17 Sampling and Sampling Distributions: Random Sampling, Non Random Sampling

Dr. Uday Khanna

1.       Learning Outcome

2.       Introduction

3.       Basic principles of sampling

4.       Characteristics of sampling

5.       Types of sampling

6.       Types of probability sampling

7.       Types of non probability sampling

8.       Types of error

9.       Summary

1.     Learning outcomes:

i.        Understanding the basic concept of sampling

ii.      Determine the reasons for sampling.

iii.    Develop an understanding about different sampling methods.

iv.    Distinguish between probability and non probability sampling.

v.      Decide when and how to use various sampling techniques.

vi.    Discuss the relative advantages & disadvantages of each sampling methods

2. Introduction

Most of us spontaneously undergo the process of sampling. If some of us try some new clothes in the market which is trendy and stylish, others too in the group assume that this might be the newest trend or fashion. The basic idea of sampling is to draw inferences about the population by selecting some element of population. The certain terminologies of sampling are given below

2.1 Sampling

Sampling is a statistical procedure that is concerned with the selection of certain individual observation from the target population. It helps to make statistical inferences about the population. Some of the basic terminologies are as follows

2.2 Population

A population is any complete group (i.e., people, sales territories, stores, etc.) sharing some common set of characteristics. It can be defined as including all people or items with the characteristic one wish to understand and draw inferences about them.

2.3 Population frame

A list, map, directory, or other source used to represent the population

2.4 Census

A census is an investigation of all the individual elements making up the population—a total listing rather than a sample.

2.5 Sample

A sample is a subset or some part of a larger population. It is “a smaller (but hopefully representative) collection of units from a population used to determine truths about that population” (Field, 2005).

The sample has many advantages over a census or complete enumeration. When designed carefully, the sample may give results which are just accurate and sometimes more accurate than those of a census and is also considerably cheaper than the census. Hence a carefully designed sample may actually be better than a poorly planned and executed census (Rosander).

2.6 Sample design

A sample design is a definite plan for obtain a sample from a given population (Kothari, 1998). It helps to decide the number of items to be selected in the sample i.e. the size of the sample. Purpose of sampling is to estimate an unknown characteristic of a population. It is all about selecting a random sample which is true representative of the population under study. The idea is to compute a suitable value from the sample data relating to test statistic by using the appropriate distribution. It constitutes a certain portion of the population or universe.

2.7 Sampling design

Sampling design refers to the technique or procedure, the researcher undergoes for selecting items as samples from the population or universe.

Diagrammatic representation of sampling process

3. Basic principles of sampling

Theory of sampling is based on the following laws

a.      Law of Statistical Regularity – This law comes from the mathematical theory of probability. According to King,” Law of Statistical Regularity says that a moderately large number of the items chosen at random from the large group are almost sure on the average to possess the features of the large group.” According to this law the units of the sample must be selected at random.

b.        Law of Inertia of Large Numbers – This law states that the other things being equal– the larger the size of the sample; the more accurate the results are likely to be.

4. Characteristics of Sampling

There are several interesting reasons to go for sampling. These might be (

1) lower cost

(2)saves time

(3) better accuracy

(4) much reliable

(5) greater speed of data collection

(6)precision. The reasons why one must avoid sampling are

(1) lack of representative samples

(2) chances of bias

(3) problems of accuracy

(4) sampling errors.

5.  Types of sampling

A)  Probability sampling

B)  Non probability sampling

A) Types of Probability Sampling

1.      Simple Random Sampling

2.      Systematic Sampling

3.      Stratified Random Sampling

a.       Proportionate

b.      Disproportionate

4.      Cluster (or Area) Sampling

5.      Multistage sampling

B. Types of non probability sampling

1.      Convenience sampling

2.      Judgment sampling

3.      Snowball sampling

4.      Quota sampling

6. Important Fact about the Term Random

The term which differentiates probability from non probability sampling is ‘random.’ In sampling the term random has entirely different meaning from its dictionary meaning. In dictionary the term random stands for ‘without pattern’ or ‘haphazard’ while in sampling the term random selection implies the controlled procedure where each element of the population has an equal chance of being selection. Here the procedure is never haphazard. In fact it is probability samples which give the precise estimate of the population under study.

7. Types of Random Sampling

1.    Simple Random Sampling

It is a sampling procedure where each element in the population will have an equal chance of being selected in the sample. This process is simple because it requires only one stage of sample selection process. Here we number each frame unit from 1 to N. Then use a random number table or a random number generator to select n distinct numbers between 1 and N, inclusively. It is easier to perform for small populations but cumbersome for large populations.

2. Systematic Random Sampling

It is convenient and relatively easy to measure. Here an initial starting point is selected by a random process; then every nth number on the list is selected.

The first sample element is selected randomly from the first k population elements. Thereafter, sample elements are selected at a constant interval, k from the ordered sequence frame.

k = N/n

where:

n= sample size

N= population size

k = size of selection interval

For example one wishes to take a sample of 50 from a list consisting of 10,000 purchase orders. Purchase orders for the previous fiscal year are serialized 1 to 10,000 (N = 10,000). A sample of fifty (n = 50) purchases orders is needed for an audit. k = 10,000/50=    200. First sample element randomly selected from the first 200 purchase orders. Assume the 45th purchase order was selected. Subsequent sample elements: 245, 445, 645 . . .

