Sampling

Prof Tauseef Irfan

Definition Sampling: is the process of selecting a few (a

sample) from a bigger group, the sampling population, to become the basis for estimating or predicting the prevalence of an unknown piece of information, situation or outcome regarding the bigger group.

Sample: is a subgroup of population you are interested in.

Adv. & Disad. Of Sampling ProcessAdvantages

Saves time Saves financial and human resources

Disadvantages Unable to find out the information about the

population’s characteristics of interest to you but you only estimate or predict them

The possibility of an error in your estimation exists

Sampling Terminology Term Term Definition Definition

Population/study population

The large general group of many cases from which a researcher draw a sample and are usually denoted by the letter (N)

Sample A smaller set of cases a researcher selects from a larger group and generalizes to the population

Sample size The number of selected cases from larger population from who you obtain the required information and is usually denoted by the letter (n)

Sampling design/strategy

The method you use to select your sample

Sampling unit/ sampling element

The name for a case or single unit to be selected

Sampling frame The list of units composing a population from which a sample is selected

Sample statistics

Information obtained from your respondents

Population parameters/population mean

A characteristic of the entire population that is estimated from a sample

Principles of Sampling Principle One: In a majority of cases of

sampling there will be a difference between the sample statistics and the true population mean, which is attributable to the selection of the units in the sample

Average age of four people: A, B, C & D.

A is 18 yrs, B is 20, C is 23 & D is 25

Average age is : 21.5 (18+20+23+25 = 86 divided by 4)

By selecting a sample of two we can estimate their average age.

And we can have six possible combinations of two: 1. A & B 2. A & C 3. A & D 4. B & C 5. B & D 6. C & D

Difference between Sample average & population Average (2 cases)

Sample Sample average

Population mean

Difference bet 1 & 2

1 19.0 21.5 -2.5

2 20.5 21.5 -1.5

3 21.5 21.5 0.0

4 21.5 21.5 0.0

5 22.5 21.5 +1.0

6 24.0 21.5 +2.5

1.1. A & B 2. A & C 3. A & D 4. B & C 5. B & D 6. C & D

Principle Two: The greater the

sample size, the more accurate will be the estimate of the true population mean

Average age of four people: A, B, C & D.


Average age is : 21.5 (18+20+23+25 = 86 divided by 4)

By selecting a sample of three we can estimate their average age.

And we can have four possible combinations of three: 1. A + B+C 2. A + B+D 3. A + C+D 4. B + C+D

Difference between Sample & Population Average (3 cases)


Population mean


1 20.33 21.5 --1.17

2 21.00 21.5 -0.5

3 22.00 21.5 +0.5

4 22.67 21.5 +1.17

11. A + B+C 2. A + B+D 3. A + C+D 4. B + C+D

Principle Three: The greater the

difference in the variable under study in a population for a given sample size, the greater will be the difference between the sample statistics and the true population mean


Average age is: 29 (18+26+32+40 = 116 divided by 4)

Difference between Sample Statistics & Population Mean (2 cases)


Population mean


1 22 29.00 -7.00

2 25 29.00 -4.00

3 29 29.00 0.00

4 29 29.00 0.00

5 33 29.00 +4.00

6 36 29.00 +7.00

1.1. A & B 2. A & C 3. A & D 4. B & C 5. B & D 6. C & D

Difference between Sample and Population Average (3 cases)


Population mean


1 25.33 29.00 --3.67

2 28.00 29.00 -1.00

3 30.00 29.00 +1.00

4 32.66 29.00 +3.66

1.1. A + B+C A + B+C 2.2. A + B+D A + B+D 3.3. A + C+D A + C+D 4.4. B + C+D B + C+D

Factors affecting the inferences of sample The size of the sample The extent of variation in the sampling

population

Aims in selecting a sample To achieve maximum precision in your

estimates within a given sample sizeTo avoid bias in the selection of your sample Bias in the selection of a sample can occur if: Sampling is done by a non-random methodThe sampling frame does not cover the

sampling population accurately and completely

A section of a sampling population is impossible to find or refuses to cooperate

Random/probability sampling DesignsEach element in the population has an equal and

independent chance of selection in the sample.

Equal : means the probability of selection of each element in the population is the same.

That is, the choice of an element in the sample is not influenced by other considerations such as personal preference.

Independent : means that the choice of one element is not dependent upon the choice of another element in the sampling

That is, the selection or rejection of one element does not affect the inclusion or exclusion of another.

A sample can only be considered a random/probability sample and representative of the population under study if these conditions are met. If not, bias can be introduced into the study.

Advantages of Random/Probability Samples

As they represent the total sampling population, the inferences drawn from such samples can be generalized to the total sampling population.

Some statistical tests based upon the theory of probability can be applied only to data collected from random samples. Some of these tests are important for establishing conclusive correlations.

Method of drawing a random sample

1. The fishbowl draw 2. Computer program 3. A table of random numbers

Procedure for using a table of random numbers

Identify the total number of elements in the study population.

The total number of elements in a study population may run up to four or more digits.

