Sampling and Sampling Distribution

Sampling and sampling Distribution
INTRODUCTION
Inferential statistics is a systematic method of inferring satisfactory conclusions about

the population on the basis of examining a few representative units termed as sample.
The process of selecting samples is called sampling. Generalization of the sample data
results to the population, which is one of the characteristic features of research, needs
scientific approach of searching for facts. Therefore, sampling must be scientific.
Definition of Sample and Census Survey
A subset of the population selected for the study is known as sample. The group from
which the samples are selected is called Universe or Population.
Sample survey: is a procedure, which makes one able to draw inferences about the
population by observing or measuring few items.
Census survey: - is a method of inquiry, which makes one able to draw inferences by
observing each item constituting the population.
Objectives of sampling are:
1- To obtain maximum information about the characteristics of the population with

less time, energy and expenditure
2- To obtain the best possible values of parameter.
Sampling refers to the method of selecting a sample from the universe. A proper
procedure is to be adopted for evaluating the sample plan in order to select
representative units of the universe. Sampling occupies a key role in the study and has
acquired the status of a technical job.
The number of units in the sample is called Sample size. Not on a new line
* Sample size should never be too small nor too large but optimum. Optimum fulfills
the needs of efficiency, representativeness, reliability and validity.
The size of sample for a study is determined on the basis of the following factors
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i- the size of the population
ii- the availability of resources
iii- the degree of accuracy
iv- the homogeneity or heterogeneity of the population
v- the nature of the study
vi- the method of sampling technique adopted
vii- the nature of respondents
ADVANTAGES AND DISADVANTAGES OF SAMPLE SURVEY
If the sample is drawn on scientific approach, the adopted sample design is good and
the sample size is adequate. Sample method has some merits over the census method.
That are:
1- Sampling saves time and money.

2- It is much convenient as it involves less personal staff.
3- It is useful when population is infinitely large.
4- It can be more accurately supervised and data can be carefully selected.
5- It is useful in case of inspecting the quality of units, which we have to resort to
sampling, such as testing the quality of bulbs, tubes, strength of stencils, testing
explosives, etc.
Sampling method has its limitations and problems, which are:
1- It would give unreliable data if not designed and executed carefully. Samples are
like medicines. They can be harmful if taken carelessly or without knowledge of
their effect.
2- The service of skilled, trained, qualified personnel for supervision; and
sophisticated equipment and statistical techniques are required. In the absence of
these, it may not be reliable.
3- Sample survey is not useful when information is needed about each and every
unit of the population.
TYPES OF SAMPLING TECHNIQUES
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1 INTRODUCTION
Statistical methods are especially appropriate for handling data (information), which
are subject to variations, and for which we can observe only a fraction of the totality of
observations, which may exist. Under this situation, techniques must be devised by
which we can make inferences about the nature of the totality of the universe from the
particular observation we have.
TYPES OF SAMPLING TECHNIQUES
Sampling technique refers to the method of selecting a sample from the universe
(population). It occupies a key role in a study and has acquired the status of being a
technical job. The right type of sampling technique is of paramount importance in the
execution of a sample survey in accordance with the objectives and the scope of the
inquiry. The sampling methods may broadly be classified as:
1- Probability sampling (simple, stratified, & systematic)
2- Non-probability sampling (judgment, convenient, quota, incidental, purposive,
self-selected, etc.)
3- Mixed sampling (cluster sampling)
RANDOM (PROBABILITY) SAMPLING
Random sampling method is a method of selection of a sample such that each item within the
population has equal chance of being selected.
In this method, there is no place for investigator’s bias in sample selection since it
depends on probability. It provides more accurate estimates in the sense of greater
precision.
I. Simple Random Sampling Method (SRSM): involves very simple method of drawing a
sample from a given population. The selection of samples is random in character.
The oldest method adopted in simple RS is the use of lottery system.
II Stratified Random Sampling Method (STRSM)
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Under this method, the whole population is divided into a number of homogeneous
groups or strata. From each of these strata, random sample of size n is selected. Thus,
stratified RS means selecting a number of random samples, one from each stratum of
the universe. It is used when each group has small variation within itself but wide
variation between the groups.
III. Systematic Random Sampling Method (SYRSM)
In this method, a random starting point is selected from the list representing the
universe and the remaining units are automatically selected in a definite sequence at an
equal spacing from one another. This method is recommended if the sample units are
arranged in systematic order such as chronological, geographical, alphabetical, etc. and
also if the sample units in the universe are uniquely identified. Systematic sampling is
also called sampling by regular intervals or sampling by fixed intervals.
NON-RANDOM (NON-PROBABILITY) SAMPLING METHOD
In this method, the chance of including any elementary unit of the population in the
sample cannot be determined. It is simple to adopt and no complicated procedure is
needed to draw a sample.
There are many non-random sampling techniques. Some of which are Judgment,
Convenient and Quota sampling.
Judgment Sampling: - The exercise of good perception and appropriate strategy are
taken into account. Samples are selected deliberately by the investigator. It is a personal
view. So it becomes satisfactory with regards to one’s research needs. For example, if a
sample of 10 students is to be singled out from a class of 50 for analyzing the habits of
students, the investigator would select ten students, who in his opinion are
representative of the class.
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Convenient Sampling: - Elements of the sample are selected by taking those elements
of the population, which are readily available or convenient for the investigator.
Example: Asking people form one area.
Quota sampling: - In this technique, quota is set up according to given criteria, but the
sample with in prescribed quota is selected by personal judgment of the investigator. It
is suitable in market and public opinion surveys where stratification is very difficult.
However, it suffers from representativeness as the interviewer may select samples
convenient for him with regards to location and sample unit.
It is the combination of judgment and stratified sampling methods. so it enjoys the
merits of both .
Example: - If we ask about Canada dry for a prescribed quota of 20 households, 15

