Sampling

Sampling Design Population • The whole group of people, items, objects, events etc. having some

common characteristic and which is being researched on is called a population.

• A single person, item etc. is called an element of the population.

Sample• A sample is a part of a population. • The process of selection of one or more elements from the

population is called sampling.• The elements in a sample are selected in such a way that the

sample represents the population in every possible characteristic and feature.

Representativeness

• Sample

_

X,

S,

S2

• Population

µ .σ .σ 2

Normal Curve

Why Sampling?

Benefits of sampling • Cost effective• Saves time• Can be more accurate• In a situation where the research results in destruction,

deformation, mutilation or contamination of the elements sampled sampling is essential

Total study• in this case sampling is not required • this is done in a case where the population is too small • this is done when the research so intends that all the

elements in the population must be included in the study

Sampling design

• Sampling design is created keeping in view the purpose and focus of the research.

• Sampling design consists of five sequential and interrelated steps.• Each step has relevance to all aspects of the research.• A sample selected using a biased or technically wrong method will

lead to irrelevant information, which in turn will lead to incorrect or distorted conclusions of the research.

• Steps in a sampling design• 1. Define the target population• 2. Specify the sampling frame• 3. Decide on a sampling procedure• 4. Determine a method of determining the sample size• 5. Determine the optimum sample size

Define the target population• The target population is that entire group of items or individuals or

cases from where the information is to be collected.• This may also be called the ‘subject’ of research.• In an empirical study, the target population consists of physical

objects like people or items or events.• In a case study it contains just one object or event.• In fundamental research it can be infinite, where it is required to

know something that is true for every object or event of the given type in the universe.

• A total study gives a complete and accurate description of the population, but it is possible only if the population is not too large and if all the elements in the population are available for study.

Specify the sampling frame

• A sampling frame is a list of all the elements in the target population

• Telephone directory, mailing list, register maintained at office are examples of sampling frames

Sampling Procedure

Probabilistic methods Non-probabilistic methods

(1) Simple random sampling(2) Stratified random sampling(3) Cluster sampling(4) Systematic sampling(5) Multi-stage sampling

(1) Convenience sampling(2) Judgment sampling (purposive)(3) Quota sampling (proportional)(4) Snowball sampling

Probabilistic MethodsSimple Random Sampling

Every element in the population has an equal

probability of being selected in the sample Pros• 1. Comparatively easy method • 2. Softwares for generating

random numbers are available and simple to use.

Cons• If the population has

subgroups that may be of research interest, they may not be adequately and proportionately represented by the sample.

• 2. If the population size is too large, allocating numbers to its elements and

Stratified random samplingThe population is divided into strata. A stratum is a subset

of the population that share at least one common characteristic. Every element in a stratum has an equal

probability of being selected in the sample.

• This is a more representative form of the population.

• Gives good results when studies involve subgroups as gender, age, income group, education level, socio-economic category, religion, geographical location, etc.

• Calculation more complicated that simple random sampling.

• Population and sample size for each strata should be known.

Cluster sampling divides the population into groups or clusters. A

number of clusters are selected randomly to represent the population, and then all units within selected clusters are included in the sample. No units from non-selected clusters

are included in the sample. This differs from stratified sampling, where some units are selected from each group.

• 1. Clustering helps in reducing data collection time and cost.

• 2. In case it is impossible and impractical to get the list of the entire population, this method is useful.

• Usually the general assumption is that the clusters are alike – if this is violated the sample will be biased.

• 2. It is better to increase the number of clusters and thereby reduce the cluster size.

Systematic samplingEvery ith numbered element is selected. That is there is

uniform gap between selected elements.• Very convenient to

use.• Only the 1st element

needs to be selected randomly.

• If there is an existing recurring pattern in the population, this may produce a bias in the sample.

Multi-stage sampling similar to cluster sampling, but involves selecting a

sample within each chosen cluster. • 1. This does not require a

complete list of members in the target population, which greatly reduces sample preparation cost.

• 2. The list of members is required only for those clusters used in the final stage.

• Same as in cluster sampling

Non Probabilistic MethodsConvenient sampling :Elements in the population who / that

are readily available is included in the sample.

• Cost-effective, time-saving practical method

• Since the sample is so chosen, it is unlikely to be representative of the population.

Judgement sampling(Purposive sampling)

The researcher selects the sample based on judgment. • 1. Useful in

exploratory research.• 2. Makes certain that

the widest variety of elements is chosen in the sample.

• 1. The researcher should be fully aware of the purpose and objective of the research.

• 2. The bias of the researcher may affect the representativeness of the sample.

Quota samplingThe population is divided into groups. Then convenience or judgment sampling is used to select the required number of

subjects from each group.

• Useful when prior knowledge of groups exist.

• Records relating to proportions of groups must be complete, correct and up-to-da

Snowball samplingThis method is used when the desired sample

characteristic is difficult to find or cost prohibitive Snowball sampling relies on references from initial

subjects to generate additional subjects.

• 1. This unique technique can reduce research costs.

• 2. This is a good method for such populations that are not well defined or properly listed

• Data collected from ‘snowballed’ sample may not be a measure of what is to be actually collected.

Determine a method of determining the sample size

Sample Size is the number of elements in the sample. The concern is to decide on the size of a sample, so that the sample

• will not lose its usability,• will give us data reliable enough about the population,• will be able to represent the population in its truest form.

Five interrelated factors that play a role in decision about the sample size:• heterogeneity of the population• required precision level • sampling procedure• resources available• time constraints• number of major sub-divisions in the research, each needing separate

sampling, and sample sizes to be determined for each of these samplings.

Determine the optimum sample size

The size of the sample may be determined in two ways – subjective and objective.

Subjective• the researcher decides subjectively on the size according to his

understanding of the research,• past experience with similar type of research• time and cost constraints• availability of elements to be included in the sample • this method has no consideration for statistical theory

Objective• statistically decided sample size, • predetermined limits of sampling error and confidence level are

required,• the researcher’s subjectivity has no role to play in this method.

The following table gives optimum sample sizes for ± 5% sampling error with 95%

confidence level.Population Size Sample Size Percentage of the population

size

10 10 100

20 19 95

50 44 88

100 80 80

250 152 61

500 217 43

1,000 278 28

2,500 333 13

5,000 350 7

10,000 370 4

Exercise

A medical inspector desires to estimate the overall average monthly occupancy rates of the cancer wards in 80 different hospitals that are evenly located in the different suburbs of Delhi NCR

ExerciseIn an article in the wall street journal titled “Kellogg to study work of

salaried staff, setting stage for possible job cutbacks”, it was started that the kellogg’s earnings remained under heavy competitive pressure and its cereal market continued to slip. It was also stated that kellogg was seeking to regain its lost momentum through the first three strategies listed below, to which last two are added.

1. Increasing production efficiencies2. Developing new products3. Increasing product promotion through advertising effectiveness4. Tapping creative ideas from organizational members at different

levels5. Assessing perception of organizational health and vitality

Discuss sampling design for each of the five strategies. Give the reasons for ur choice.

Exercise

Care for elderly relatives is a concern for many working parents. If you were to do a scientific study of this , what kind of sampling design you would use? Discuss your response with reasons for the choice of population and sample

Any doubts?

Thank you