Number each element starting from 1. If the table for random numbers is on more than one page,

choose the starting page by a random procedure. Again select a column or row that will be your starting

point with a random procedure and proceed from there in a predetermined direction

Corresponding to the number of digits to which the total population runs, select the same number, randomly, of columns or rows of digits from the table

Decided on your sample size Select the required number of elements for your sample

from the table If you happen to select the same number twice, discard it

and go to the next

Difference Systems of Drawing a Random Sample Sampling without replacementSampling with replacement

Type of Specific Random/Probability Sampling Designs Simple random sampling (SRS) Stratified random sampling Cluster sampling

Procedure for Selecting Simple Random Sampling

1. Identify by a number all elements or sampling units in the population

2. Decide on the sample size (n)3. Select (n) using either the fishbowl draw,

the table of random numbers or a computer program

Stratified Random SamplingIn this sampling the researcher attempts to

stratify the population in such a way that population within a stratum is homogeneous with respect to the characteristic on the basis of which it is being stratified.

It is important that the characteristics chosen as the basis of stratification are clearly identifiable in the study population

For example, it is much easier to stratify a population on the basis of gender than on the basis of age, income or attitude.

Once the sampling population has been separated into non-overlapping groups you select the required number of elements from each stratum, using the simple random sampling technique.

Types of stratified Random Sampling

Proportionate stratified sampling : the number of elements from each stratum in relation to its proportion in the total population is selected.

Disproportionate stratified sampling: consideration is not given to the size of the stratum.

Cluster Sampling Based on the ability of the researcher to

divide the sampling population into groups, called cluster, and then to select elements within each cluster, using the SRS technique.

Depending on the level of clustering, sometimes sampling may be done at different levels. These levels constitute the different stages (single, double or multi-stage cluster sampling).

Non-random/non-probability Sampling Designs These are used when the number of elements

in a population is either unknown or cannot be individually identified.

In such situations the selection of elements is dependent upon other considerations.

Types of Non-random/non-probability Sampling Designs 1. Quota sampling 2. Accidental sampling 3. Judgmental or purpose sampling 4. Snowball sampling

Quota SamplingThe researcher is guided by some visible

characteristic, such as gender or race, of the study population

The sample is selected from a location convenient to the researcher, and whenever a person with this visible relevant characteristic is seen that person is asked to participate in the study.

The process continues until the researcher has been able to contact the required number of respondents (quota).

Quota Sampling Advantages:

It is the least expensive way of selecting a sample You do not need any information, such as a sampling

frame, the total number of elements, their location, or other information about the sampling population

It guarantees the inclusion of the type of people you need Disadvantages:

The resulting sample is not a probability one, the findings cannot be generalized to the total sampling population

The most accessible individuals might have characteristics that are unique to them and hence might not be truly representative of the total sampling population

Accidental samplingWhereas quota sampling attempts to

include people possessing an obvious/visible characteristic, accidental sampling makes no such attempt.

The method of sampling is common among market research and newspaper reporters.

It has same advantages and disadvantages as quota sampling.

As you are guided by any obvious characteristics, some people contact may not have the required information

Judgmental or purpose samplingIs the judgment of the researcher as to who

can provide the best information to achieve the objectives of the study.

The researcher only goes to those people who in his/her opinion are likely to have the required information and be willing to share it.

This type of sampling is extremely useful when you want to construct a historical reality, describe phenomenon or develop something about which only a little is known.

Snowball samplingIs the process of selecting a sample using

networks. To start with, a few individuals in a group or

organization are selected and the required information is collected from them.

They are then asked to identify other people in the group or organization, and the people selected by them become a part of the sample.

This process continued until the required number or a saturation point bas been researched.

This method is useful for studying communication patterns, decision making or diffusion of knowledge within a group.

Mixed Sampling Design : Systematic Sampling Design

Systematic Sampling has the characteristics of both random and non-random sampling designs

In systematic sampling the sampling frame is first divided into a number of segments called intervals.

If the first interval is the fifth element, the fifth element of each subsequent interval will be chosen

Procedure for Selecting a Systematic Sample

Prepare a list of all the elements in the study population (N)

Decide on the sample size (n)Determine the width of the interval (k) = total population sample size Using the SRS, select an element from the

first interval (nth order)Select the same order element from each

subsequent interval

Calculation of sample SizeDepends on what you want to do with the

findings and what type of relationships you want to establish.

In qualitative research the question of sample size is less important as the main focus is to explore or describe a situation, issue, process or phenomenon.

Calculation of sample Size In qantative research and particularly

for cuase-and-effect studies, you need to consider the following:

1. At what level of confidence do you want to test your results, findings or hypotheses?

2. With what degree of accuracy do you wich to estimate the population parameters?

3. What is the estimated level of variation (standard deviation, with respect to the main variable you are studying, in the study population?

Calculation of Sample Size The size of the sample is important for testing a

hypothesis or establishing an association, but for other studies the general rule is the larger the sample size, the more accurate will be your estimates.

In practice, your budget determines the size of your sample.

Your skills in selecting a sample, within the constraints of your budget, lie in the way you select your elements so that they effectively and adequately represent your sampling population.

Technology

Sampling