SAMPLING

Introduction

Most of the researchers are based on samples rather than population.  The reason is that it is impracticable to observe the total population or to apply a questionnaire or any other tool on the total population under controlled condition.  Shortage of time or money is another problem. 

Study of the total population is neither possible nor needed because if sample is representative to the population, it will give the same result.  For example, when we go to the market to buy rice we do not check the total quantity of rice there.  We only take a handful of rice and check it. If it is found good, rice is bought.  Same is the case in researches also.  We study only a sample and then generalize the results to the population.

Meaning of Sampling

Sampling is the process by which a relatively small number of individuals, objects or events is selected and analysed to find out something about the total population from which the sample was drawn.  It helps to reduce expenditure, time and energy of the researcher and can produce greater precision and accuracy due to better controlling.

Meaning of the sample

Representative proportion of the population is called sample.  This proportion is not fixed sometimes.  Less than 1 % proportion of the population may provide a representative sample but sometimes a bit larger sample is needed.

NEED FOR SAMPLING

          Sampling is used in practice for a variety of reasons such as:

1.   Sampling can save time and money.  A sample study is usually less expensive than a census study and produces results at a relatively faster speed.

2.   Sampling may enable more accurate measurements for a sample study is generally conducted by trained and experienced investigators.

3.   Sampling remains the only way when population contains infinitely many members.

4.   Sampling remains the only choice when a test involves the destruction of the item under the study.

5.   Sampling usually enables to estimate the sampling errors and, thus, assists in obtaining information concerning some characteristic of the population.

Steps in sampling

(A) Defining the population

(B) Listing the population

(C) Selecting a representative sample

(D) Obtaining an adequate good sample (Proper size of the sample)

(A) Defining the population :

     A population refers to any collection of specified group of humans and non humans, such as objects, institutions, time units, geographical area or events.  It is also called universe.

     The population may be finite or infinite both.  Population may be existent (like the population.

     Exact definition of the population is necessary before selecting any sample.  For example, if we want to survey the achievement of students in mathematics, the researcher will have to specify the following things:

I.             Age and grade of students

II.           Type of school – public or government

III.          Place of population

IV.         Socio – economic status of students

V.           Academic year for which data is to be collected.

          Exact definition of the population will help the researcher to select truly representative sample.

(B) Listing the population:

          After defining the population, a comprehensive and accurate list of the population is also prepared.  It is technically called sampling frame.  It is very difficult to prepare a perfect sampling frame in large scale surveys.  In such cases special care is necessary so that no unit or group of the population is left out.

(C) Selecting a representative sample

          After preparing a list, sample is selected from the frame.  A sample must have at least the following characteristics: 

1.   It must be unbiased and true representative of the population

2.   It must be adequate enough to represent the entire population

3.   It must provide all the information about the population from which the sample is drawn.

4.   It must have all the characteristics of the populations.

5.   Sample must adequately represent all the units or groups of populations from which it is drawn.

6.   It must be adequate enough to provide statistical treatment of the data.

(D) Obtaining an adequate sample

          If population is homogeneous, a relatively small sample may serve the purpose.  But if population is heterogeneous, larger sample will be needed.  Similarly, if study is clinical and experimental, small sample is needed because we can control them easily and since each subject is measured repeatedly, so, it will be less time consuming.  Large sample is needed when the differences between variables under study are small and variables are not highly correlated.  The size of the sample will also depend upon the method used in drawing the sample.

METHODS OF SAMPLING

(A) Non Probability Method

Convenience Sampling

          In this method the researcher will decide the choice of sampling units based on their convenience.

Judgment Sampling

          The sampling units are selected on the advice of some expert or by the intuition/opinion of the researcher himself.

Quota Sampling

          The population is classified into a number of groups based on some criterion. After that one can use any one of the other non probability methods like convenience sampling or judgement sampling.

Snowball Sampling

          It is a restrictive multi-stage sampling. Certain numbers of sampling units are randomly selected. Later, additional sampling units are selected based on referral process.

