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Theory Of sampling in statistics

Theory Of sampling in statistics

Theory of Sampling in Statistics
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Theory Of sampling   

Sampling is a process by which we draw inferences about the whole group by examining a small proportion of the group. Examining the small part of whole helps us to know about the whole system. For example, a small pinch of blood can be tested know the entire blood condition, a spoon of rice can be taken to taste whole pot of rice, a drop of water can be tested to know arsenic level whole water, etc. to understand the basic of sampling we should understand following terminology one by one


in statistics, a population is an entire pool from which a small portion or parts are drawn to examines the entire pool. It means population is groups of different things. For example, a population is an entire group of people, objects, events, observations, measurements, etc. hence it can also be defined as the aggregate observation of different items. In a broad sense, 25 cows in a certain farm is population, 100 numbers of students in a particular class of school are population, total numbers of keys in a keyboard is population, group 50 farmers in a particular small village is population. Hence population is groups of those items having few similarities.


It is a small part or portion of the entire population. It means the smaller, manageable version of the larger group. In another word, it is a subset containing the characteristics of the larger population. We draw a small part or portion (called sample) from the population to study the characteristics of the population. For example 25 boys out of 100 students in a certain class of the school, a spoon of rice out of a pot of rice, 10 farmers out of 50 farmers in a village, 10 lions out of pride of 100 lions, etc are samples. Here, the sample has represented a small part or portion of the whole population. This sample helps us to know about the characteristics of the whole population.


It is the process of drawing samples from the population. It means sampling is a process used in statistical analysis in which a predetermined number of observations are taken from a given larger population.  Hence sampling is a selection of a subset (a statistical sample) of individual from within a statistical population to estimate characteristics of the population as a whole. the size of the sample may be small or large based on sample size which indicate the numbers of items in the sample. The size of the sample i.e. numbers of observations is denoted by n.

The size of the sample is the numbers of items in the sample and denoted by n. w


The parameter is the value of variables or attribute which represent the characteristics of the respective domain. These parameters usually represent the characteristics of the population. Generally, parameters are unknown so we need to estimate them using various techniques. For example, mean, standard deviation, correlation coefficient, etc.


It is the values of variables or attributes that are calculated using sample parameters to estimate the value of the population parameter. It means statistics represent the function of the sample parameter.

Sampling distributions:

It can be defined as the probability distribution of the statistics. In another word, A sampling distribution is a probability distribution of a statistic obtained from a larger number of samples drawn from a specific population. The sampling distribution of a given population is the distribution of frequencies of a range of different outcomes that could possibly occur for a statistic of a population.

Objective of sampling:

The primary objective of the sampling is to get a representative sample from a large population and study the whole characteristics of the population parameter with more accuracy at minimum cost, time, and effort. Few objectives of sampling are discussed below:

i.                To study the characteristics of the population parameter using sample parameter.

ii.              To save time, energy, and money by taking only a small sample.

iii.            to test the population parameter using sample parameters.


Census vs. sample surveys


Approaches to Sampling: Nonprobability and Probability Sampling Techniques


  Nonprobability Sampling

Non probability sampling is defined as a sampling technique in which the sample are drawn on the basis of subjective judgment of sampler. It means each unit in population does not have a specified probability of being selected. In non-probability samplings, sampling does not select their unit from the population in a mathematical random way. This method is mainly used for opinion surveys. This sampling method depends heavily on the expertise of the sampler or researcher. However, in general this sampling method cannot estimate given population parameter in precise an accurate way. It is carried out by observation, and researchers use it widely for qualitative research. Hence this sampling technique is only used when there are less chances of random probability sampling method. The type of non-samplings are

a.    Haphazard or Accidental sample:

It is sampling procedure in which a researcher selects any cases which are available to him without any manner. It means research collect data haphazardly or accidently without any procedure or manner. This process may be applicable when we don’t need any accurate result and no sufficient time and budgets. For example, if the researcher has to know the certain values of the particular group of people then he selects any people whom he can meet easily and who are ready to provide information. This method is biased method being lack of accuracy and precise measurement. Even Being cheap and quick, this method is full of systematic errors


b.   Quota Sampling

It Is an the improvement over haphazard sampling. In quota sampling, a researcher first identifies relevant categories of people like age, sex, gender, income, education, health status, wealth and then decides how many to get in each category. Thus, the number of people in various categories of the sample is fixed. It means in quota sampling, samples are specified according to some assigned categories like income, age, sex, education, health like characteristics, and corresponding examination is performed. During quota sampling, first of all population of particular characteristics are studies, the population are divided into certain required categories as a sample and finally, each member of samples is interviewed to know particular information.


c.    Purposive or Judgmental Sample

This is the method of sampling in which sampler or researcher selects the sample according to his own judgement and purpose. It means sample choose those sample items from a population which are under his choices and convenience.  These techniques useful when it is difficult to reach population needs to be measured.  Hence In this sampling techniques, the researcher choose vary limited sample items which are just significant and useful for research.


