# Test of Practicality of a measuring instrument

The practicality attribute of a measuring instrument can be estimated regarding its economy, convenience and interpretability. From the operational point of view, the measuring instrument needs to be practical. In other words, it should be economical, convenient and interpreted.

Economy consideration suggests that some mutual benefit is required between the ideal research project and that which the budget can afford. The length of measuring instrument is an important area where economic pressures are swiftly felt. Even though more items give better reliability, in the interest of limiting the interview or observation time, we have to take only few items for the study purpose. Similarly, the data-collection methods, which are to be used, occasionally depend upon economic factors.

Convenience test suggests that the measuring instrument should be easily manageable. For this purpose, one should pay proper attention to the layout of the measuring instrument. For example, a questionnaire with clear instructions and illustrated examples is comparatively more effective and easier to complete than the questionnaire that lacks these features. Interpretability consideration is especially important when persons other than the designers of the test are to interpret the results. In order to be interpretable, the measuring instrument must be supplemented by the following:

1. detailed instructions for administering the test,
2. scoring keys,
3. evidence about the reliability, and
4. guides for using the test and interpreting results.

# Random Sample From an Infinite Universe

It is relatively difficult to explain the concept of random sample from an infinite population. However, a few examples will show the basic characteristics of such a sample. Suppose we consider the 10 throws of a fair dice as a sample from the hypothetically infinite population that consists of the results of all possible throws of the dice. If the probability of getting a particular number, say 7, is the same for each throw and the 10 throws are all independent, then we say that the sample is random. Similarly, it would be said to be sampling from an infinite population if we sample with replacement from an infinite population and our sample would be considered as a random sample if in each draw all elements of the population have the same probability of being selected and successive draws happen to be independent. In brief, one can say that the selection of each item in a random sample from an infinite population is controlled by the same probabilities and that successive selections are independent of one another.

In other words, if we have to take a sample of grain from a bag, it is not possible to assign a number to each grain or particle constituting the universe and as such the methods of constructing card population or of random sampling numbers cannot be used. In such cases a thorough mixing of the grain may be done and by dividing and sub-dividing the lot in parts, a sample of an adequate size can be obtained. The contents of the bag after thorough mixing may be divided in two equal parts of which one may be selected and this may further be divided in two parts after mixing. In this way the process can be continued till one of the sub-divisions is equal to the size of the desired sample.

# 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.

# 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.

# Research Design

A research design can be defined as the preparation of conditions, for the collection and analysis of data in such a manner, which aims at combining relevance to the research purpose with economy in procedure. In other words, the design arrangement of a research project is commonly known as the “research design”. Besides, the decisions like what, where, when, how, etc., in regard to a research study, creates a research design. In fact, the research design is the conceptual structure within which a research is conducted. Moreover, it comprises the outline for the collection, measurement and analysis of data. Hence, the design carries a blueprint of what the researcher will do, from composing the hypothesis and its operational implications to the final analysis of data. Overtly, the design decisions happen to be in respect of:

1)  What is the research?

2)  Where and why will the research be conducted?

3)  What data is required for the research?

4)  Where can be the data found?

5)  What will be the time period of the research?

6)  What will be the sample design?

7)  What methods will be used for data collection?

8)  How will be the data analysed?

9)  In which style will be the research report prepared?

Based on the above mentioned design decisions, the complete research design may be divided into the following parts:

(a)  Sample design: this deals with the technique of selecting items and thus requires careful observation for the given research study.

(b)  Observational design: this relates to the conditions under which the experiments are to be conducted.

(c)  Statistical design: this concerns the question of how many items are to be observed, and how are the collected data and information going to be analysed.

(d)  Operational design: this deals with the methods by which the procedures specified in the sample, observational and statistical designs can be conducted.

The essential characteristics of a research design are as the following.

(a)  It is a plan, which specifies the sources and types of data relevant to the research problem.

(b)  It is a strategy, which decides the approach that will be used to collect and analyse the data.

(c)  Since most of the research studies are conducted under these two controls, it also includes the time and cost budgets.

In short, the research design must contain the followings.

(i)  A clear and concise statement of the research problem,

(ii)  The population to be studied, and

(iii)  The various procedures, methods, and techniques to be used for collecting and analysing the data.