Advantages of non probability sample

          These methods are very useful in the situation when,

I.             The sample to be selected is small and researcher wants to get some idea about the population characteristics

II.           The researcher wants to understand the problem by contacting with only informed people.

III.          Different units of the populations have total characteristics of their respective units, and then selection few units out of so many is considered sufficient.

Limitations of non probability methods

1.   Such sample can be biased and hence generalization of results for the entire population may be misleading.

2.   Sampling errors in these samples cannot be determined because they can affect variance within the groups as well as between groups.

3.   Such samples depend on uncontrolled factors and researcher’s insight which cannot be relied on all time.

4.   Such sampling frame does not adequately cover the population.

(B) Probability Methods

          In this method of sampling, each unit of the population has equal chance of being selected.  That is why they are also called random samples. 

Characteristics of Probability Samples

1.   Each unit in the sample has some known probability of entering the sample.

2.   Weights appropriate to the probabilities are used in the analysis of the sample.

3.   The process of sampling is automatic in one or more steps of selection of units of in the sample. 

These methods can help the researcher in the following ways:

1.   The researcher can know the size of the sample which is needed for a desired level of accuracy.

2.   He can tell the chance of each unit being selected.

3.   He can calculate sampling error.

4.   He can determine the level of confidence.

Types of Random methods

Simple or Unrestricted Random Sampling

          In this type of sampling, each unit of the population has equal chance of being selected.  The law of chance operates here.  Several devices are used here to draw samples from population. 

(a)  Lottery method: If there are N numbers in a population, each unit is assigned numbers from one to last.  Then they are properly mixed up.  After that required numbers of units are taken out from the lot one by one.  This method is applied when size of the population is small and numbering of all the units of the population is possible.

(b)  Use of random table: Fisher and Yates have prepared a random table.  After assigning consecutive numbers to all units of the population the investigator starts from any point on the random table and reads consecutive numbers in any direction, horizontally, vertically or diagonally.  He reads the number on the table and picks up that very number of unit one by one and in this way the required number of units is selected.  If the number of population is less than 999 (of three digits only) Investigator takes only three digits of the random table from the left and matches the numbers of the table to the number given to different units of the population.

     Ex: Following random numbers are given in the table in 5 columns

                     1                   2                   3                 4                 5

                              10480          15011            01536         02011        90700

                   If we have to select a sample out of 280, we will select the following units 104^th, 150^th, 015^th, 020^th only.  The last 907 will not be selected; because, it is more than 280.  The remaining sample will be selected by using the table in the same way. 

          Besides, if the number of units of the population is less than 99, only two digits from the numbers of random table will be taken into account.

Limitation:

1)   Simple random sampling procedure is an ideal plan theoretically but, practically it is tough job, if number of units of population is very large.

2)   Simple random sampling procedure fails when lists of units of the population are not available.

3)   This procedure fails when population is infinite.

4)   It is again not good to use this method, when different units of the population is very much heterogeneous in characteristics.

Stratified Random Sampling 

          This method is used to overcome the above four problems. Here, the researcher first divides his whole population into different strata.  On the basis of certain characteristics and random sample is drawn from each stratum.  This stratification of the population makes different small homogeneous groups of the population and simple random technique can be applied to each group to select the required number of sample.  This makes sample more representative to the population.  For example, we can divide the whole population into upper class, upper middle class, middle class, lower middle class and lower class first and then we can select the sample from each group. 

          A population can be stratified on many grounds such as age, sex, grade, economic condition, place of residing, occupation, castes, etc.  The efficiency of stratified random sample depends on the allocation of sample size to strata.  Percentage method is the best method of allocating sample size among strata. 

Ex : Economic strata  :     UC     UMC   MC    LMC     LC

       N of population    :  1000     500    400   2000    1500

       Sample size 5%    :     50       25      20     100       75

          Lottery method or random table method may be used to obtain this 5% sample from each data. 

