22 Probable Sampling Technique I

R. Saratha

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Introduction

 

As narrated in the previous chapter, the purpose of effective sampling is to do research with a small representative group by applying manageable control mechanisms to get objective results to a large extent, which can be applied to the population for the purpose of generalization and further work. The probable sample technique or a simple random sampling technique addresses this specific purpose in research. Population is generally denoted by “N” and the sample is represented by “n” and the percentage of sample with respect to the population depends on the type of analysis the researcher intends to do and also on the basis of the variables. This chapter describes the nature of simple random sampling including their advantages and limitations, Systematic sampling, its advantages and disadvantages.

 

2.Learning Objectives:

 

At the end of this session you will be able to:

  • Acquire a clear picture on simple random sampling, its methods, merits and demerits.
  • Understand well about systematic sampling, its significance, merits, and demerits

3.SIMPLE RANDOM SAMPLING

 

Simple random sampling is a procedure where the researcher selects the required number of subjects for the study from a population in such a way that every subject in the population has an equal chance of getting included for the study.

 

Let us take an example where the researcher wants to select 40 Home Science students to know their views about the food items that are rich in protein. The list of students of the University specializing in Home Science course may be the population from where the researcher wants to select the required number. There are different methods to select this number.

 

a.Lottery Method:

 

The researcher may write the names of all the 298 students of the University in pieces of papers, put them in a box and ask a neutral person to pick 40 students. This is called a lot system and more systematic in nature as everyone in the University has an equal chance of getting selected. One may argue that this procedure involves cost and requires more human resources and therefore, researchers usually apply this technique when the population is small.

 

b. Table of Random Numbers:

 

The researcher may obtain the list of students of the University specializing in Home Science and select 298 students using the table of random numbers. List of random numbers does not follow a pattern and as indicated in the name, the numbers are simply random in nature the first 40 random numbers may be used to get the required sample from the list of the students of the University. This method is generally used by the researchers as it is easy to administer and does not involve cost and more resources. However some researchers may try to adopt other methods of simple random sampling.

 

c. Selecting from a Sequential List:

 

In this method, the names are first arranged in alphabetical order or any simple serial order. And from that every 10th or any other sequential name will be selected.

 

d.   Grid System

 

Under grid system, this specializes in selection of a sample area, in this, the map of a entire area is prepared and a screen with squares is placed on the map, so as to select the areas that fall under the squares as the samples.

 

3.1 SELECTING A SIMPLE RANDOM SAMPLE:

 

3.1.1 Deciding the population:

 

If a researcher is determined to study 1500 University students, we can say that the entire 1500 students can become our sampling frame. If the researcher is interested only in those who have opted for Home Science as their course, all the other students could be excluded from creating our sampling frame, which would be much less than 1500 students. Hence, deciding the population is the first important step.

 

3.1.2 Choosing the Sample Size:

 

Let’s assume that we select a sample size of 200 students. The sample is expressed as n. This number is chosen as it reflects the limit of our budget and the time we have to distribute our questionnaire to students. However, we could have also determined the sample size we needed using a sample size calculation, which is a particularly useful statistical tool.

 

3.1.3 Listing the population:

 

In order to select a sample of 200 students, we need to identify all 1500 students at the University. For actually carrying out this research, the researcher will have to view a list of all students studying at the University.

 

3.1.4  Assigning numbers to each unit:

 

The researcher has to assign a consecutive number from 1 to N, next to each of the students. In our case, this would mean assigning a consecutive number from 1 to 1500 (i.e., N = 1500; the population of students at the University).

 

3.1.5  Finding random numbers:

 

After assigning numbers, the next step is to prepare a list of random numbers from the total list of 1500 students. These random numbers can be found using any of the methods mentioned above.

 

3.1.6 Selecting the sample:

 

Finally, we select the sample from the entire population of 1500 students which will be invited to take part in the research. In this case, this would mean selecting 200 random numbers from the random number table. Imagine the first three numbers from the random number table were:

 

0011      (the 11th student from the numbered list of 10,000 students)

1331      (the 1331st  student from the list)

981         (the 981st student from the list)

 

We would select the 11th, 1331st and 981st students from our list to be part of the sample. We keep doing this until we have all 200 students that we want in our sample.

 

3.2 Advantages:

  1. Simple random sampling is certainly an ideal sampling technique procedure.
  2. Simple random technique largely reduces the non-sampling error provided the procedures are applied well in collecting data.
  3. For large surveys involving huge population, simple random technique is effective.
  4. This method is used extensively in researches.
  5. Ease of use represents the biggest advantage of simple random sampling. Unlike more complicated sampling methods such as stratified random sampling and probability sampling, no need exists to divide the population into subpopulations or take any other additional steps before selecting members of the population at random.
  6. A simple random sample is meant to be an unbiased representation of a group. It is considered a fair way to select a sample from a larger population, since every member of the population has an equal chance of getting selected.

3.3 Disadvantages:

  1. Collection of data using this procedure takes time.
  2. Sometimes, effective control over the variables used in the study also becomes an issue.
  3. A sampling error can occur with a simple random sample if the sample does not end up accurately reflecting the population it is supposed to represent.

