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Sampling methods

Sampling

Sampling is the process by which inference is made to the whole by examining only a part. In other words it is the process of getting information about the totality or universe or population by performing examination of only some parts of the population under investigation. For example, a doctor tests a drop of blood of a patient to know about the characteristic of the whole blood of that patient.

Objective of sampling

The major objectives of sampling techniques are as follows:
To obtain maximum information about the population under consideration by examining number picked up in the sample
To ascertain confidence interval to the estimate of the population parameter.
To test the significance of the population parameter at given level of significance.

Population

In statistics, the term population or universe refers to the all totality of cases (or items) under investigation.

There are three types of population: finite, infinite and hypothetical population.

Finite population If the number of units constituting the population is fixed then it is known as finite population. For example, the number of leprosy patients in a community, all HIV positive persons, all diabetic patients etc.

Infinite population If the population contains an infinite number of members it is called infinite population. For example, all possible hemoglobin (Hb) values in a given interval, all possible height within the range 150 cm to 165 cm etc.

Hypothetical population A hypothetical population is one which is assumed for theoretical purpose. Suppose a few guinea pigs are given vitamin A-deficient diet and they are watched for vitamin A deficiency symptoms within a predetermined period, the result observed is generalized to all such groups of guinea pigs fed on a vitamin A-deficient diet. All such groups constitute a population. This is only a imaginary population which exist hypothetically.

Sampling frame

Sampling frame is a list of sampling elements with identification particulars or a map showing the positions of the sampling elements. A Sampling frame represents the population under investigation. This sampling frame is the base for drawing a sample and therefore, it should be made up to date, i.e. free from omission and duplications.

Sample

Some units selected from the population is known as sample and the process of selecting some units from the population in order to draw conclusion about the population is known as sampling.

Census survey

The complete enumeration of all units of population is known as census survey. It is the process

of complete enumeration in which every member of the defined population is included.

Parameter and statistic

Parameter is the value of a variable or attribute calculated from the population under study. The

parameter is generally unknown and is fixed. Statistic refers to that value of a variable or

attribute calculated from a sample taken out of a population. Statistic may vary depending upon

the sample. But the average of statistic is always equals to the parameter.

Sampling and non-sampling errors

The errors occurred in the process of collecting, processing and analyzing data may be classified

into the following types: sampling errors and non-sampling errors.

Sampling errors

Different samples selected from the population will give different results as the elements

included in the sample will be different. This will give rise to the sampling errors. Because of

these errors there may be difference between sample mean and population mean. These errors or

biases are because of number of reasons. Some of these reasons will be as follows:

Incomplete or faulty selection of samples
By substituting certain units whose characteristics are not homogeneous with the
characteristics of the original sampling units
Applying improper statistics for estimating the population parameter.
Not using proper sampling design.

Non-sampling errors

Non-sampling errors can occur at the different stages of observation, ascertainment and

processing of data in both complete enumeration survey and the sample survey. Hence it should

be noted that data collected through the complete census may possess non-sampling error

whereas data collected through the sample survey may have possessed both sampling and nonsampling

errors.

Non-sampling errors can occur at different stages of planning and implementing of census or

sample survey. It is quite difficult to make complete list of all the source of non-sampling errors.

However, following are some important factors involved in non-sampling errors.

Inappropriate planning or definitions
Response and non-response errors
Compiling and publication errors etc.

Method of sampling

The method of selecting a sample is of fundamental importance in sampling theory and usually

depends upon the nature of investigation. The sampling procedures, which are commonly used,

may be broadly classified under the following heads.

