1. Business Research Process (Step-6): Research Design- Sampling
Chapter 8
Business Research Process (Step-6): Research Design- Sampling
References:
Research Methods For Business (Uma Sekaran)
VU Book of BRM
Business Research Methods (William G. Zikmund)
Internet
Resource Person: Furqan-ul-haq Siddiqui

2. The Business Research Process
The Business Research Process
Problem definition
Theoretical
Framework
Variables
Identification and labelling
Generation of
Hypothesis
Observation
 Broad problem area 1
Preliminary Data Gathering  5 4 2 3
Scientific
Research
Design 6
Data Collection, analysis & interpretation NO
Deduction
Research Question Answered?
Decision
Making
Report
Presentation
Report
Writing
Yes

3. Elements of Research Design:
the purpose of the study (exploratory, descriptive, and explanatory)
the unit of analysis (individuals, dyads, groups)
time dimension (Cross sectional & longitudinal)
Researcher Control of Variables (In an experiment, the researcher attempts to control and/or manipulate the variables in the study and with an ex post facto design, investigators have no control over the variables in the sense of being able to manipulate them. They can only report what has happened or what is happening.
Choice of Research Design: Mode of Observation (survey, experiment, content analysis, field observation, case study, focus group discussion.)
Sampling Design
Observation Tools
Field Data Collection
Data Processing and Data Analysis

4. 2. Unit of Analysis
Refers to the level of aggregation of the data during data analysis stage (individual, or at group, or at organization level)
the problem statement focuses on how to raise the motivational levels of employees.
the unit of analysis is the individual

5. the unit of analysis is the dyads
Study two person interaction – then several two person groups will become the unit of analysis (husband-wife, supervisor-subordinate, teacher-student)
the unit of analysis is the dyads
Study three persons relationship (polygamy etc)
the unit of analysis is triad
Group effectiveness – unit of analysis is group. Comparing different departments in the work organization.
Similarly: organizations, geographical units may be unit of analysis
The research question determines the unit of analysis. Keeping the research question in view, it is necessary to decide on the unit of analysis since the data collection methods, sample size, and even the variables included in the framework may sometimes be determined or guided by the level at which the data are aggregated for analysis.

6. Population and Sampling Terminologies
Population- the collection of all individuals, families, groups, organizations, and events that we are interested in finding out about. For example, all individuals of Pakistan enrolled in MBA. the pool of all available elements is population.
Target Population-Target population is the complete group of specific population elements relevant to the research project. Target population may also be called survey population i.e. that aggregation of elements from which the survey sample is actually selected. MBA Students of IMS.
Population Element- An individual unit of a specific population.

7. Census- Investigation of all individual elements that make up a population
Sample- Subset of Population
Subject- A single unit of sample.
Sample size- “The number of subjects in the obtained sample.”
Sampling- The process of selecting sufficient number of elements from population to make conclusions about the whole population. It enables the researchers to estimate unknown characteristics of the population.
Sampling Frame or working population- In actual practice the sample is be drawn from a list of population elements that is often different from the target population that has been defined. A sampling frame is the list of elements from which the sample may be drawn. Eg. list of all college students meeting the criteria of target population and who are enrolled on the specified date.

8. Sampling Frame Error- A sampling frame error occurs when certain sample elements are excluded or when the entire population is not accurately represented in the sampling frame. The error that occurs when certain sample elements are not listed or available and are not represented in the sampling frame.
Sampling Unit- A sampling unit is that element or set of elements considered for selection in some stage of sampling. Sampling may be done in single stage or in multiple stages. In a simple, single-stage sample, the sampling units are the same as the elements. In more complex samples, however, different levels of sampling units may be employed. For example, a researcher may select a sample of Mohallahs in a city, and then select a sample of households from the selected Mohallahs, and finally may select a sample of adults from the selected households. The sampling units of these three stages of sampling are respectively Mohallah, households, and adults, of which thee last of these are the elements. More specifically, the terms “primary sampling units,” “secondary sampling units,” and “final sampling units” would be used to designate the successive stages.

9. Parameter- a numerical summary of a population or a number which describes a characteristic of a population (population mean, population standard deviation, population variance)
Static- Any numerical measure computed from a subset of the population (typically a sample).
Sampling error or estimation error- is the error caused by observing a sample instead of the whole population. The sampling error can be found by subtracting the value of a parameter from the value of a statistic.

10. Reasons of Sampling Impossible to observe all relevant events.
Cuts costs, reduces labor requirements and gathers vital information quickly.
If properly selected is sufficiently accurate in most cases.
Sampling may be the Only Way- Many research projects, especially those in quality control testing, require the destruction of the items being tested. If the manufacturer of firecrackers wished to find out whether each product met a specific production standard, there would be no product left after testing.
Time factor

12. Stages in the Selection
of a Sample

13. Types of Sampling Probability Sampling
“This is the one in which each person in the population has the same chance of being selected.” A probability sampling scheme is one in which every unit in the population has a chance (greater than zero) of being selected in the sample
Types of Probability Sampling
Sample Random Sampling
Systematic Sampling (Interval Random Sampling)
Stratified Sampling (Proportionate or disproportionate)
Cluster Sampling

14. Simple Random Sampling
A simple random sample is a subset of individuals (a sample) chosen from a larger set (a population). Each individual is chosen randomly and entirely by chance, such that each individual has the same probability of being chosen at any stage during the sampling process
Advantages
ideal for statistical purposes
Disadvantages
hard to achieve in practice
expensive to conduct as those sampled may be scattered over a wide area

15. One of the most obvious limitations of simple random sampling method is its need of a complete list of all the members of the population. Please keep in mind that the list of the population must be complete and up-to-date. This list is usually not available for large populations. In cases as such, it is wiser to use other sampling techniques.