For example, in our simple random sample of 25 employees, it would be possible to draw 25 men even if the population consisted of 125 women and 125 men. For this reason, simple random sampling is more commonly used when the researcher knows little about the population. If the researcher knew more, it would be better to use a different sampling technique, such as stratified random sampling, which helps to account for the differences within the population, such as age, race or gender.

 

Besides surveys, simple random sampling technique is used in longitudinal studies and cross-sectional studies too and some of the instances are given below:

 

3.4 Sampling in a Longitudinal Study:

  • Longitudinal study is conducted over a period of time to investigate the pattern of changes.
  • Cohort, trend and panel studies are the different types of longitudinal study.
  • In cohort studies, population remains the same, but the sample varies in every data collection point.
  • In trend study, both the population and sample change at every data collection point.
  • In panel study, the same sample is studied over a period of time.

3.5 Sampling in Cross-Sectional Study:

  1. The researcher predetermines the sample
  2. When the sample is not predetermined and when the researcher selects the entire population for the study, it is called census.
  3. Gallop polls adopt cross-sectional research study procedures

Some examples:

  • In a medical study, the population might be all adults over age 50 who have diabetes
  • In another study, the population might be all hospitals in India that perform liver transplantation surgery.

Selecting a simple random sample in examples 1 and 2 is much harder. A good way to select a simple random sample for Example 2 would proceed as follows:

 

First, obtain or make a list of all hospitals in India that perform liver transplantation surgery. Number them 1, 2 … up to the total number ‘M’ of hospitals in the population. (Such a list is called a sampling frame.)

 

Then use some sort of random number generating process to obtain a simple random sample of size’ n ‘from the population of integers 1, 2, …, M. The simple random sample of hospitals would consist of the hospitals in the list that correspond to the numbers in the simple random samples of numbers

 

4.  SYSTEMATIC SAMPLING:

 

Systematic sampling is a technique to create a random probability sample. In this, the researcher will select the units from the population, at a fixed interval for inclusion into the sample. For e.g.: If the researcher wants to select 200 students of a University out of the total enrolled students of 1500, the researcher would select the first item or unit in the population, from the table of random numbers and then select the further units at a specified interval. If the researcher is selecting the 4th unit then he might tend to select the other units at an interval of 9 units. Thus after the 4th, the 13th, 22nd, 31st, 40th, 49th, 58th …. so on will be selected until the 200 sample size is obtained.

 

In few situations, the most practical way of sampling is to select every ith item on a list, which is the strategy used in systematic sampling. A criterion of randomness is introduced into this method of sampling by using random numbers to pick up the unit with which to start. For instance, if a 4 per cent sample is desired, the first item would be selected randomly from the first twenty-five and thereafter every 25th item would automatically be included in the sample.

 

Thus, in systematic sampling only the first unit is selected randomly and the remaining units of the sample are selected at fixed intervals. Although a systematic sample is not a random sample in the strict sense of the term, but it is often considered reasonable to treat systematic sample as if it were a random sample.

 

4.1. CREATING A SYSTEMATIC SAMPLE:

 

The process of obtaining the systematic sample is much like an arithmetic progression.

 

1.   Deciding the starting number:

 

The researcher selects an integer that must be less than the total number of individuals in the population. This integer will correspond to the first subject.

 

2. Deciding the Interval:

 

After deciding the first item, the researcher selects another number which will serve as the constant difference between any two consecutive numbers, the integer is typically selected so that the researcher obtains the correct sample size.

 

For example, the researcher has a population total of 1500 individuals and need 200 subjects. He first chooses the starting number; 5.Then the researcher picks his interval, 4. The members of his sample will be individuals 5, 9, 13, 17, 21, 25, 29, 33, 37, 31, 45, 49, 53, 57, 61, 65, 69.

 

Other researchers use a modified systematic random sampling technique wherein they first identify the needed sample size. Then, they divide the total number of the population with the sample size to obtain the sampling fraction. The sampling fraction is then used as the constant difference between subjects

 

Though the usual steps in selecting a sample by the systematic sampling technique is described above, you can use a different method from it, by selecting a different element from each interval with the simple random sampling (SRS) technique. By adopting this, systematic sampling can be classified under probability sampling designs.

 

To select a random sample you must have a sampling frame. Sometimes this is not possible, or obtaining one may be too expensive. However, in real life there are situations where a kind of sampling frame exists, for example records of enrolment lists of students in a school or University, electoral lists of people living in a district or an area, or records of the staff employed in an organization. All these can be used as a sampling frame to select a sample with the systematic sampling technique. This convenience of having a ‘ready-made’ sampling frame may be at a price: in some cases it may not truly be a random listing. Mostly these lists are in alphabetical order, based upon a number assigned to a case, or arranged in a way that is convenient to the users of the records. If the ‘width of an interval’ is large, say, 1 in 30 cases, and if the cases are arranged in alphabetical order, you could preclude some whose surnames start with the same letter or some adjoining letter may not be included at all.