          We can stratify a sample on more than one ground like age + sex   or age + economic condition and so on.   The more we stratify a population on different grounds, the more the different units of the population become homogeneous and standard deviation of each group decreases. Moreover, if two characteristics of the population are perfectly correlated, Stratification on the basis of one characteristic will lead to perfect stratification on the basis of the other characteristic.  If this correlation is weak, stratification will be also imperfect.

ADVANTAGES:

1.   It can overcome most of difficulties of simple random sampling

2.   It can make different units of population homogeneous and small and thus we can use the lottery method for each stratum very easily.

3.   It can be used when lists of all units of the population is not available.

4.   This method is especially useful in opinion surveys when we have to a large and scattered population.

SYSTEMATIC SAMPLING

          When a population is finite and can be properly listed, this method is used. Here all the units of population are listed in an alphabetical order first.  Then if we have to select 100 units out of 1000 units of population,
we will keep interval of 10 units throughout the population.  For example, if we have selected 4^th unit then we will select 14^th, 24^th, 34^th, 44^th and so on and thus required sample will be drawn. 

          If population is homogeneous, this method of sampling is as good as simple random method and researcher can apply his own bias here. 

Limitations:

          This method will not work properly in two situations,

1.   If population is showing some trend in its characteristics, then the trend will not change from beginning to end and the sample may be biased to a particular trend.  For example, selection of 2^nd,12^th, 22^nd, 32^nd etc., may not have the same characteristics as 10^th, 20^th, 30^th, 40^th etc., may have.

2.   This method will also not work in case of cyclic variables.  If attendance of students of a school is generally very low on Mondays due to certain reasons, and we select only Monday of the week for the whole year as a sample for studying the attendance of students, our sample will not give correct result.

CLUSTER SAMPLING

          This method is used when,

1)   The population is infinite.

2)   List of all units of population is not available

3)   Population is scattered over a wide geographical area

4)   Individuals have to be studied as a group

5)   Individual units cannot be sampled due to administrative reasons.

For example, we cannot list all the students of class 8^th or 9^th of the whole state, so, we will form cluster of students.  In this method we form different clusters of whole population to do large area of the population.  That is why it is also called area sample. The Individuals in these clusters have almost all the characteristics of their respective groups.  Suppose, we want to study any problem of secondary student in upper primary, we will not select all the secondary schools.  We will select only few representative schools and study their problem.  Then the result will be generalized to the whole state. 

Explanation

          Suppose we want to estimate the proportion of machine parts in an inventory which are defective.  Also assume that there are 20000 machine parts in the inventory at a given point of time, stored in 400 cases of 50 each. Now using a cluster sampling, we would consider the 400 cases as clusters and randomly select ‘n’ cases and examine all the machine parts in each randomly selected case.

MULTISTAGE SAMPLING:

          It is used in large scale surveys for making the study more comprehensive.  Sampling here is done in two or three or four stages.  In large scale surveys we generally use mailed questionnaire to collect data.  The missing data to do incomplete response are not return of the questionnaire might introduce a bias.  In such cases, double stage or triple stage sampling is used to make the sample representative to the population.  The researcher draws a second sample at random from non respondents and contacts them personally to collect the required information with the help of interview. Then generalizes the information to the entire non-respondent population.  One more example is that if we want to study the attitude of teachers across the country towards the particular textbook, we will first sample states from across the country, then, sample of few districts will be selected from each state.  Finally, sample of few schools will be selected from each district and the survey will be undertaken.

Explanation

          Suppose we want to investigate the working efficiency of nationalized banks in India we want to take a sample of few banks for this purpose. 

          The first stage is to select large primary sampling unit such as states in a country.  Then we may select certain districts and interview all banks in the chosen districts.  This would represent a two-stage sampling design with the ultimate sampling units being cluster of districts.

          If instead of taking a census of all banks within the selected districts, we select certain towns and interview all banks in the chosen towns.  This would represent a three stage sampling design.  If instead of taking census of all banks within the selected towns, we randomly sample banks from each selected town, then it is a case of using a four-stage sampling plan.  If we select randomly at all stages, we will have what is known as ‘multi-stage random sampling design’.