students and 10 children, then this method is quota sampling.
MIXED SAMPLING METHOD (CLUSTER SAMPLING)
Groups of items (clusters), homogenous in character, are formed on location or class

basis. Here a sample of cluster is selected and next within cluster, sub groups are
identified for inclusion in the sample. It is also known as Area sampling as selection of
units is made on the basis of place. The clusters may or may not be equal in size. The
smaller the size of the cluster, the greater will be the accuracy. It is economical and
much easier.
Example: - Suppose a survey is conducted about students’ capacity in auditing. From 10

colleges in Addis Ababa if college X is selected and from 50 classes of college X if 6
classes are selected randomly and considered for the study, then this technique is
cluster sampling.
Errors in sample survey:

There are two types of errors
a) Sampling error:
 Is the discrepancy between the population value and sample value.
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 May arise due to in appropriate sampling techniques applied
b) Non sampling errors:
Are errors due to procedure bias such as:
 Due to incorrect responses
 Measurement
 Errors at different stages in processing the data.
SUMMARY
In a field of statistical analysis, it is not possible to take the entire population for
consideration due to time, cost and other constraints. Therefore, random samples are
taken from the population, which are analyzed properly and lead to generalizations
that are valid for the entire population. A small sample properly selected may be a true
representative of the universe while a large sample poorly chosen may be unreliable. So
the selection of a sample should be done in a manner that every item in the universe
must have an equal chance of inclusion in the sample. Thus a good sample possesses
two characteristics, which are:
i) Representativeness of the Universe
ii) Adequate in Size
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Sampling and sampling Distribution

Inferential statistics is a systematic method of inferring satisfactory conclusions about

Objectives of sampling are:

1- To obtain maximum information about the characteristics of the population with

1- Sampling saves time and money.

TYPES OF SAMPLING TECHNIQUES

The oldest method adopted in simple RS is the use of lottery system.

II Stratified Random Sampling Method (STRSM)

III. Systematic Random Sampling Method (SYRSM)

NON-RANDOM (NON-PROBABILITY) SAMPLING METHOD

Example: Asking people form one area.

Example: - If we ask about Canada dry for a prescribed quota of 20 households, 15

MIXED SAMPLING METHOD (CLUSTER SAMPLING)

Groups of items (clusters), homogenous in character, are formed on location or class

Example: - Suppose a survey is conducted about students’ capacity in auditing. From 10

Errors in sample survey:

i) Representativeness of the Universe

ii) Adequate in Size

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