This document discusses sampling and sampling distributions. It defines sampling as selecting a subset of a population for study. Random sampling gives each member of the population an equal chance of being selected, while non-random sampling uses other factors like convenience. The document outlines the steps in sampling design and describes different random and non-random sampling methods. It also distinguishes between sampling errors and non-sampling errors and discusses the concept of sampling distributions and how they allow inferences to be made about population parameters from sample statistics.

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Sampling and Sampling
Distributions

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Learning Objectives
Upon completionof this chapter, you will be able to:
➢ Understand the importance of sampling
➢ Differentiate between random and non-random sampling
➢ Understand the concept of sampling and non-sampling errors
➢ Understand the concept of sampling distribution and the
application of central limit theorem
➢ Understand sampling distribution of sample proportion

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Sampling
A researcher generally takes a small portion of the population for
study, which is referred to as sample. The process of selecting a
sample from the population is called sampling.

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Importance of Sampling
➢ Sampling saves time.
➢ Sampling saves money.
➢ When the research process is destructive in nature, sampling
minimizes the destruction.
➢ Sampling broadens the scope of the study in light of the scarcity
of resources.

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Figure : Steps in the sampling design process

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The Sampling Design Process
Step 1: Target population must be defined
➢ Target population is the collection of the objects which possess the
information required by the researcher and about which an
inference is to be made.
Step 2: Sampling frame mustbe determined
➢ This list possesses the information about the subjects and is called
the sampling frame.
➢ Sampling is carried out from the sampling frame and not from the
target population.

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The Sampling Design Process (Contd.)
Step 3: Appropriate sampling technique must be selected
➢ Non probabilitysampling
➢ Probabilitysampling
Step 4: Sample size must be determined
➢ Sample size refers to the number of elements to be included in the
study.
Step 5: Sampling process must be executed

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Random Versus Non-random Sampling
➢ In random sampling, each unit of the population has the same
probability (chance) of being selected as part of the sample.
➢ In non-random sampling, members of the sample are not
selected by chance. Some other factors like judgment or
convenience, etc. are the basis of selection.

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Figure 5.2: Random and non-random sampling methods

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Random Sampling Methods
➢ Simple Random Sampling
▪ In simple random sampling, each member of the population has an
equal chance of being includedin the sample.
▪ Ex. Lottery Method
➢ StratifiedRandom Sampling
▪ In stratified random sampling, elements in the population are
dividedinto homogeneous groups called strata.
▪ Then, researchers use the simple random sampling method to select
a sample from each of the strata. Each group is called stratum.

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Random Sampling Methods (Contd.)
➢ Cluster (or Area) Sampling
▪ In stratified sampling, strata happen to be homogenous but in cluster
sampling, clusters are internally heterogeneous.
Figure 5.6: Diagram for cluster sampling

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Systematic (or Quasi-random) Sampling
➢ In systematic sampling, sample elements are selected from the
population at uniform intervals in terms of time, order, or space.

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Multi-Stage Sampling
➢ As the name indicates, multistage sampling involves the selection
of units in more than one stage.
Figure 5.7: Multi-stage (four stages)sampling

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Non-Random Sampling
Sampling techniques where selection of the sampling units is not
based on a random selection process are called nonrandom sampling
techniques.
➢ Quota Sampling
▪ In quota sampling, quota are fixed according to the requirement of
research. a researcher uses non-random sampling methods to gather
data from one stratum until the required quota fixed by the researcher is
fulfilled.
➢ Convenience Sampling
▪ In convenience sampling, sample elements are selected based on the
convenience of a researcher.

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➢ Judgement Sampling
▪ In judgement sampling, selection of the sampling units is based on
the judgement of a researcher.
➢ Snowball Sampling
▪ In snowball sampling, survey respondents are selected on the basis
of referrals from other survey respondents.

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Sampling and Non-Sampling Errors
Sampling Error
Sampling error occurs when the sample is not a true representative
of the population. In complete enumeration, sampling errors are not
present.
Sampling errorscan occur due to some specificreasons:
➢ Faulty selection of the sample.
➢ Sometimes due to the difficulty in selection a particular
sampling unit, researchers try to substitute that sampling unit
with another sampling unit which is easy to be surveyed.

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Non-Sampling Errors
All errors other than sampling can be included in the category of non-
sampling errors.
The following are some commonnon-sampling errors:
➢ Faulty designing and planning of survey
➢ Response errors
➢ Errors in coverage

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Key things to keep in mind
• Parameters- characteristic of population( what
we actually want to know)
• Statistic- Characteristic of sample – (what we
have with our data)
• Sampling distribution-the means by which we
will go from our sample to the population

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sampling distribution(cont….)
• A sampling distribution is the probability
distribution for all possible values of the
sample statistic.
• Each sample contains different elements so
the value of the sample statistic differs for
each sample selected. These statistics
provide different estimates of the parameter.
The sampling distribution describes how these
different values are distributed.

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Sampling distribution(Cont…)
• Sampling distribution is a theoretical
distribution that describes all possible values
of means, medians, etc.
• Some important sampling distributionsare
• 1-sampling distribution of mean
• 2-sampling distribution of proportion
• 3- t distribution
• 4- f distribution

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Sample Distribution of Sample Proportion
Figure : Using sample proportion to make an inference about the
population proportion