3.      Stratified Random Sampling

Here the population is divided into non overlapping subpopulations called strata. A random sample is selected from each stratum. Each stratum is then sampled as an independent sub-population, out of which individual elements can be randomly selected. Every unit in a stratum has same chance of being selected.

a) Proportionate — the percentage of the sample taken from each stratum is proportionate to the percentage that each stratum is within the population.

b)    Disproportionate — proportions of the strata within the sample are different than the proportions of the strata within the population.

4.   Cluster Sampling

It is also called as ‘two-stage sampling’. In first stage a sample of areas is chosen. In second stage a sample of respondents within those areas is selected. Here population is divided into non overlapping clusters or areas of homogeneous units usually based on geographical dispersed population. Each cluster is a miniature, or microcosm, of the population. A subset of the clusters is selected randomly for the sample. If the number of elements in the subset of clusters is larger than the desired value of n, these clusters may be subdivided to form a new set of clusters and subjected to a random selection process.

i) Comparison between Stratified and Cluster sampling

ii)  Comparison between Stratified and Cluster Sampling

5. Multistage Sampling

Multi-stage sampling (also known as multi-stage cluster sampling) is a more complex form of cluster sampling which contains two or more stages in sample selection. In multi-stage sampling large clusters of population are divided into smaller clusters in several stages in order to make primary data collection more manageable in terms of cost effectiveness and time effectiveness. It is quite effective in primary data collection from geographically dispersed population where face-to-face contact is required (e.g. semi-structured in-depth interviews).

8. Types of Non Probability Sampling

1)    Convenience Sampling: A type of nonprobability sampling which involves the sample being drawn from that part of the population which is close to hand. That is, readily available and convenient. It is also termed as grab or opportunity sampling or accidental or haphazard sampling. Sample elements are selected for the convenience of the researcher. The researcher using such a sample cannot scientifically make generalizations about the total population from this sample because it would not be representative enough. This type of sampling is most useful for pilot testing.

2)    Judgment Sampling: Here the sample elements are selected by the judgment of the researcher. The researcher chooses the sample based on who they think would be appropriate for the study. This is used primarily when there are a limited number of people that have expertise in the area being researched.

3)    Quota Sampling: Here the population is first segmented into mutually exclusive sub-groups, just as in stratified sampling. Then judgment is used to select subjects or units from each segment based on a specified proportion. In quota sampling the selection of the sample is non-random. For example, an interviewer may be told to sample 200 females and 300 males between the age of 45 and 60. He might be tempted to interview those who look most helpful.

4)    Snowball Sampling: survey subjects are selected based on referral from other survey respondents. In social science research, snowball sampling is a similar technique, where existing study subjects are used to recruit more subjects into the sample.

9. Types of Error

i) Sampling error

If researchers are not careful in planning and defining the sampling process, it can lead to faulty research findings. Sampling error is the error that occurs because of a representative sample from the population rather than the entire population. In statistical terminology, it’s the difference between the statistic you measure and the parameter you would find if you took a census of the entire population. Sample error can’t be eliminated, but it can be reduced. In general, it works like the larger the sample, the smaller the margin of error.

Non Sampling error

This is due to poor data collection methods (like faulty instruments or inaccurate data recording, missing data, selection bias, non response bias (where individuals don’t want to or can’t respond to a survey), poorly conceived concepts, vague definitions and defective questions. Increasing the sample size will not reduce these errors. They key is to avoid making the errors in the first place with a well-planned design for the survey or experiment.

10. Summary

A sample is a subset of a population (group of individuals of interest to the researcher). The type of sample selected determines the degree to which research results can be generalized to the population as a whole (external validity). Probability samples are representative of the population. They permit generalization to the population from which they are drawn. Non probability sampling is subjective in nature and based on the discretion of the researcher. There are two sources of error that limit generalizability: sampling error (chance variation) and sample bias (constant error) which results from inadequate research design.

Learn More:

1. Vohra N.D. (2009). Quantitative Techniques in Management (4th Edition) New Delhi: Mc Graw Hill Publication.
2. Tulsian P.C. and Pandey V. (2002). Quantitative Techniques, Theory & Problems (1st edition). New Delhi: Pearson India.
3. Kothari C.R. (2013). Quantitative Techniques (3rd Edition). New Delhi :Vikas Publishing House
4. Field, A.P. (2005). Discovering statistics using SPSS (2nd edition).London: Sage.
5. http://www2.hawaii.edu/~cheang/Sampling%20Strategies%20and%20their%20Advantages%20and%20Disadvantages.htm
6. https://www.google.co.in/urlsa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwiNhJfx04zQAhVKtI8KHeLdB3QQFggfMAA&url=https%3A%2F%2Ffacul ty.elgin.edu%2Fdkernler%2Fstatistics%2Fch08%2F8-