AMITY INSTITUTE OF FORENSIC SCIENCESPAPER NAME:- Research Methodology and StatisticsPAPER CODE:- STAT122TOPIC:- Sampling, sampling distribution, scaling SUBMITTED TO:-Mr. Amit ChauhanSUBMITTED BY:- Manisha Verma B.Sc. 1st year, 2018-21 Section C’ Enrollment no.- A5905918170 INTRODUCTIONResearch in general means search for knowledge. According to Advanced Learner’s Dictionary of Current English Research’ means a careful investigation or inquiry specially through search for new facts in any branch or knowledge. According to Dr. Chakravarti, Research comprises defining or redefining problems, formulating the hypothesis or suggested solutions, collecting data, organising the data and evaluation, discussion or interpretation, conclusion.

The purpose of research is to find or to discover the solutions to any problem, which is of interest of the researcher, by the application of scientific procedure. The Research process includes- formulation of the problem, Extensive literature survey or Review of Literature, Development of research hypothesis, Research design, Determination of Research design, Collection of Research design, Collection of Research design or samples, Execution of the project, Analysis of Data, Hypothesis testing, Interpretation, Report writing.

17145-381000 Research means to find new solutions or new ideas for a particular problem which in turn makes progress possible as those new solutions will become new inventions which in turn will make people’s life easy. Research is the basis of the new government policies introduced by the government. For example, a budget is made according to the needs and requirements of the common people. Research has significance in markets and business where one need to know the interest or demand of people in a particular product. Other importance of research is for students who are doing master’s in a subject or writing thesis for Ph.D. or for people who are professionally involved in research. SCALINGScaling means the process of assigning numbers to various degree of opinion, attitude and other concepts. It can be done in two ways either by making judgement about some characteristic individual and then placing them directly on a scale that has been defined in terms of that characteristic or by preparing questionnaires which will help to score a person who had filled that questionnaire. A scale is a continuum which consists of a highest point and a lowest point between which intermediate points are there. SCALING TECHNIQUESSome of the important scaling techniques are-Rating scales:- it involves qualitative description of limited number of aspects of traits of a person. It does not have any specific rule that we should use a two-point scale or five-point scale. But in practice we use two-point till seven-point scale.Scale construction technique:- it is used in social studies to measure the attitudes of a person by preparing opinionnaire. An opinionnaire is an information form that attempts to measure the attitude or belief of an individual. In this, the person who is filling up the form expresses his/her agreement or disagreement to the statement relevant to the issue.Arbitrary scales:- It is based on ad hoc and are designed by the researcher’s own subjective selection of items. The important advantage of this scale is it can be made easily, quickly and is less costly.Differential scale;- it is also called as Thurstone-type scales. It is developed using consensus scale approach. In this, the selection of items is made by the team of judges who evaluate the items whether they ae relevant to the topic area and unambiguous in implication.Whenever we are doing a complete enumeration of all the items in the field in which we need information (also called as population’ or universe’) is called as census inquiry. But this method is quite time consuming and costly so only a large organisation like government can only use it and that so rarely. Also, since the items to be inquired is large so even a slightest bias in such inquiry can lead to problems in drawing conclusions and we have to resurvey or recheck which is practically impossible in such a large universe’. So, we select a few respondents or select a few items out of the whole population’. These selected respondents are called as Sample’ and the selection process is called as sampling technique. Hence, the survey is called as sample survey. The sample is the representative of the total population so produces miniature cross section. There is technique or process that is adopted by researcher for selecting items for the sample. This is called as sample designing and is done before data collection. So, a researcher has to prepare a sample design which is suitable for his/her research. STEPS FOR SAMPLE DESIGNINGThe points that should be keep in mind while preparing the sample design are-Type of universe:- The researcher must clearly define the set of objects i.e., universe’ which is to be studied. The universe can be finite (number of items is fixed) or can be infinite (number of items is not fixed).Examples of finite universe is number of employees working in a company or population of a city.Examples of infinite universe is number of stars in the sky.Sampling unit:- Before the selection a sampling unit has to be decided. It can be a geographical area like a state, village, etc., or it can be a flat, house. It may be a social unit like club, family or it may be a person. A researcher may decide one or more such units which he has to study.Source list:- Source list or sampling frame is the name of the items of a universe or sample but only case of finite universe. In case, if source list is not available the researcher has to make it. The list must be correct, reliable, suitable and comprehensive.Size of sample. As the name size of sample’ suggests it is related to the number of items in the universe. Out of these we will select a few items that will constitute our sample. It is a major problem for the researcher, as he has to form the sample in such away that it should not be too large as well as not too small. It must be optimum that means the sample should be efficient, representative, reliable and flexible. So , the size of sample should be prepare while keeping these characteristics in mind. A large sample will create problems for the researcher while his/her research and also will not be cost effective.Parameter of interest:- While determining the sample design, the researcher should take into account the question of the specific population parameters which are of interest. For example, the researcher may be interested in knowing something average among the population of a city so, he/she should consider that parameter to be researched while preparing the sample design.Budgetary constraint:- Obviously, whether it is any research or sample designing budget is an important aspect in any of these. It can be said that cost is a practical aspect in sample designing. It is dependent on the type of sample or on the size of sample.Sampling procedure:- At last the researcher should decide the type of technique he will use while selecting the sample.CHARACTERISTICS OF A GOOD SAMPLE DESIGNThe characteristics of a good sample design are-Sample design should be such that it should have minimum sampling error.It must be viable in the context of funds available for research.A sample design must be in a way in which systematic bias can be controlled to minimise any errors.The results which we will get from a sample design should be applicable to the entire universe from which we took the sample. So, sample deign should be in that way.WHY DO WE DO SAMPLING?The reasons for why do we do sampling are-It is time saving and less expensive as compared to census survey.It may provide a researcher more accurate measurements as he/she is working on a items selected from entire universe or population.It is quite useful in population of large number of items.SAMPLING DISTRIBUTIONWe do sample distribution in sampling analysis. For instance, if a researcher is working for a sample and if he/she is calculates or compute statistical measures like mean, standard derivation, etc., then we can find that each sample may give its own value for statistics under consideration. All such values of a particular statistics, like mean, together with their relative frequencies will constitute the sampling distribution of the particular statistics, like mean.SOME IMPORTANT SAMPLING DISTRIBUTIONSSome of the important sampling distributions are as follows:Sampling distribution of mean:- it refers to the probability distribution of al possible means of random samples of a given size that we have take from a universe. If population is normal, N (µ, p), the sampling distribution will also be normal with mean µx=µ and standard deviation will be p n1/2. Here µ = mean of population and p is standard deviation.Sampling distribution of proportion:- it is sampling distribution of proportion. This occurs in statistics of attributes. Assume we need to work out the proportion of defective parts in large number of samples like for instance 100 which have been taken from an infinite population and plot a probability distribution of the said proportions, we obtain sampling distribution of the said proportion.Student’s t-distribution:- When population standard deviation is not known and sample is of small size (i.e., less than 30), we use t-distribution for sampling distribution of mean.Chi-square distribution this is used when we have to deal with collection of values in which squares are added up. Variance of samples require us to add a collection of squared quantities thus will have distributions that are related to chi-square distribution. REFERENCESMr. C.R. Kothari; Research Methodology methods and techniques; second edition; 55-58, 76-83,155-157.