# Complex Random Sampling Designs

Complex random sampling designs are probability sampling done with restricted sampling techniques. They are also called mixed sampling designs as they tend to combine probability and non-probability sampling procedures during sample selection.

### Some of the popular complex random sampling designs are as follows:

(i) Systematic sampling: The researchers sometimes select every ith item from a list, this is known as systematic sampling. The first unit is a random number and the next unit onwards they are selected at the same fixed intervals.

(ii) Stratified sampling: In a very diverse universe stratified sampling is used were the population is divided into several groups that are more similar and then items are selected from each strata as a sample. The strata is a subjective choice of the researcher based on his experience and judgment by using simple random sampling.

(iii) Cluster sampling: In cluster sampling within the population there might be similar groups these are divided into a number of small homogeneous subdivisions then some of these clusters are randomly selected as sample. Cluster sampling is highly economic. The difference between stratified sampling and cluster sampling is that in stratified sampling a random sample is drawn from each of the strata, whereas in cluster sampling only the selected clusters are studied.

(iv) Area sampling: In area sampling a large area is divided into smaller parts and then samples are selected randomly.  This is a type of cluster sampling were the cluster of units is based on geographic area.

(v) Multi-stage sampling: Multi-stage sampling is a complex type of cluster sampling. Multi-stage sampling is used in researches where the entire universe is very large, for example the entire country; the researcher selects samples in various levels. The researcher after selecting clusters from all universe than randomly selects elements from each cluster. This type of sampling is cost effective and easy to administer.

(vi) Probability proportional to size (PPS) sampling: Probability proportional to size (PPS) sampling: Sometimes cluster sampling units lack equal number of elements; in such cases the researcher uses a random selection process where the probability of selection of each sub group is proportional to the size of the cluster. The actual numbers selected are indicative of the clusters chosen and selected. PPS avoids under representation of any one group.

(vii) Sequential sampling: This is a complex sampling design was the size of the sample is not fixed earlier but is determined according the need of the researcher. In this type of sampling method, the researcher does his research on a particular sample if not satisfied takes another sample unit and so on. The researchers keeps fine tuning the experiment and decides only after doing the experiment whether more samples are needed or not.

# Selecting a Random Sample

Random sample is the basic sampling method. Its main advantage is that, each member of the group is given an equal chance of being chosen. Thus, the statistical conclusions deduced from a random sample analysis are deemed to be valid. Though it sounds easy, the process of selection of a random sample is quite complex.

Lottery Method: This is the most commonly used method. Every member is assigned a unique number. These numbers are put in a jar and thoroughly mixed. After that, the researcher picks some numbers without looking at it and those people are included in the study.

Random Number Table: This table consists of a series of digits (0-9) that are generated randomly. The numbers are arranged in rows and columns and can be read in any direction. All the digits are equally probable.

Computer: In case of large population, selecting random samples manually becomes tedious and very time-consuming. In these cases, specific computer softwares are used to generate numbers randomly. This process is very fast and easy.

With and Without Replacement: When a population element is given the chance to be chosen more than once, it is known as sampling with replacement; when it can be chosen only once, it is known as sampling without replacement.

# Types of Sample Designs

Basically, there are two different types of sample designs, namely, non-probability sampling and probability sampling. Each of the two is described below.

(1) Non-probability sampling: This type of sampling is also known as deliberate sampling, purposive sampling, or judgement sampling. In this sampling procedure, the organisers of the inquiry deliberately choose the particular units of the universe to compose a sample on the basis that the small mass selected out of a large one would represent the whole. For example, if economic conditions of the population living in a state are to be studied, a few cities and towns can be deliberately selected for intensive study on the principle that they can represent the entire state. Besides, the investigator may select a sample yielding results favorable to his point of view. In case that happens, the entire inquiry may get vitiated. Thus, there exists the danger of bias entering into this type of sampling technique. However, if the investigators are impartial, work without bias and have the necessary experience so as to take sound judgement, the obtained results of an analysis of deliberately selected sample may be tolerably reliable.

Quota sampling is also an example of non-probability sampling. In this type of sampling the interviewers are simply given quotas to be filled from the different strata, with some instructions regarding filling up the quotas. Moreover, this type of sampling is relatively inexpensive and quite convenient.