 

Let’s assume, there are 100 students in a class and you want to select 50 students using the systematic sampling technique. The first step is to determine the width of the interval (100/50 = 2). This means that from every two you have to select one element. Using the SRS technique, from the first interval (1–2elements), select one of the elements. Suppose you selected the second element. From the rest of the intervals you would select every second element.

 

4.2 Advantages of Systematic Sampling:

 

Systematic sampling has many advantages and it can be considered as betterment over simple random sampling:

  • The systematic sampling is very simple to use. It allows the researcher to add a degree of system or process into the random selection of subjects.
  • The population will be evenly sampled. The samples will be evenly distributed over the population.
  • This method is less costly and it can be used for large populations.
  • Implementing and using systematic sampling is quite easier and it can be conveniently used in case of large populations.
  • Systematic sampling can produce a research that is free from bias, as it eliminates the possibility of selecting elements that create bias.

4.3 Disadvantage of Systematic Sampling

  1. The process of selection can interact with a hidden periodic trait within the population. If the sampling technique coincides with the periodicity of the trait, the sampling technique will no longer be random and representativeness of the sample is compromised.
  2. When creating a systematic sample, the researcher must take care to ensure that the interval of selection does not create bias by selecting elements that share a trait.
  3. For instance, every 25th item produced by a certain production process is defective. If we are to select a 4% sample of the items of this process in a systematic manner, we would either get all defective items or all good items in our sample depending upon the random starting position.
  4. If all elements of the universe are ordered in a manner representative of the total population, i.e., the population list is in random order, systematic sampling is considered equivalent to random sampling. But if this is not so, then the results of such sampling may, at times, not be very reliable.

4.4.Risks Associated with Systematic Sampling

 

Systematic sampling puts forth one inevitable risk to the researcher viz. when conducting a systematic sampling, the researchers must take into consideration the manner in which the list used is being organized. If the subjects placed on the list are organized in a cyclical pattern that matches the sampling interval, the selected sample may be biased. For example, a University’s administration wants to pick a sample of lectures and ask how they feel about Universities policies. Lecturers are grouped in teams of 20, with each team headed by a Coordinator. If the list used to pick the sample size is organized with teams clustered together, the researcher risks picking only Coordinators (or no coordinators at all) depending on the sampling interval.

 

Summary

 

In this chapter we have thoroughly discussed the important features of simple random sampling and systematic sampling, their advantages and limitations as well. Simple random sampling is a procedure where the researcher selects the required number of subjects for the study from a population in such a way that every subject in the population has an equal chance of getting included in the study. This feature of providing equal chance for everyone to get selected for the study makes the simple random sampling preferable for most of the research studies. However, the chances of specific groups getting selected can’t be ruled out even when the samples are selected randomly. Lot system, use of table of random numbers, etc., are most common methods of simple random sampling and there is a general consensus that simple random sampling will largely reduce the bias in a research.

 

In systematic sampling, the researcher selects the units from the population, at a fixed interval for inclusion into the study. Though this is convenient from the point of view of resources, bias can’t be ruled out as every person in the population does not get an equal chance to participate in the study. Again the time and convenience factors should also be taken into consideration in these exercises. If a research simply wants to know about the trend of the population towards the particular variable or an entity, systematic sampling may be an easy procedure but the limitations should also be understood in this process.

 

Therefore, selection of sample is a factor of time and resources too and these aspects have been enumerated in this chapter.

you can view video on Probable Sampling Technique I

Web links

  • https://www.ma.utexas.edu/users/parker/sampling/srs.htm
  • https://onlinecourses.science.psu.edu/stat100/node/18
  • https://www.socialresearchmethods.net/kb/sampprob.php
  • http://www.investopedia.com/terms/s/systematic-sampling.asp
  • https://explorable.com/systematic-sampling
  • https://www.thoughtco.com/systematic-sampling-3026732

Suggested References

  • C.R. Kothari (2004), Research Methodology, methods & techniques second edition, revised. New Delhi, India: New Age Publishing Company, P55-67
  • Ranjit Kumar (2011), Research Methodology a step-by-step guide for beginners, third edition, New Delhi, India, Sage Publications , P 175- 189
  • John W. Creswell & Vicki. L .Plano Clark (2006), Designing and conducting Mixed Methods Research, second edition, California, Sage Publications, P 195 & 196
  • Santhosh Gupta(2001) Research Methodology and Statistical technique, , New Delhi, India , Deep& Deep publications ISBN 81-7100-501-2
  • G.R. Basotia &K.K. Sharma (2002) Research Methodology, Jaipur, India , Mangal Deep Publications, ISBN: 81-7594-090-5
  • P.Saravanavel (2007) Research Methodology, Allahabad, India, Kitab Mahal Publications, ISBN: 81-2225-0010-2
  • R.Panneerselvam(2004), New Delhi, India, Phi Learning Private Limited, ISBN: 978-81-203-2452-7
  • Welter R. Borg & Meredith D. Gall, Educational Research- An Introduction, fourth edition, New York & London, Longman Publications, ISBN: 0-582-28246-2