Population: Population refers to any group of people or objects that
form the subject of study in a particular survey and are similar in
one or more ways.
Element: An element comprises a single member of the population.
Sample: It is a subset of the population. It comprises only some
elements of the population.
Sampling unit: A sampling unit is a single member of the sample.
Sampling: It is a process of selecting an adequate number of
elements from the population so that the study of the sample will
not only help in understanding the characteristics of the population
but will also enable us to generalize the results.
Census (or complete enumeration): An examination of each and
every element of the population is called census or complete
ADVANTAGES OF SAMPLE OVER
saves time and cost.
are situations where a sample is the only
study of a sample instead of complete
enumeration may, at times, produce more
A census is appropriate when the population size is
SAMPLING VS NON-SAMPLING
Sampling error: This error arises when a sample is not
representative of the population.
Non-sampling error: This error arises not because a
sample is not a representative of the population but
because of other reasons. Some of these reasons are listed
Plain lying by the respondent.
The error can arise while transferring the data from the
questionnaire to the spreadsheet on the computer.
There can be errors at the time of coding, tabulation and
Population of the study is not properly defined
Respondent may refuse to be part of the study.
There may be a sampling frame error.
TYPES OF SAMPLING
Probability Sampling – Probability Sampling are
used in conclusive research. In a probability sampling
design, each and every element of the population has a
known chance of being selected in the sample.
Types of Probability Sampling
random sampling with replacement
random sampling without replacement
SIMPLE RANDOM SAMPLING
Each element in the population has a known
and equal probability of selection.
Each possible sample of a given size (n) has a
known and equal probability of being the
sample actually selected.
This implies that every element is selected
independently of every other element.
The sample is chosen by selecting a random
starting point and then picking every ith element in
succession from the sampling frame.
The sampling interval, i, is determined by dividing
the population size N by the sample size n and
rounding to the nearest integer.
When the ordering of the elements is related to the
characteristic of interest, systematic sampling
increases the representativeness of the sample.
If the ordering of the elements produces a cyclical
pattern, systematic sampling may decrease the
representativeness of the sample.
For example, there are 100,000 elements in the
population and a sample of 1,000 is desired. In
this case the sampling interval, i, is 100. A
random number between 1 and 100 is selected. If,
for example, this number is 23, the sample
consists of elements 23, 123, 223, 323, 423, 523,
and so on.
A two-step process in which the population is
partitioned into subpopulations, or strata.
The strata should be mutually exclusive and
collectively exhaustive in that every population
element should be assigned to one and only one
stratum and no population elements should be
Next, elements are selected from each stratum by a
random procedure, usually SRS.
A major objective of stratified sampling is to increase
precision without increasing cost.
The elements within a stratum should be as
homogeneous as possible, but the elements in
different strata should be as heterogeneous as
The stratification variables should also be closely
related to the characteristic of interest.
Finally, the variables should decrease the cost of
the stratification process by being easy to
measure and apply.
In proportionate stratified sampling, the size of
the sample drawn from each stratum is
proportionate to the relative size of that stratum in
the total population.
In disproportionate stratified sampling, the
size of the sample from each stratum is not
proportionate to the relative size of that stratum
and to the standard deviation of the distribution of
the characteristic of interest among all the
elements in that stratum.
The target population is first divided into mutually
exclusive and collectively exhaustive
subpopulations, or clusters.
Then a random sample of clusters is selected,
based on a probability sampling technique such as
For each selected cluster, either all the elements
are included in the sample (one-stage) or a sample
of elements is drawn probabilistically (two-stage).
Non-probability Sampling - In case of nonprobability sampling design, the elements of the
population do not have any known chance of being
selected in the sample.
Types of Non-Probability Sampling Design
Convenience sampling attempts to obtain a
sample of convenient elements. Often, respondents
are selected because they happen to be in the right
place at the right time.
of students, and members of social
intercept interviews without qualifying the
stores using charge account lists
on the street” interviews
Judgmental sampling is a form of convenience
sampling in which the population elements are
selected based on the judgment of the
engineers selected in industrial
witnesses used in court
Quota sampling may be viewed as two-stage restricted
The first stage consists of developing control categories, or
quotas, of population elements.
In the second stage, sample elements are selected based on
convenience or judgment.
In snowball sampling, an initial group of
respondents is selected, usually at random.
being interviewed, these respondents are
asked to identify others who belong to the target
population of interest.
respondents are selected based on
DETERMINATION OF SAMPLE
The size of the population does not influence the size of
Methods of determining the sample size in
may arbitrary decide the size of sample
without giving any explicit consideration to the
accuracy of the sample results or the cost of sampling.
total budget for the field survey in a project
proposal is allocated.
may decide on the sample size based on
what was done by the other researchers in similar
DETERMINATION OF SAMPLE
Confidence interval approach for determining the size
of the sample
The following points are taken into account for determining
the sample size in this approach.
variability of the population: Higher the variability as
measured by the population standard deviation, larger will
be the size of the sample.
confidence attached to the estimate: Higher the
confidence the researcher wants for the estimate, larger will
be sample size.
allowable error or margin of error: Greater the
precision the research seeks, larger would be the size of the
DETERMINATION OF SAMPLE
Sample size for estimating population mean The formula for determining sample size is given as:
n = Sample size
σ = Population standard deviation
e = Margin of error
Z = The value for the given confidence interval
DETERMINATION OF SAMPLE
Sample size for estimating population
1. When population proportion p is known
2. When population proportion p is not known
Ex1. An economist is interested in estimating the average
monthly household expenditure on food items by the households
of a town. Based on past data, it is estimated that the standard
deviation of the population on the monthly expenditure on food
items is Rs. 30. With allowable error set at Rs. 7, estimate the
sample size required at a 90 percent confidence.
Given a population with standard deviation of 8.6.
Determine the sample size needed to estimate the mean of the
population with in ± 0.5 with a 99percent confidence. Ans: 1962
Ex3. A Manager of Departmental store would like to women’s
spending per year on cosmetics. He is interested in knowing the
population proportion of women who purchases their cosmetics
primarily from his store. If he wants to have a 90% confidence of
estimating the true proportion to be within ±0.045, what sample
size is needed?
Ex4. A consumer electronics company wants to determine the job
satisfaction levels of its employees. For this, they ask a simple
question, 'Are you satisfied with your job?’ It was estimated that
no more than 30 percent of the employees would answer yes.
What should be the sample size for this company to estimate the
population proportion to ensure a 95 percent confidence in result,
and with 0.04 of the true population proportion?
Business Research Methods – Cooper, Schindler; Tata Mc Graw
Marketing Research – G C Beri; Tata Mc Graw Hills.
Business Research Methods – William G Zikmund; Thomson.
Marketing Research – Tull, Hawkin; PHI
February 6, 2014