SAMPLING

SAMPLING CONCEPTS 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 enumeration.

ADVANTAGES OF SAMPLE OVER CENSUS

Sample saves time and cost.

There are situations where a sample is the only option.

The study of a sample instead of complete enumeration may, at times, produce more reliable results.

A census is appropriate when the population size is small.

SAMPLING VS NON-SAMPLING ERROR

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 below:

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 computation.

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

Simple random sampling with replacement

Simple random sampling without replacement

Systematic sampling

Stratified random sampling

Cluster sampling

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.

SYSTEMATIC SAMPLING

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.

SYSTEMATIC SAMPLING

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.

STRATIFIED SAMPLING

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 omitted.

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.

STRATIFIED SAMPLING

The elements within a stratum should be as homogeneous as possible, but the elements in different strata should be as heterogeneous as possible.

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.

STRATIFIED SAMPLING

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.

CLUSTER SAMPLING

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 SRS.

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).

SAMPLING TYPES

Non-probability Sampling - In case of non-probability 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

Judgemental sampling

Snowball sampling

Quota sampling

CONVENIENCE SAMPLING

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.

use of students, and members of social organizations

mall intercept interviews without qualifying the respondents

department stores using charge account lists“people on the street” interviews

JUDGMENTAL SAMPLING

Judgmental sampling is a form of convenience sampling in which the population elements are selected based on the judgment of the researcher.

test markets

purchase engineers selected in industrial marketing research

expert witnesses used in court

QUOTA SAMPLING

Quota sampling may be viewed as two-stage restricted judgmental sampling.

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.

Population Samplecomposition composition

ControlCharacteristic Percentage Percentage NumberSex Male 48 48 480 Female 52 52 520

____ ____ ____100 100 1000

SNOWBALL SAMPLING

In snowball sampling, an initial group of respondents is selected, usually at random.

After being interviewed, these respondents are asked to identify others who belong to the target population of interest.

Subsequent respondents are selected based

on the referrals.

DETERMINATION OF SAMPLE SIZE

The size of the population does not influence the size of the sample

Methods of determining the sample size in practice:

Researchers may arbitrary decide the size of sample without giving any explicit consideration to the accuracy of the sample results or the cost of sampling.

The total budget for the field survey in a project proposal is allocated.

Researchers may decide on the sample size based on what was done by the other researchers in similar studies.

SLIDE 9-6

DETERMINATION OF SAMPLE SIZEConfidence interval approach for determining the size of the sample

The following points are taken into account for determining the sample size in this approach.

The variability of the population: Higher the variability as measured by the population standard deviation, larger will be the size of the sample.

The confidence attached to the estimate: Higher the confidence the researcher wants for the estimate, larger will be sample size.

The allowable error or margin of error: Greater the precision the research seeks, larger would be the size of the sample.

SLIDE 9-7

DETERMINATION OF SAMPLE SIZESample size for estimating population mean - The formula for determining sample size is given as:

Where

n = Sample sizeσ = Population standard deviatione = Margin of errorZ = The value for the given confidence interval

DETERMINATION OF SAMPLE SIZESample size for estimating population proportion – 1. When population proportion p is known

2. When population proportion p is not known

EXERCISE: 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. Ans: 50

Ex2. 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? Ans: 335

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? Ans: 505

SUMMARY

SAMPLING

April 10, 2023

1. Business Research Methods – Cooper, Schindler; Tata Mc Graw Hills

2. Marketing Research – G C Beri; Tata Mc Graw Hills.3. Business Research Methods – William G Zikmund; Thomson.4. Marketing Research – Tull, Hawkin; PHI

REFERENCES:

April 10, 2023

April 10, 2023

Q & A

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