SAMPLING IN EDUCATIONAL RESEARCH

 

SOME IMPORTANT TERMS IN SAMPLING

Population

            By population we mean the aggregate or totality of objects or individuals regarding which inferences are to be made in a sampling study. A population is any group of individuals that have one or more characteristics in common that are of interest of the researcher.

Sample

            A sample is a small proposition of a population selected for observation and analysis. By observing the characteristics of the sample, one can make certain inferences about the characteristics of the population from which it is drawn.

Sampling

It is the process of selection of sample from the population. For this purpose, the population is divided into a number of parts called sampling units.

Parameter

            A parameter is the population value representing any trait or characteristics of the population as a whole.

Statistics

            A statistics is the sample value representing any trait or characteristic of the members of the sampling.

Sampling Error

            Sampling error is simply the difference between the value of parameter and that of corresponding statistic or the difference between population value and sample value.

Sampling Distribution

            The sampling distribution is the relative frequency distribution of an infinity of determinants of the value of this statistic.

Sampling Bias

            If the mean of the sampling distribution of a statistic coincides with or equals that of the corresponding parameter it is said to be unbiased. If, on the other hand, the mean of its sampling distribution does not coincide with the parameter, it is said to be biased.

Standard Error

            The standard error of any statistic is the standard deviation of its sampling distribution.

Importance of sampling

·        When the population is very large it can be satisfactorily corrected by sampling.

·        It saves a lot of money, time, energy etc.

·   Especially when the units of the area are homogeneous sampling technique is merely useful.

·        When the data’s are unlimited the use of this method is readily useful.

Characteristics of a good sampling:

1. True representative:

A good sample is a true representative of the population corresponding to its properties.

2. Free from bias:

A good sample is free from bias. It does not permit prejudicious, preconceptions and imagination to influence its choice.

3. Objective:

A good sample is an objective one. It prefers to objectivity in selection procedure or absence of subjective elements from the situation.

4.  Accurate:

A good sample maintains accuracy. It gives accurate estimates or statistics and does not involve errors.

5. Comprehensive:

A good sample is comprehensive in nature. A comprehensive sample is controlled by specific purpose of the investigator.

6. Economical:

            A good sample is economical in terms of energy, time at any point of view.

7. Approachable:

The subjects of good sample are easily approachable. The research tools can be easily administrated on them and the data can be easily collected.

 

 

 

8. Good size:

The size of good sample is such that it yields an accurate result. The probability of errors can be estimated.

9. Feasible:

A good sample makes the research work more feasible.

METHODS OF SAMPLING

Bloomers and Lindquist have said, in general sampling schemes may be classified into two they are:

a)     Probability Sampling

b)     Non-probability Sampling

a) Probability Sampling:

·        In probability sampling every individual of the population has equal chance of selecting.

·        Probability sample may be representative of the population.

·        The observations (Data) of the probability sample are used for the inferential purpose.

·        Inferential or parametric statistics are used for probability sample.

·        There is a risk for drawing conclusions from probability sample.

b) Non-Probability Sampling:

·        There is no probability of selecting any individual.

·        The observations of non-probability sample are not used for generalization purpose.

·        Non-parametric or non-inferential statics are used in non-probability sample.

·        There is no risk for drawing conclusions from non-probability sample.

 

 

Probability Sampling Techniques

1. Simple Random Sampling

            A simple random sample is one in which each element of the population has an equal and independent chance of being included in the sample. It is defined as a sampling technique where every item in the population has an even chance and likelihood of being selected in the sample. Here the selection of items entirely depends on luck or probability, and therefore this sampling technique is also sometimes known as a method of chances. Randomization is done by using a number of techniques as: Tossing a coin, Throwing a dice, Lottery method etc. For example to select a sample of 200 students from a population of 10,000 students using simple random sampling, the researcher has to number all the 10,000 students as 1,2,3,….10,000. Then using random number table or a computer generated random numbers, a list of 200 students are prepared and invited to be the sample for the research study.

Advantages

•  It is free from subjectivity and free from personal error.

•  It provides appropriate data for the purpose of research.

•  The observations of the sample can be used for inferential purpose.

Dis-advantages

•      The inferential accuracy of the finding depends upon the size of the sample. So the greater     the sample size, the greater is the accuracy of results.

•      The representativeness of a sample cannot be ensured by this method.

•      Inappropriate for heterogeneous sample.

