# Sampling Procedure – Selection Criteria

In a sampling analysis, two types of costs are involved: cost of collecting data and cost of an incorrect inference resulting from the data. A researcher must take into account the two causes of incorrect inferences:

systematic bias and sampling error. Systematic bias arises due to errors in the sampling procedures; also, it cannot be reduced or eliminated by increasing the sample size. The causes of these errors are detectable and can be rectified. Generally, systematic bias results due to one or more of the following factors:

1. Inappropriate sampling frame: In case the sampling frame is inappropriate (a biased representation of the universe), it results in a systematic bias.
2. Defective measuring device: When the measuring device shows constant error, it results in systematic bias. In a survey, if the questionnaire or the interviewer is biased, it results in systematic bias. Similarly, if the physical measuring device is defective, it shows systematic bias in the data collected through such a measuring device.
3. Non-respondents: If all the individuals included in the sample are not involved, it might cause systematic bias. This is because, in such a situation the possibility of establishing contact from an individual is often correlated with what is to be estimated.
4. Indeterminacy principle: Individuals act differently when kept under observation compared to non-observed situations. For instance, if workers are aware that they are being watched during a work study (which will determine their average length of time to complete a task and quota for piece work), they generally tend to work quite slowly. Thus, the indeterminacy principle may also be the cause of systematic bias.
5. Natural bias in data reporting: Natural bias of respondents often causes systematic bias in many inquiries. We can find a downward bias in the income data collected by government, whereas we find an upward bias in the income data collected by some social organization. People tend to understate their income if asked about it for tax purposes. But, they overstate the same when it is a question of their social status.

Sampling errors are random variations in the sample estimates. They occur randomly and can be in either direction, are compensatory in nature, and their expected value of such errors is equal to zero. Sampling errors decrease with an increase in the sample size and are of a smaller magnitude in case of a homogeneous population.

Measurement of sampling error is usually called precision of the sampling plan. An increase in sample size improves the precision. But, increasing the sample size has its own limitations: a large-sized sample increases the cost of data collection and also adds to systematic bias. The most effective way to increase precision is to select a sampling design, which has smaller sampling error for a given sample size at a given cost. However, people prefer less precise design because it is easier to adopt the same and also because of the fact that systematic bias can be controlled in a better way in such a design.

# Steps for Sample Design

The researcher must keep in mind the following points while preparing a sample design.

(i) Universe: While preparing a sample design, it is foremost required to define the set of objects to be studied.

Technically, it is also known as the Universe, which can be finite or infinite. In case of a finite universe, the number of items is limited. Whereas, in an infinite universe the number of items is limitless.

(ii) Sampling unit: It is necessary to decide a sampling unit before selecting a sample. It can be a geographical one (state, district, village, etc.), a construction unit (house, flat, etc.), a social unit (family, club, school, etc.), or an individual.

(iii) Source list: In other words, it is called the ‘sampling frame’ from which the sample is drawn. It comprises the names of all items of a universe (finite universe only). If source list/sampling frame is unavailable, the researcher has to prepare it by himself.

(iv) Sample size: This is the number of items, selected from the universe, constituting a sample. The sample size should not be too large or too small, but optimum. In other words, an optimum sample accomplishes the requirements of efficiency, representativeness, reliability and flexibility.

(v) Parameters of interest: While determining a sample design, it is required to consider the question of the specific population parameters of interest. For example, we may like to estimate the proportion of persons with some specific attributes in the population, or we may also like to know some average or other measure concerning the population.

(vi) Budgetary constraint: Practically, cost considerations have a major impact upon the decisions concerning not only the sample size but also the sample type. In fact, this can even lead to the use of a non-probability sample.

(vii) Sampling procedure: The researcher, at last, decides the techniques to be used in selecting the items for the sample. In fact, this technique/procedure stands for the sample design itself. Apparently, such a design should be selected, which for a provided sample size and cost, has a smaller sampling error.

# Census And Sample Survey

A Universe or Population consists of all the items in a field of inquiry. A complete enumeration of all these items in the population is called a census inquiry. This inquiry is completely accurate with no element of probability. However, it is not practical as the element of bias cannot be examined in such an inquiry. Moreover, it is time-consuming, expensive, and exhaustive.

Alternatively, a sample of a population can be studied to obtain sufficiently accurate results. This method has practical applications and consumes less time and money. The respondents selected for the inquiry is termed as a sample and the selection process is called sampling technique. The survey is known as a sample survey. A researcher needs to prepare a sample design for his study that should represent the total population, i.e., he needs to plan how and what size of the sample should be selected for his study.

### Implications of a sample design:

A sample design is a technique that a researcher adopts to select items for the sample that represents a given population. A researcher may prepare many sample designs, but he needs to choose the design that should be reliable and appropriate for his research study.

# Basic Principles of Experimental Designs

There are three basic principles of experimental designs: Randomization, Replication, and Local Control. Each of them is described below in brief:

(1) Randomization: This is the first principle of an experimental design. This process randomly assigns treatments to the experimental units. It implies that every allotment of treatments ends up with the same probability. When dividing research participants into the different groups, random assignment ensures that every participant has an equal chance of being assigned to both the experimental group and the control group. Randomizations purpose is to remove bias and other sources of extraneous variation, which are uncontrollable. It is the basis of any valid statistical test. Therefore, the treatments must be assigned randomly to the experimental units.

(2) Replication: This is the second principle of an experimental design. It is a repetition of the basic experiment. In all experiments, some variation exists because the experimental units, such as, individuals or plots of land, cannot be physically identical. This variation is removable by using a number of experimental units. Therefore, the basic experiment is performed repeatedly. Researchers repeat the same studies on different research participants to see if they produce the same statistically significant results each time. A replicate is an individual repetition. Its number, shape, and size are influenced by the nature of the experimental material. Replication helps in: obtaining an accurate estimate of the experimental error; decreasing the experimental error, thereby increasing precision; and obtaining a more precise estimate of the mean treatment effect.

(3) Local Control: Randomization and Replication do not remove all extraneous sources of variation. A more refined experimental technique is required for that. A design should be chosen such that all the extraneous sources of variation come under control. For this purpose, local control, which refers to the amount of balancing, blocking and grouping of the experimental units, is used. Balancing implies that the treatments should be assigned to the experimental units such that the result is a balanced arrangement of treatments. Blocking means that, similar experimental units should be collected together to form a relatively homogeneous group. The main purpose of local control is to increase the efficiency of an experimental design by minimizing the experimental error. In this case, local control should not be confused with the word control. Control in experimental design is used for a treatment. It does not receive any treatment, but the effectiveness of other treatments should be found through comparison.