d.   Convenience sampling

A convenience sample is a type of sampling method where the sample is taken from a group of people easy to contact or to reach i.e., they are convenience to get and reach. This type of samplings is also known as the grab sampling or availability samplings. It means sampling Is possible only when there is availability of data as our conveniences. For example, asking people to answer standing at supermarket, asking question to people during travelling is same bus etc. one important thing for convenience sampling is that there should be availability of correspondent and correspondent should will to correspond the question of interviewer.

e.   Sequential sampling

sequential sampling is that sampling technique where sampler or researcher select a single or a group of subjects in a given time interval conducts his study, analyzes the results then picks another group of subjects if needed and so on in the firm of continuous sequence.  In this sampling techniques, a group of one sample is drawn one after another hence researcher has enough schedule to select each group of samples. Similarly, the researcher has the limitless option to choose sample sizes.

f.     Snowball sampling

It is also known as network, chain referral, or reputational sampling. is a method for identifying and sampling the cases in a network? It begins with one or a few people or cases and spreads out on the basis of links to the initial cases.

Probability samplings:

Probability sampling is a sampling technique in which samples are drawn from large population using a method based on the theory of probability. It means in this sampling technique each unit of population has a specifiable pre-assign probability of being selected. It is observed that each population unit has equal chances of being selected. For example, if you have a population of 100 people, every person would have odds of 1 in 100 for getting selected the probability of being selected depends upon the sample size. A larger sample size will have lower chances of being selected and vice-versa. Probability sampling is a more precise and accurate sampling procedures and far better than non-probability samplings. Hence Probability sampling gives you the best chance to create a sample that is truly representative of the population. There are different types of probability sampling which are discussed below:

Simple random sampling:

It is random method of selecting sample. During the selection process, each unit has an equal probability of being selected in each random selection or draw. It means simple random selection is process of selecting that random sample which is a subset of the statistical population in which each observation has an equal probability of being selected. Hence simple random sample unbiasedly represent the true figures of the population.   For example, a random selection of 25 employees out of 100 employees, random selection of 120 eggs out of  1020 eggs etc. here in each case, we draw n sample out of N population. During the sample random selection process, we can select with or without replacing observations. Few examples of the random selection process are

i.                Lottery method

This is most popular method and simplest method. In this method, all the items of the universe are numbered on separate slips of paper of same size, shape and color. They are folded and mixed up in a drum or a box or a container. A blindfold selection is made. Required numbers of slips are selected for the desired sample size. The selection of items thus depends on chance. For example, if we select 5 students out of 50 students on slips of the same size and mix them, then we make a blindfold selection of 5 students. This method is also called unrestricted random sampling because units are selected from the population without any restriction. This method is mostly used in lottery draws. If the universe is infinite, this method is inapplicable. There is a lot of possibility of personal prejudice if the size and shape of the slips are not identical.


ii.              Random numbers table

 Random numbers table is an arrangement of the number ranging from 0 to 9 in particular patterns. The arrangement patterns of numbers are generally either in linear or rectangular forms arranged in rows and columns. By using a random number table, all members in the population will have an equal and independent chance of being selected for the sample group. There are different random numbers table in practice like tippets random number table, Kendall and smith table, fishers and yates table, etc.

Systematic sampling:

Systematic sampling is a statistical technique of selecting a sample from a population-based on some systematic procedure. Systematic procedure refers to the procedure of selection in which researcher first randomly and automatically picks the first item or subject from the population and rest are get selected with some predefined patterns of selection. For example, let there are N numbers of the population out of which we draw n sample then first observations is drawn automatically and remaining observation are drawn in some patterns and rule. Let there are 100 eggs in tray numbered from 1 to 100. We have to choose only 10 eggs i.e. sample size of 10 eggs. First researcher chooses randomly and automatically 8th eggs and the remaining eggs are chosen with some predefined pattern let be a difference of 8. The remaining sample will be 16, 24, 32, ….80. here 8 is called sampling interval.

Multistage samplings:

Multistage sampling is defined as a sampling method in which at first clusters are selected and later each unit of items from the cluster are again selected. Sine process involves two times selection or selection from population and later selection from selected sample or cluster hence it is also defined as the subsampling or two-stage samplings. If the stage of samplings is more than two-stage then these samplings are called multistage samplings. The motive behind dividing into sub-sampling is to make it easier for the collection of primary data with more accuracy and significance.

divides the population into groups (or clusters) for conducting research. It is a complex form of cluster sampling, sometimes, also known as multistage cluster sampling. During this sampling method, significant clusters of the selected people are split into sub-groups at various stages to make it simpler for primary data collection.

Multistage sampling allows researchers to apply cluster or random sampling after determining the groups. Which makes it easier to the procedure. In this sampling method, the researcher has a limitless option to choose sample size so that researcher can proceed continuously forward until the end is reached. There is no restriction for researchers to divide the population which has created flexibility for works. This procedure is more helpful in collecting primary data where the population is more dispersed geographically. 


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