17. b. Systematic Sampling/Interval Random Sampling
Systematic random sampling is simple random sampling with a short cut for random selection.
Here are the steps you need to follow in order to achieve a systematic random sample:
number the units in the population from 1 to N
decide on the n (sample size) that you want or need
k = N/n = the interval size
randomly select an integer between 1 to k
then take every kth unit

19. Distinction between a systematic random sample and a simple random sample
Let us assume you had a school with 1000 students, divided equally into boys and girls, and you wanted to select 100 of them for further study. You might put all their names in a bucket and then pull 100 names out. Not only does each person have an equal chance of being selected, we can also easily calculate the probability of a given person being chosen, since we know the sample size (n) and the population (N) and it becomes a simple matter of division:
n/N or 100/1000 = 0.10 (10%)
This means that every student in the school has a 10% or 1 in 10 chance of being selected using this method. Further, all combinations of 100 students have the same probability of selection.
If a systematic pattern is introduced into random sampling, it is referred to as "systematic (random) sampling". For instance, if the students in our school had numbers attached to their names ranging from 0001 to 1000, and we chose a random starting point, e.g. 0533, and then pick every 10th name thereafter to give us our sample of 100 (starting over with 0003 after reaching 0993). In this sense, this technique is similar to cluster sampling, since the choice of the first unit will determine the remainder. This is no longer simple random sampling, because some combinations of 100 students have a larger selection probability than others - for instance, {3, 13, 23, ..., 993} has a 1/10 chance of selection, while {1, 2, 3, ..., 100} cannot be selected under this method.

20. Stratified Random Sampling
When the population is heterogeneous, the use of simple random sample may not produce representative Sample. Stratified Random Sampling, also called proportional or quota random sampling, involves dividing your population into homogeneous subgroups and then taking a simple random sample in each subgroup. In more formal terms:
Objective: Divide the population into non-overlapping groups (i.e., strata) N1, N2, N3, ... Ni, such that N1 + N2 + N Ni = N. Then do a simple random sample of f = n/N in each strata.

21. Types of Stratified Random Sampling
Proportionate Stratified
The number of sampling units drawn from each stratum is in proportion to the population size of that stratum.
Disproportionate Stratified
The sample size for each stratum is allocated according to analytical considerations.

22. Example of Stratified Sampling
Problem: The Pakistan Radio Corporation wants to know about the listener’s interest regarding FM 101.
The population is divided into homogenous groups ( Population is divided by age)
Population under study: 10,000
Sample size = 50% of total population.

23. Example of Stratified Sampling
Age of Listeners
No. of listeners in population (Age – wise)
Proportion of listeners in population.
10 – 20 years old
2000
20%
20 – 30 years old
5000
50%
30 – 40 years old
40 and above
1000
10%
Total
10,000
100%

24. Example of Proportionate Stratified Sampling
Age of Listeners
Proportion of listeners in sample.
No. of listeners in population.
(5000*Proportion)
10 – 20 years old
20%
1000
20 – 30 years old
50%
2500
30 – 40 years old
40 and above
10%
500
Total
100%
5000

25. Example of Disproportionate Stratified Sampling
Age of Listeners
Proportion of listeners in sample.
No. of listeners in population.
(5000*Proportion)
10 – 20 years old
25%
1250
20 – 30 years old
30 – 40 years old
40 and above
Total
100%
5000

26. d. Cluster (Area) Sampling
The population is divided into mutually exclusive groups (such as city), and the researcher draws a sample fro there.

27. Steps of Cluster Sampling
Identify the Population
Determine the sample size
Identify the logical clusters
List all the clusters
Estimate the average no. of population members per cluster. (Estimated size of cluster)
Determine the no. of cluster by dividing the sample size with the estimated size of cluster.
Randomly select the clusters.

28. Example of Cluster Sampling
Dividing the FM 101 listeners into heterogeneous groups.
Population = 10,000 listeners
Sample size = 5,000
Divided the population city-wise.
No. of cities where FM 101transmit its programs in Balochistan is 10.

29. 4. List of all cities (clusters)
S.No
Cities (clusters)
No. of Listeners 1.
Quetta
3000 2.
Mastung
2000 3.
Pishin 4.
Khuzdar
500 5.
Sibi
400 6.
Loralai 7.
Zhob 8.
Chaman
300 9.
Noshki
600
10.
Kalat
200

30. 5. Estimation of average no. of listeners per city.
Total no. of listeners of all cities / No. of cities.
= 10,000/10 = 1000 listeners per city
So the estimated size of cluster will be 1000 listeners per city.
6. Determination of no. of clusters.
Sample size / Estimated size of cluster
= 5000 / 1000 = 5 cities (Clusters)
7. Randomly select the 5 cities (clusters)

31. 2. Non-probability Sampling
Convenience sampling- The researcher selects the most accessible population members
Judgment sampling- The researcher selects population members who are good prospects for accurate information.
Quota sampling- The researcher finds and interviews a prescribed number of people in each of several categories.
Snowball Sampling- Type of sampling in which selection of respondents is based on referrals from the initial respondants.

32. Sample Size determination
Population size:
Margin of error (Confidence Interval) : A percentage that describes how closely the answer your sample gave is to the “true value” is in your population. The smaller the margin of error is, the closer you are to having the exact answer at a given confidence level.
Confidence level: A measure of how certain you are that your sample accurately reflects the population, within its margin of error. Common standards used by researchers are 90%, 95%, and 99%.
Statistical Test: The types of analyses you are going to undertake (many statistical techniques have a minimum threshold).
Cost, time, experience, ease or difficulty in data availability etc.

33. Sample Size Determination