(2) Probability sampling: This type of sampling is also known as random sampling or chance sampling. This sampling procedure gives each element in the population an equal chance of getting selected for the sample; besides, all choices are independent of one another. The obtained results of probability sampling can be assured in terms of probability. In other words, we can measure the errors of estimation or the significance of obtained results from a random sample. In fact, due to this very reason probability sampling design is superior to the deliberate sampling design. Probability sampling ensures the law of Statistical Regularity, which states that if the sample chosen is a random one, the sample will have the same composition and characteristics as the universe. Hence, probability sampling is more or less the best technique to select a representative sample.

# Characteristics of a Good Sample Design

In a field study due to time and cost involved, generally, only a section of the population is studied. These respondents are known as the sample and are representative of the general population or universe. A sample design is a definite plan for obtaining a sample from a population. It refers to the technique or the procedure for obtaining a sample from a given population.

Following are the characteristics of good sample design:

1. Sample design should be a representative sample: A researcher selects a relatively small number for a sample from an entire population. This sample needs to closely match all the characteristics of the entire population. If the sample used in an experiment is a representative sample then it will help generalize the results from a small group to large universe being studied.

2. Sample design should have small sampling error:  Sampling error is the error caused by taking a small sample instead of the whole population for study. Sampling error refers to the discrepancy that may result from judging all on the basis of a small number.Sampling error is reduced by selecting a large sample and by using efficient sample design and estimation strategies.

3. Sample design should be economically viable: Studies have a limited budget called the research budget. The sampling should be done in such a way that it is within the research budget and not too expensive to be replicated.

4. Sample design should have marginal systematic bias: Systematic bias results from errors in the sampling procedures which cannot be reduced or eliminated by increasing the sample size. The best bet for researchers is to detect the causes and correct them.

5. Results obtained from the sample should be generalized and applicable to the whole universe: The sampling design should be created keeping in mind that samples that it covers the whole universe of the study and is not limited to a part.

# 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.

In hypothesis-testing research studies, also known as experimental studies, the researcher generally tests the hypotheses of causal relationships among variables. Besides, such type of studies needs those kinds of procedures, which will not only reduce the bias and increase reliability, but will also approve the drawing inferences about causality. Hence, when we discuss about the research design in such studies, we usually mean the experimental designs.

Experimental designs were discovered and developed by Professor R. A. Fisher, who was working at the Rothamsted Experimental Station, at the Centre for Agricultural Research in England. In fact, the study of experimental designs originated in agricultural research. Professor Fisher divided the agricultural fields/plots into different blocks and conducted experiments in each of them. Consequently, whatever information was collected from this, he found them to be very reliable. In this way, he was inspired to develop certain experimental designs to test the hypotheses about scientific investigations. In recent time, the experimental designs are being used in researches related to phenomena of several disciplines. Besides, since experimental designs originated in the context of agricultural operations, we still use, although in a technical sense, several agricultural terms, such as, treatment, yield, plot, block, etc., in the experimental designs.

# Different Research Designs

Exploratory research studies, also known as formulative research studies, are conducted when there are very few or no earlier studies for reference. In this type of research design, a vague problem is chosen, which is followed by an exploratory research to find a new hypothesis. It lays emphasis on discovery of ideas and possible insights that help in identifying areas for future experimentation.

Purpose

1) It provides information to form a more precise problem definition or hypothesis.

2) It establishes research priorities.

3) It gives the researcher a feel of the problem situation and familiarizes him with the problem.

4) It collects information about possible problems in carrying out the research using specific collection tools and specific techniques for analysis.

In exploratory studies, the following three methods are generally used:

1) Survey of relevant literature

2) Survey of experienced individuals

3) Analysis of selected examples

Survey of Relevant Literature

Published literature are very good sources for the purpose of hypothesis generation and problem definition. Much of the published and unpublished data is available through books, journals, newspapers, periodicals, government publications, individual research projects, and data collected by the trade associations. Some of it could be relevant to the given problem situation. An analysis of existing literature may not provide the solution to the research problem, but, it surely gives a direction to the research process.

Survey of Experienced Individuals

Talking to individuals who have expertise and ideas about the research subject can be very useful for the study. Attempt should be made to gather all possible information about the subject of research from people who have specific knowledge about it. In this case, the experimenter must prepare a systematic interview schedule to collect information from the respondents. The success of this survey depends upon the freedom of response given to the respondent, expertise and communication skills of the respondents, and the conversational skills of the experimenter in extracting maximum information from the respondents.

Analysis of Selected Examples

This method involves the selection of examples, which reflect the problem situation. A thorough analysis of the examples is conducted. In certain cases, such type of study helps in identifying the possible relationships that exist between the variables. The relationships, their extent, and direction are then measured using conclusive research designs.