata) N1, N2, ) N1, N2, N3, ... Ni, such that N1 + N2 + N3 + ... + Ni N3, ... Ni, such that N1 + N2 + N3 + ... + Ni = N. Then do a simple random sample of f = = N. Then do a simple random sample of f = n/N in each strata.n/N in each strata.

Systematic samplingSystematic sampling– Selecting (say) every Selecting (say) every 1010th name from the th name from the

telephone directory is called an telephone directory is called an every every 1010thth sample, which is an example of systematic sample, which is an example of systematic sampling. sampling.

– It is a type of nonprobability sampling unless It is a type of nonprobability sampling unless the directory itself is randomized. the directory itself is randomized.

– It is easy to implement and the stratification It is easy to implement and the stratification induced can make it efficient, but it is induced can make it efficient, but it is especially vulnerable to periodicities in the especially vulnerable to periodicities in the list. list.

Systematic Random SamplingSystematic Random Sampling– Here are the steps you need to follow in Here are the steps you need to follow in

order to achieve a order to achieve a systematic random systematic random samplesample: :

number the units in the population from 1 to number the units in the population from 1 to N N

decide on the n (sample size) that you want decide on the n (sample size) that you want or need or need

k = N/n = the interval size k = N/n = the interval size randomly select an integer between 1 to k randomly select an integer between 1 to k then take every kth unit then take every kth unit

Mechanical samplingMechanical sampling– Mechanical sampling is typically used in Mechanical sampling is typically used in

sampling solids, liquids and gases, using sampling solids, liquids and gases, using devices such as grabs, scoops, thief probes, devices such as grabs, scoops, thief probes, the coliwasa and riffle splitter.the coliwasa and riffle splitter.

– Mechanical sampling Care is needed in Mechanical sampling Care is needed in ensuring that the sample is representative ensuring that the sample is representative of the frame. of the frame.

– Much work in this area was developed by Much work in this area was developed by Pierre Gy.Pierre Gy.

Convenience samplingConvenience sampling– Sometimes called Sometimes called grabgrab or or opportunityopportunity sampling, sampling,

this is the method of choosing items arbitrarily this is the method of choosing items arbitrarily and in an unstructured manner from the frame. and in an unstructured manner from the frame.

– Though almost impossible to treat rigorously, it Though almost impossible to treat rigorously, it is the method most commonly employed in is the method most commonly employed in many practical situations. many practical situations.

– In social science research, In social science research, snowball samplingsnowball sampling is is a similar technique, where existing study a similar technique, where existing study subjects are used to recruit more subjects into subjects are used to recruit more subjects into the sample.the sample.

Multi-Stage SamplingMulti-Stage Sampling– The four methods we've covered so far -- The four methods we've covered so far --

simple, stratified, systematic and cluster -- are simple, stratified, systematic and cluster -- are the simplest random sampling strategies. the simplest random sampling strategies.

– In most real applied research, we would use In most real applied research, we would use sampling methods that are considerably more sampling methods that are considerably more complex than these simple variations. The most complex than these simple variations. The most important principle here is that we can combine important principle here is that we can combine the simple methods described earlier in a the simple methods described earlier in a variety of useful ways that help us address our variety of useful ways that help us address our sampling needs in the most efficient and sampling needs in the most efficient and effective manner possible. When we combine effective manner possible. When we combine sampling methods, we call this sampling methods, we call this multi-stage multi-stage samplingsampling..

Sampling and data Sampling and data collectioncollection

Good data collection involves:Good data collection involves:– Following the defined sampling Following the defined sampling

process process – Keeping the data in time order Keeping the data in time order – Noting comments and other Noting comments and other

contextual events contextual events – Recording non-responses Recording non-responses

Review of sampling Review of sampling processprocess

After sampling, a review should be After sampling, a review should be held of the exact process followed held of the exact process followed in sampling, rather than that in sampling, rather than that intended, in order to study any intended, in order to study any effects that any divergences might effects that any divergences might have on subsequent analysis. have on subsequent analysis.

A particular problem is that of A particular problem is that of non-non-responsesresponses..

Non-responsesNon-responses In survey sampling, many of the individuals In survey sampling, many of the individuals

identified as part of the sample may be identified as part of the sample may be unwilling to participate or impossible to unwilling to participate or impossible to contact. contact.

In this case, there is a risk of differences, In this case, there is a risk of differences, between (say) the willing and unwilling, between (say) the willing and unwilling, leading to selection bias in conclusions. leading to selection bias in conclusions.

This is often addressed by follow-up studies This is often addressed by follow-up studies which make a repeated attempt to contact the which make a repeated attempt to contact the unresponsive and to characterise their unresponsive and to characterise their similarities and differences with the rest of the similarities and differences with the rest of the frame.frame.