2. Systematic Sampling

            Systematic random sampling is a type of probability sampling technique. With the systematic random sample, there is an equal chance (probability) of selecting each unit from within the population when creating the sample. The systematic sample is a variation on the simple random sample. Rather than referring to random number tables to select the cases, the researcher selects units directly from the sample frame. This method selects the individuals of the population in any systematic way. It involves selecting every K^th item (K= Sampling Interval). Which can be determined by K=No. of items in the population / No. of items in the sample. For example: Imagine that a researcher wants to study about the career goals of students at a University, and if the university has roughly 10,000 students. These 10,000 students form the population (N). In order to select a sample of 400 students from this population of 10,000 students, using systematic random sampling, the  researcher could select every 25^th student  to get a sample of 400 where 25 is the sampling interval ie. (10000/400).

Advantages

•  This is a simple method of selecting a large number of samples.

•  This method improves the possibility for the sampling units to be more evenly spread over the population.

•  This method reduces the potential for human bias in the selection of cases to be included in the sample. So it provides a highly representative sample

Dis-advantages

•   There is a chance of selecting the homogeneous group if the list of the population has some kind of standardized arrangement (order/pattern). In that case systematic sampling could pick out similar cases rather than completely random ones.

•      Attaining a complete list of the population can be a difficult task for the researcher in certain cases.

3. Stratified Sampling

Unlike the simple random sampling and the systematic random sampling, sometimes if the researcher is interested in particular strata or groups within the population such as male vs. female, rural vs urban etc., In that case, stratified random sampling method is the most useful method. In this method the population is divided into strata on the basis of some characteristics such as gender, locality, medium of instruction etc., and from each of these smaller homogeneous groups (Strata) samples are selected randomly. This stratification of the population should be relevant to the particular research study. Stratified random sampling can be classified as proportionate sampling and disproportionate sampling.

·         Proportionate sampling: In this technique, the samples are selected from each stratum as they stand in the universe ie. in the way they are distributed in the population.

·         Dis-proportionate sampling: In this technique an equal number of samples are taken from each stratum regardless of the size of strata in proportion to the universe or population.

For example if a researcher wants to select a sample of 100 from a population of 10,000 students he may choose the 100 as 50 male and 50 female.

Advantages

•   It yields a sample that is a good representative of the population.

•   It is an objective method of sampling.

Dis-advantages

•   It is difficult for the researcher to decide the relevant criterion for stratification. Also a complete list of population is needed for doing this method of sampling.

•      Bias may occur due to improper stratification

 

4. Cluster sampling

            Cluster sampling is typically used in market research. It’s used when a researcher can’t get information about the population as a whole, but they can get information about the clusters. In cluster sampling, the researcher divides the population into separate groups, called clusters. Then, a simple random sample of clusters are selected from the population. Example: Imagine an organization wants to survey the performance of smartphones across a country. They can divide the entire country’s population into cities (clusters) and select n cities among them and include all the members of the city.

Thus in cluster sampling the total population is divided into a number of relatively small subdivisions called clusters then from these clusters respondents or cases are randomly selected for inclusion in the overall sample. 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.

Advantages

•     It is an easy method and economical method.

•     It is practical and highly applicable in education.

Dis-advantages

•     Produces larger sampling error

•     May be biased in certain cases.

•     Generalizations may lack precision.

5. Multistage sampling

            Multistage sampling divides large populations into stages to make the sampling process more practical. It is a complex form of cluster sampling, sometimes, also known as multistage cluster sampling. In this method, significant clusters of the selected groups are split into sub-groups at various stages to make it simpler for primary data collection. In this method first the researcher samples inclusive groups from the population and then select subgroups from the inclusive groups. At the third stage individual cases are selected from the selected subgroups. At every level sampling is done at random. Suppose is a researcher wants to investigate the working efficiency of nationalized banks in India. The researcher using multi-stage sampling divides the population into states and take a simple random sample of states. For the next stage, the researcher takes a simple random sample of banks from within those states. Then he may randomly select certain districts and interview all banks in the chosen districts.  

Advantages

•   It is a good representation of the population.

•   It is an objective procedure of sampling.

Dis-advantages

•   It is a difficult and complex method of sampling.

•   It involves error in the primary and secondary stages of sampling.

Non-Probability Techniques

•     There is no idea of population in non-probability sampling.

•     There is no probability of selecting any individual

•     Non probability sample has a free distribution.

•     Observations are not used for generalization purpose.

•     Non Parametric or Non –Inferential statistics are used.

Non-Probability based Sampling Techniques

1. Incidental or Accidental Sampling

The term incident or accidental applied to those samples that are taken because they are most frequently available, i.e., this refers to group which are used as samples of a population because they are readily available or the researcher is unable to employ more acceptable sampling methods. It is applicable when such groups used as samples are easily available eg., Children in a school, members of a club It may be quite acceptable for certain action research projects which do not require generalizations. It is generally used in exploratory studies where much accuracy is not needed.

