sampling1- ppt
TRANSCRIPT
-
7/28/2019 Sampling1- ppt
1/31
-
7/28/2019 Sampling1- ppt
2/31
Learning Objectives
Upon completion of 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
-
7/28/2019 Sampling1- ppt
3/31
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.
-
7/28/2019 Sampling1- ppt
4/31
Sampling Concepts
Population: Population refers to any group of people or objects that formthe 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.
Sampling frame: Sampling frame comprises all the elements of a
population with proper identification that is available to us for selection at
any stage of sampling. 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 usto generalize the results.
Census (or complete enumeration):An examination of each and every
element of the population is called census or complete enumeration.
-
7/28/2019 Sampling1- ppt
5/31
Why Is Sampling Essential?
Sampling saves time.
Sampling saves money.
The study of a sample instead of complete enumeration
may, at times, produce more reliable results.
Sampling broadens the scope of the study in light of thescarcity of resources.
It has been noticed that sampling provides more accurate
results, as compared to census because in sampling, non-
sampling errors can be controlled more easily.
In most cases complete census is not possible and, hence,sampling is the only option left.
A census is appropriate when the population size is small.
-
7/28/2019 Sampling1- ppt
6/31
Figure 5.1: Steps in the sampling design process
-
7/28/2019 Sampling1- ppt
7/31
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 must be determined A researcher takes a sample from a population list, directory,
map, city directory, or any other source used to represent the
population. 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.
-
7/28/2019 Sampling1- ppt
8/31
The Sampling Design Process (Contd.)
Step 3:Appropriate sampling technique must be selected
In sampling with replacement, an element is selected from the
frame, required information is obtained, and then the element
is placed back in the frame. This way, there is a possibility of
the element being selected again in the sample.
As compared to this, in sampling without replacement, anelement is selected from the frame and not replaced in the
frame. This way, the possibility of further inclusion of the
element in the sample is eliminated.
Step 4: Sample size must be determined
Sample size refers to the number of elements to be includedin the study.
Step 5: Sampling process must be executed
-
7/28/2019 Sampling1- ppt
9/31
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 familiarity of
the researcher with the subject, convenience, etc. are the
basis of selection
-
7/28/2019 Sampling1- ppt
10/31
Figure 5.2: Random and non-random sampling methods
-
7/28/2019 Sampling1- ppt
11/31
Random Sampling Methods
Simple Random Sampling
In simple random sampling, each member of the population
has an equal chance of being included in the sample.
Stratified Random Sampling
In stratified random sampling, elements in the population are
divided into 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.
In stratified random sampling, stratum should be relatively
homogenous and the strata should contrast with each other.
-
7/28/2019 Sampling1- ppt
12/31
Random Sampling Methods (Contd.)
In cases where the percentage of
sample taken from each stratum
is proportionate to the actual
percentage of the stratum within
the whole population, stratified
sampling is termed asproportionate stratified
sampling.
In cases where the sample taken
from each stratum is
disproportionate to the actualpercentage of the stratum within
the whole population,
disproportionate stratified
random sampling occurs.
Figure 5.5: Stratified random
sampling based on educational
levels
-
7/28/2019 Sampling1- ppt
13/31
Random Sampling Methods (Contd.)
Cluster (or Area) Sampling In cluster sampling, we divide the population into non-overlapping
areas or clusters.
In stratified sampling, strata happen to be homogenous but in cluster
sampling, clusters are internally heterogeneous.
A cluster contains a wide range of elements and is a good
representative of the population.
Figure 5.6: Diagram for cluster sampling
-
7/28/2019 Sampling1- ppt
14/31
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.
A researcher wants to take a sample of size 30 from a
population of size 900 and he has decided to use
systematic sampling for this purpose.
For obtaining the sample, the first member can be selected
randomly and after that every 30th member of the population is
included in the sample. Suppose the first element 3 is selectedrandomly and after this, every 30th element, that is, 33rd, 63rd,
element up to a sample size of 30 are included in the sample.
-
7/28/2019 Sampling1- ppt
15/31
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
-
7/28/2019 Sampling1- ppt
16/31
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, certain subclasses, such as age, gender,income group, and education level are used as strata. Stratified
random sampling is based on the concept of randomly selecting
units from the stratum.
However, in case of quota sampling, 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.
-
7/28/2019 Sampling1- ppt
17/31
Non-Random Sampling (Contd.)
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.
A sampling procedure in which initial respondents are selected
by probability methods and additional respondents are
obtained from information provided by the initial respondents.
This technique is used to locate members of rare population by
referrals.
-
7/28/2019 Sampling1- ppt
18/31
Sampling and Non-Sampling Errors
Sampling Error: This error arises when a sample is not representative of
the population.
Sampling errors can occur due to some specific reasons:
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.
Sometimes researchers demarcate sampling units wrongly and
hence, provide scope for committing sampling errors.
-
7/28/2019 Sampling1- ppt
19/31
Sampling and Non-sampling Errors
(Contd.)
Non-Sampling Errors
All errors other than sampling can be included in the category of non-
sampling errors.
The following are some common non-sampling errors:
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.