Ecological SamplingEcological Sampling If we want to know what kind of plants and If we want to know what kind of plants and

animals are in a particular habitat, and how animals are in a particular habitat, and how many there are of each species, it is usually many there are of each species, it is usually impossible to go and count each and every one impossible to go and count each and every one present. It would be like trying to count different present. It would be like trying to count different sizes and colours of grains of sand on the beach. sizes and colours of grains of sand on the beach.

Samples are usually taken using a standard Samples are usually taken using a standard sampling unit of some kind. This ensures that all sampling unit of some kind. This ensures that all of the samples represent the same area or of the samples represent the same area or volume (water) of the habitat each time.volume (water) of the habitat each time.

There are three main ways of taking samples. There are three main ways of taking samples. – Random Sampling.Random Sampling.– Systematic Sampling (includes line transect and belt Systematic Sampling (includes line transect and belt

transect methods).transect methods).– Stratified Sampling. Stratified Sampling.

RANDOM SAMPLINGRANDOM SAMPLING– Random sampling is usually carried out when the Random sampling is usually carried out when the

area under study is fairly uniform, very large, and or area under study is fairly uniform, very large, and or there is limited time available. there is limited time available.

– When using random sampling techniques, large When using random sampling techniques, large numbers of samples/records are taken from different numbers of samples/records are taken from different positions within the habitat.positions within the habitat.

– A quadrat frame is most often used for this type of A quadrat frame is most often used for this type of sampling. sampling.

– The frame is placed on the ground (or on whatever is The frame is placed on the ground (or on whatever is being investigated) and the animals, and/ or plants being investigated) and the animals, and/ or plants inside it counted, measured, or collected, depending inside it counted, measured, or collected, depending on what the survey is for. This is done many times at on what the survey is for. This is done many times at different points within the habitat to give a large different points within the habitat to give a large number of different samples.number of different samples.

A better method of A better method of random sampling is to random sampling is to map the area and then to map the area and then to lay a numbered grid over lay a numbered grid over the map. the map.

A (computer generated) A (computer generated) random number table is random number table is then used to select which then used to select which squares to sample in. (squares to sample in. (Random number TableRandom number Table). ).

For example, if we have For example, if we have mapped our habitat , and mapped our habitat , and have then laid a have then laid a numbered grid over it as numbered grid over it as shown (Figure - below) , shown (Figure - below) , we could then choose we could then choose which squares we should which squares we should sample in by using the sample in by using the random number random number tabletable. .

Random number TableRandom number Table

20174228231759663861021086105155922017422823175966386102108610515592524425744904190304103353701154486352442574490419030410335370115448639460944957389470493138672342296540946094495738947049313867234229654088787137184864065722157815698432528878713718486406572215781569843252325415125402013738371293932912182732541512540201373837129393291218273030559187505758514936125396404504303055918750575851493612539640450477973614994552956985038351878556227797361499455295698503835187855622374491994989399460484906776472592637449199498939946048490677647259260851255716239102199647598965278430085125571623910219964759896527843092633726242366045065049263372624236604506504

SYSTEMATIC SAMPLINGSYSTEMATIC SAMPLING– Systematic sampling is when samples are Systematic sampling is when samples are

taken at fixed intervals, usually along a line. taken at fixed intervals, usually along a line. – This normally involves doing transects, where This normally involves doing transects, where

a sampling line is set up across areas where a sampling line is set up across areas where there are clear environmental gradients.there are clear environmental gradients.

– For example you might use a transect to show For example you might use a transect to show the changes of plant species as you moved the changes of plant species as you moved from grassland into woodland, or to from grassland into woodland, or to investigate the effect on species composition investigate the effect on species composition of a pollutant radiating out from a particular of a pollutant radiating out from a particular source .source .

– Method in this sampling:Method in this sampling: a) a) Line Transect MethodLine Transect Method       b) b) Belt Transect MethodBelt Transect Method

STRATIFIED SAMPLINGSTRATIFIED SAMPLING– Stratified sampling is used to take into Stratified sampling is used to take into

account different areas (or strata) which are account different areas (or strata) which are identified within the main body of a habitat. identified within the main body of a habitat.

– These strata are sampled separately from the These strata are sampled separately from the main part of the habitat. main part of the habitat.

– The name 'stratified sampling' comes from The name 'stratified sampling' comes from the term 'strata' (plural) or stratum (singular). the term 'strata' (plural) or stratum (singular).

– For ease of understanding, the term 'unit' will For ease of understanding, the term 'unit' will be used in the following explanation, rather be used in the following explanation, rather than stratum.than stratum.

BOOKS & BOOKS & REFERENCESREFERENCES

Hairul Hafiz MahsolHairul Hafiz MahsolInstitute for Tropical Biology Institute for Tropical Biology & Conservation& Conservation

School of Science & School of Science & TechnologyTechnology

BooksBooks

TERIMA KASIH