Advantages

·         It is very easy method of sampling.

·         It reduces the time, money and energy, i.e., it is an economical method.

Dis-advantages

·         It is not a representative of the population.

·         It is not free from error.

2. Judgement Sampling

            This involves the selection of a group from the population on the basis of available information thought it is to be representative of the total population. In this method the investigator selects a particular group and leaves the rest of the members of the group. The researcher himself judges that this is a good representative sample.

Advantages

·         Knowledge of the investigator can be best used in this technique of sampling.

·         This technique of sampling is also economical.

Dis-advantages

·         It is not free from error.

·         It includes uncontrolled variation.

3. Quota Sampling

            This is a combined form of both judgement sampling and probability sampling. The population is classified into several categories. On the basis of judgement or assumption or the previous knowledge, the proportion of population falling into each category is decided. Quota sampling is very arbitrary and likely to figure in municipal surveys.

Advantages

·         It is an easy sampling technique.

·         It is most frequently used in social surveys.

Dis-advantages

·         It is not a representative sample.

·         It is not free from error.

·         It has the influence of regional, geographical and social factors.

4. Convenience sampling

It is also known as careless, unsystematic or opportunistic sampling. In this type the researcher select certain units, which are convenient to him. No preplanning is necessary for the selection of items. This method may be used for pilot studies. It is also used when the Universe is not clear, Sampling unit is not clear and complete source list is not available.

5. Snowball Sampling

Snowball sampling or chain-referral sampling is defined as a non-probability sampling technique in which the samples have traits that are rare to find. This is a sampling technique, in which existing subjects provide referrals to recruit samples required for a research study. Snowball sampling method is purely based on referrals and that is how a researcher is able to generate a sample. Therefore this method is also called the chain-referral sampling method. The snowball sampling method is extensively used where a population is unknown and rare and it is tough to choose subjects to assemble them as samples for research.

Advantages

·         The chain referral process allows the researcher to reach populations that are difficult to sample when using other sampling methods.

·         The process is cheap, simple and cost-efficient.

·         This sampling technique needs little planning and fewer workforce compared to other sampling techniques.

Disadvantages of Snowball Sampling

·         The researcher has little control over the sampling method. The subjects that the researcher can obtain rely mainly on the previous subjects that were observed.

·         Representativeness of the sample is not guaranteed. The researcher has no idea of the true distribution of the population and of the sample.

·         Sampling bias is also a fear of researchers when using this sampling technique. Initial subjects tend to nominate people that they know well. Because of this, it is possible that the sample that the researcher will obtain is only a small subgroup of the entire population with similar characteristics.

Sampling error

Sampling error is incurred when the statistical characteristics of a population are estimated from a subset, or sample, of that population. Since the sample does not include all members of the population, statistics on the sample, such as means and quantiles, generally differ from the characteristics of the entire population, which are known as parameters. Since sampling is typically done to determine the characteristics of a whole population, the difference between the sample and population values is considered a sampling error.

Population Specification Error: This error occurs when the researcher does not understand who he/she should survey. If the researcher is not aware of the population clearly then he is likely to draw a faulty sample which may lead to sampling error.

Sample frame Error - A frame error occurs when the wrong sub-population is used to select a sample. Sometimes the researcher may choose his/her sample from a biased frame which may cause sampling error.

Selection Error - This occurs when respondents self-select their participation in the study – only those that are interested respond. Selection error can be controlled by going extra lengths to get participation.

Non-Response - Non-response errors occur when respondents are different than those who do not respond. This may occur because either the potential respondent was not contacted or they refused to respond. The extent of this non-response error can be checked through follow-up surveys using alternate modes.

These errors occur because of variation in the number or representativeness of the sample that responds. Sampling errors can be controlled by (1) careful sample designs, (2) large samples, and (3) multiple contacts to assure representative response.

Sample Size

The sample size is a term used for defining the number of subjects included in a sample size. By sample size, we understand a group of subjects that are selected from the general population and is considered a representative of the real population for that specific study. Sample size in the context of educational research refers to the number of participants in an experiment or study.

For example, if we want to predict how the population in a specific age group will react to a new product, we can first test it on a sample size that is representative of the targeted population.

The sample size is a subset, an extract, several persons extracted from that population. The population is considered infinite; in practice, we cannot study an endless number of cases.

The size of the sample should be large enough to be an accurate representation of the population and large enough to achieve statistically significant results.

For descriptive research (ex: aviators), a number of 20% of the respective population is sufficient. The larger the population, the smaller the percentage. Ex: 20% of 1000 people = 200 people; 10% of 5000 people = 500 people. For small populations (under 100 persons), the sample size is approximately equal to the population.