1. Probability sampling (random sampling)

2. Non probability sampling (non random sampling)

Probability sampling

Probability sampling is the scientific method of selecting samples according to some laws of

chance in which each unit in the population has some definite pre assigned probability of being

selected in the sample. Some of the probability sampling methods are:

1. Simple random sampling

2. Stratified sampling

3. Systematic sampling

4. Cluster sampling

5. Multistage sampling

Simple random sampling

The simplest and common most method of sampling is the simple random sampling (SRS) in

which the sample drawn is unit by unit with equal probability of selection for each unit at each

draw. Therefore, SRS is method of selecting ‘n’ units out of a population of size ‘N’ units by

giving equal probability to all units. Sampling in this method can be done either with

replacement or without replacement.

Sampling with replacement

The unit drawn in the first draw is replaced before the second draw. The possible samples of size

‘n’ out of ‘N’ units of the population is Nn and the probability of selecting each sample is n N

Procedures of selecting random sample

i. Lottery method ii. Use of random number tables

Stratified sampling

When the population characteristics are heterogeneous, the SRS does not serve as a good design

so as to represent the sample units from each characteristic. Then the entire population is divided

into different groups called strata in such a way that within strata they are homogeneous in nature

and between strata heterogeneous. Then a simple random sampling procedure is used to draw

samples from each stratum.

Systematic sampling

Systematic sampling is a commonly used technique if a complete and up to date sampling frame is available. In this sampling the first unit is selected randomly and the remaining units are selected automatically with some predetermined pattern. Suppose N units of the population are numbered from 1 to N in some order. Let N = nk where n is the sample size and k is an integer known as sampling interval and a random number called random start is selected between 1 to k. Then every kth unit will be selected automatically.

For example, let us consider the population of size 100 starting from 1 to 100. Let us take a sample of size 10. To select 10 samples out of 100, a number is selected at random and other 9 numbers are selected at equal sampling interval.

Sampling interval (k) = N/n = 100/10 = 10

Select a number (which is less than or equal to k), say a number 3 is taken first, then other numbers will be 13, 23, 33, 43, 53, 63, 73, 83 and 93.

Cluster sampling

This sampling method is also appropriate if the population characteristics are not homogeneous. In this method, the population is classified into sub population, called cluster in such a way that the characteristics within the cluster are heterogeneous and between cluster homogeneous. A cluster is then selected for the desired sample.

Multistage sampling

As the name suggests, multistage sampling refers to the sampling technique which is carried out in various stages. Multistage sampling consists in sampling first stage units by suitable methods of sampling. From among the selected first stage units, a sub sample of secondary stage is drawn by some suitable method of sampling which may be same or different from the method used in the first stage. Further stages may be added to arrive at a sample of desired sampling units.

Non probability sampling

This is the method of selecting samples, in which the choice of sampling units depends entirely on the judgment of the sampler. This method is mainly used for opinion surveys, but can not be recommended for general use at it is subject to the drawbacks of prejudice and bias of the investigator. The types of non probability sampling are:

1. Judgment or purposive sampling

2. Convenience sampling

3. Quota sampling

Judgment or purposive sampling

A sampling method, in which the researcher selects the sample according to personal judgement, is called purposive sampling. This method is suitable only when a universe is small and a quick decision is needed. For example, medical representative contacts to the popular and busy doctor purposively. This method gives valid results when used properly i.e. if the researcher is skilled and apply the method unbiasedly otherwise because of personal judgment, biases and prejudices lead improper conclusions.

Convenience sampling

The investigator selects the samples on the basis of the convenience of the investigator. This is

also known as chunk sampling.

Quota sampling

Some quotas are set up according to some criteria and selection of quota is made accordingly to

the personal judgment of the investigator. In this method, the investigator is told in advance the

number of the sample units he is to enumerate.

Snowball sampling

This technique is used by the researchers to identify the potential subjects in studies where the

subjects are hard to locate. This type of sampling technique works like chain referral. So it is

also known as chain sampling or chain- referral sampling or referral sampling. After observing

the initial subject, the researcher asks for the assistance from the subject to help identify people

with a similar trait of interest.

References

Aryal, U. R. (2014). Biostatistics for Medical Sciences . Kathmandu : Makalu Publication .