-
7/28/2019 Sampling1- ppt
20/31
Determination of Sample Size
The size of the population does not influence the size of thesample
Methods of determining the sample size in practice:
Researchers may arbitrary decide the size of samplewithout giving any explicit consideration to the accuracy ofthe sample results or the cost of sampling.
The total budget for the field survey in a project proposal isallocated.
Researchers may decide on the sample size based onwhat was done by the other researchers in similar studies.
-
7/28/2019 Sampling1- ppt
21/31
Determination of Sample Size
Confidence interval approach for determining the size of thesample
The following points are taken into account for determining thesample size in this approach.
The variability of the population: Higher the variability asmeasured by the population standard deviation, larger will be thesize of the sample.
The confidence attached to the estimate: Higher the confidencethe researcher wants for the estimate, larger will be sample size.
The allowable error or margin of error: Greater the precision theresearch seeks, larger would be the size of the sample.
-
7/28/2019 Sampling1- ppt
22/31
Determination of Sample Size
Sample size for estimating population mean -The formula for determining sample size is given
as:
Where
n = Sample size
= Population standard deviatione = Margin of error
Z = The value for the given confidence interval
-
7/28/2019 Sampling1- ppt
23/31
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 estimatedthat the standard deviation of the population on the monthly
expenditure on food item is Rs.30. With allowable error set at
Rs.7, estimate the sample size required at a 90 per cent
confidence interval. (z=1.645)
Example 1
It is desired to estimate the mean life time of a certain kind of
vacuum cleaner. Given that the population std. dev. is 320
days, how large a sample is needed to be able to assert witha confidence level of 96 per cent that the mean of the sample
will differ from the population mean by less than 45 days?
(z=2.055)
Example 2
-
7/28/2019 Sampling1- ppt
24/31
You have a population of approximately 1500 patients and wish
to find out their attitudes to a new voucher scheme. There is
insufficient time & money to collect data from all of them usinga questionnaire and so you decide to send the questionnaire to
a sample.
Your calculation of sample size reveals that to obtainacceptable levels of confidence & accuracy you need an actual
sample size of approximately 300 patients to whom you will
send the questionnaire.
You decide to select them using systematic sampling.
First you need to work out the sampling fraction:
300/1500=1/5
Sampling fraction of 1/5 means you need to select every 5th
patient from the sampling frame.
Case let 1: Systematic Sampling
-
7/28/2019 Sampling1- ppt
25/31
You use a random number to decide where to start on the
sampling frame. As your sampling fraction is1/5, the starting
point must be one of the first five patients. You therefore select
a one-digit random number between 1 to 5.
Once you have selected your first patient at random you select
every fifth patient until you have gone right through yoursampling frame.
If the random number you selected was3, then you would
select following patient numbers.3 8 13 18 23 28 33 38
and so on until 300 patients had been selected.
Cont
-
7/28/2019 Sampling1- ppt
26/31
Ceri needed to select a sample of firms to undertake an interview
based survey about the use of photocopiers.
As she had limited resources with which to pay for travel and other
associated data collection costs she decide to interview firms in 4
geographical areas selected from a cluster grouping of local
administrative areas.
A list of all local administrative areas formed her sampling frame.
Each of the local administrative areas (clusters) was given a unique
number, the first being 1 and so on.
The four sample clusters were selected from this sampling frame oflocal administrative areas using simple random sampling.
Ceris sample was all firms within the selected clusters.
She decided that the appropriate telephone directories would provide
a suitable list of all firms in each cluster.
Case let 2: Cluster Sampling
-
7/28/2019 Sampling1- ppt
27/31
A market research organisation needs you to interview a sample of
400 households in England & Wales.
The electoral register provides a possible sampling frame. Selecting
400 households using either systematic or random sampling would
probably result in these 400 households being dispersed throughout
England & Wales.
The time and cost of travelling to and interviewing your sample would
be enormous. By using multi-stage sampling these problems can be
overcome.
In the first stage the geographical area (England & Wales) is split intodiscrete sub areas (countries). These form the sampling frame. After
numbering, a small no. of countries are selected using simple
random sampling.
Since each case (household) is located in a country each has an
equal chance of being selected for the final sample.
Case let 3: Multi stage Sampling
-
7/28/2019 Sampling1- ppt
28/31
As the countries selected are still too large the selected countries are
subdivided into smaller geographically discrete areas (electoral
wards), which form the next sampling frame (Stage 2).
Another random sample is selected. A larger no. of wards are
selected to allow for likely important variations in households
between wards.
A sampling frame is generated for each ward using a combination of
the electoral register and UK Royal Mails postcode address file.
The cases (households) that will be interviewed are then selected
using either random or systematic technique.
Cont
-
7/28/2019 Sampling1- ppt
29/31
The distribution of the annual earnings of the employees of a cementfactory is normally distributed. This distribution has a mean of Rs
25,000 and standard deviation of Rs 3000. If a researcher draws a
random sample of size 50, what is the probability that their average
earnings will be more than Rs 26,000?
Example 1
-
7/28/2019 Sampling1- ppt
30/31
Figure 5.10: Probability that the average
earnings of employees is more than Rs
26,000
Figure 5.11: Corresponding zscores
for probability of average earnings
more than Rs 26,000
Example 1 (Contd.)
-
7/28/2019 Sampling1- ppt
31/31
END OF CHAPTER