Sampling in Statistics: Subject-Matter and Designs

In this article we will discuss about Sampling in Statistics:- 1. Subject-Matter of Sampling 2. Sampling Designs 3. Selection of Samples 4. Selection of Appropriate Sampling Method 5. Sampling and Non-Sampling Errors.

Contents:

1. Subject-Matter of Sampling
2. Sampling Designs
3. Selection of Samples
4. Selection of Appropriate Sampling Method
5. Sampling and Non-Sampling Errors

1. Subject-Matter of Sampling:

The total number of individuals belonging to a particular species in a particular area from which all possible data pertaining to an experiment are drawn is called population. In other words, the population is the total set of actual or possible variables.

A population may be finite or infinite and the variables continuous or discrete. In biological experiments it is difficult to study each and every individual of entire population. Therefore, it is advised to select a part of population with the objective of study.

That is called sample. The selected sample must have relationship with population. Data originate from samples. The process of collecting samples is called sampling. The number of individuals considered in a sample is basically referred to as the sample size.

The sampling is done with the following objectives:

(i) Research objectives,

(ii) Experimental designs, and

(iii) Practical considerations.

If the sampling process is correct, the conclusions drawn from the data will be truly representative. The accuracy of the result depends largely on the sampling process and the size of the samples in relation to population. It is, therefore, important that the sampling methods must be correct and the sample size must be large enough to give reliable data about the population under study.

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2. Sampling Designs:

The sampling process can be grouped under the following two categories:

1. Random sampling designs.

2. Non-random sampling designs.

1. Random Sampling Designs:

In random sampling all the individuals of population have equal and independent chance for being included in the sample. Random samples are character by the ways in which they are selected. Random is not used in the sense of “haphazard” or “miss”. To ensure randomness in sample selection one adopts either the lottery system or consults the tables of random numbers.

Lottery Method:

In this method, all items of the population are numbered and named on separate paper slips of identical shapes and sizes. The slips are folded and rolled and then mixed up in a container or beaker. This is followed by blindfold selection of rolled paper slips in desired number.

For example, suppose we want to take a sample of 100 plants out of a population of II plants, the procedure is to write the number of plants from one to hundred on separate slips of paper, fold and roll those 100 slips, mix them thoroughly in a beaker or container and then select any 10 slips at random.

Table of Random Numbers:

Several standard tables of random numbers are available which have been tested extensively for randomness.

Some of the standard Tables are mentioned here:

(i) Tippett’s Table (1927),

(ii) Fisher and Yates Table (1938), and

(iii) Rao, Mitra and Matthai’s Table (1966).

The advantages of random sampling are as under:

(i) It provides essentially unbiased estimates and has measurable precisions.

(ii) It does not depend upon the detail information.

(iii) With the help of probability sampling it is possible to evaluate the relative efficient various sampling designs. However, there are certain limitations to probability sampling.

These are as follows:

(i) It requires high level of skill and experience for use.

(ii) It is a time taking process.

(iii) It is a costly sampling process.

2. Non-Random Sampling Process:

It is a process of sample collection without randomization. The sampling is made at regular intervals and the selection of samples is done on the basis of consequences or investigators’ judgement.

The most important difference between random and non-random sampling is that the pattern of selecting samples can be ascertained in random sampling while in case of non-random sampling, there is no way of knowing pattern of variability of the process.

There are three types of non-random samplings:

(i) Judgement Sampling,

(ii) Convenience Sampling, and

(iii) Quota Sampling.

(i) Judgement Sampling:

In this type of non-random sampling, the choice of sample items depends on the discretion of investigator. For example, suppose for estimating grain yield if a sample of 10 plants is to be selected from a population of 100 plants, the investigator would select 10 plants which in his opinion are the representatives of population under study. This sampling technique is often used in solving business and economic problems.

Though this method of sampling is easy and simple yet it has the following limitations:

(a) It is not a scientific method,

(b) It involves risk of wrong conclusions, and

(c) It cannot be recommended for general use because of possible subjectiveness

(ii) Convenience Sampling:

In this type of non-random sampling, a faction of population under study is selected neither by probability nor by judgment but by convenience. Convenience sampling is done by interview. The result of convenience sampling can hardly be representative of population and hence they are generally biased and unsatisfactory.

(iii) Quota Sampling:

This is a type of judgment sampling. In this technique, quota are set up according to specified characteristics such as so many in each age-group, so many in each of several income groups and so on. This sampling technique is used in public opinion studies. It provides satisfactory results if the interviewers are properly trained and they follow the instructions carefully.

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3. Selection of Samples:

Samples are of two types:

1. Qualitative samples.

2. Quantitative samples.

1. Qualitative Samples:

These samples are selected on the basis of quality characters of individuals. The quality characters are considered when two samples or objects are to be compared, e.g., colours of fruits, size of fruits (small or big), heights of plants (tall or dwarf).

2. Quantitative Samples:

These samples represent the quantities and the data are expressed in numerical figures, such as the measured heights of plants, total number of fruits per plant, total number of seeds per plant, 100 or 1,000 seed weight, number of days for fruit maturity and so on. Numerical measurements provide definite information about a particular population.

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4. Selection of Appropriate Sampling Method:

Sampling method to be adopted in a particular experiment has important bearing in biometry and the size of sample is important matter to be considered while adopting a sampling technique. Some statisticians are of the opinion that the size of sample should be 5% of the population size while others hold the view that sample size should be at least 10% of the size of population.

The following two points should be considered while deciding the appropriate size of the sample:

1. The size of sample should increase as the variation in the individual items increases.

2. The larger the size of sample, the greater will be the accuracy.

The sampling technique should have the following merits:

(i) It should be less time taking.

(ii) It should involve less cost.

(iii) It should provide more detailed information.

The sampling process has, no doubt, several advantages yet there are limitations with it wins are mentioned below:

1. Sample survey must be done carefully otherwise the results obtained may not be accurate.

2. It generally requires the services of experts.

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5. Sampling and Non-Sampling Errors:

If the inferences are drawn about the population on the basis of a few observations or if proper care is not taken in selecting samples, some errors in result arise and the results obtained may not be accurate. These errors are called sampling errors.

The errors arising only due to ascertainment are called non- sampling errors. In other words, these errors arise due to factors other than the inductive process of making inferences about population from samples.

Sampling errors are of following two types:

(i)Biased errors, and

(ii) Unbiased errors.

The biased errors arise from the bias committed during selection of samples or ignoring certain members of population during sampling process. The unbiased errors arise due to chance of different between such members of population as are included in the sample and those not included in the sample.

The reasons for biased errors may be:

(i) Faulty selection process,

(ii) Faulty method of analysis, and

(iii) Defective method of data collection.

Non-sampling errors may occur at any stage of planning and arise due to the following reason:

(i) Defective method of interview or data collection,

(ii) Errors due to non-response from the unit during interviews,

(iii) Defective tabulation of data,

(iv) Errors in data processing such as coding, bunching, verification, etc., and

(v)Errors committed during interpretation of data and presentation of results.

Sometimes, the non-sampling errors may be big and deserve proper attention of the investigator Chances for sampling errors decrease with the increase in sample size whereas non-sampling errors tend to increase with the increasing sample size. The non-sampling errors should be controlled and reduced to a level at which they do not spoil the final results.