E-LESSON-9,

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M.B.A 2 All right are reserved with CU-IDOL QUANTITATIVE TECHNIQUES FOR MANAGERS Course Code: MBA602 Semester: First SLM UNITS : 9 Unit: 7 www.cuidol.in Unit-9 (MBA602)

QUANTITATIVE TECHNIQUES FOR 33 MANAGERS OBJECTIVES INTRODUCTION Student will be able to : To gain information about a given population Analse the sampling method may not be feasible if the population is very Explain the sampling utility large. We then find a method which can speak about the characteristics of a total population based on the analysis of certain representative members of that population. This gives rise to 'Theory of Sampling'. Discuss the errors in sample survey The sample is a small part or a representative section selected from a Elaborate the probability sampling and non- population. The process of such a selection probability sampling is called 'sampling'. www.cuidol.in Unit-9 (MBA602) Thus, samples can help us in determining the reliability of our estimates. INASllTITriUgThEt aOrFeDreISsTeArNveCdE AwNitDh OCNUL-IIDNOE LLEARNING

TOPICS TO BE COVERED 4 > Sampling Method > Parameters and Characteristics > Basic Sampling Concepts > Sampling Utility > Steps in Sample Survey > Errors in Sample Survey > Types of Sampling > Sampling Distribution www.cuidol.in Unit-9 (MBA602) All right are reserved with CU-IDOL

Sampling & Sampling Distribution 5 www.cuidol.in Unit-9 (MBA602) All right are reserved with CU-IDOL

SAMPLING 6 SAMPLING- In statistics, quality assurance, and survey methodology, sampling is the selection of a subset of individuals from within a statistical population to estimate characteristics of the whole population. Sampling is a process used in statistical analysis in which a predetermined number of observations are taken from a larger population. The methodology used to sample from a larger population depends on the type of analysis being performed, but it may include simple random sampling or systematic sampling. • Certified Public Accountants use sampling during audits to determine the accuracy and completeness of account balances. • Types of sampling include random sampling, block sampling, judgement sampling, and systematic sampling. • Companies use sampling as a marketing tool to identify the needs and wants of their target market. www.cuidol.in Unit-9 (MBA602) All right are reserved with CU-IDOL

TERMINOLOGY  Population or Universe: 7 It refers to the group of people, items or units under All right are reserved with CU-IDOL investigation and includes every individual.  Sample: It is a collection consisting of a part or subset of the objects or individuals of population which is selected for the purpose, representing the population  Sampling: It is the process of selecting a sample from the population. For this population is divided into a number of parts called Sampling Units.  Sampling: It is the process of selecting a sample from the population. For this population is divided into a number of parts called Sampling Units. www.cuidol.in Unit-9 (MBA602)

NEED OF SAMPLING 8  Large population can be conveniently covered  Time, money and energy is saved  Helpful when units of area are homogenous  Used when percent accuracy is not acquired  Used when the data is unlimited Unit-9 (MBA602) All right are reserved with CU-IDOL www.cuidol.in

ADVANTAGES OF SAMPLING 9 Economical: Reduce the cost compare to entire population Increased speed: Collection of data, analysis and Interpretation of data etc take less time than the population Accuracy: Due to limited area of coverage, completeness and accuracy is possible Rapport: Better rapport is established with the respondents, which helps in validity and reliability of the results www.cuidol.in Unit-9 (MBA602) All right are reserved with CU-IDOL

DISADVANTAGES OF SAMPLING 10  Biasedness: Chances of biased selection leading to incorrect conclusion  Selection of true representative sample: Sometimes it is difficult to select the right representative sample  Need for specialized knowledge: The researcher needs knowledge, training and experience in sampling technique, statistical analysis and calculation of probable error  Impossibility of sampling: Sometimes population is too small or too heterogeneous to select a representative sample. www.cuidol.in Unit-9 (MBA602) All right are reserved with CU-IDOL

CHARACTERISTICS OF A GOOD SAMPLE 11  A true representative of the population  Free from error due to bias  Adequate in size for being reliable  Units of sample should be independent and relevant  Units of sample should be complete precise and up to date  Free from random sampling error  Avoiding substituting the original sample for convenience. www.cuidol.in Unit-9 (MBA602) All right are reserved with CU-IDOL

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TYPES OF SAMPLING 13  Probability Sampling: A probability sample is one in which each member of the population has an equal chance of being selected.  Non-Probability Sampling: Nonprobability Sample a particular member of the population being chosen is unknown.  In probability sampling, randomness is the element of control.  In Non-probability sampling, it relies on personal judgment. www.cuidol.in Unit-9 (MBA602) All right are reserved with CU-IDOL

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Probability Sampling 1. Simple Random Sampling: 15 Here all members have the same chance (probability) of being selected. Random method provides an unbiased cross selection of the population.  For Example: We wish to draw a sample of 50 students from a population of 400 students. Place all 400 names in a container and draw out 50 names one by one. www.cuidol.in Unit-9 (MBA602) All right are reserved with CU-IDOL

2. Systematic Sampling: Each member of the sample comes after an equal interval from its previous 16 member. For Example, for a sample of 50 students, the sampling fraction is 50/400 = 1/8 i.e. select one student out of every eight students in the population. The starting points for the selection is chosen at random. www.cuidol.in Unit-9 (MBA602) All right are reserved with CU-IDOL

3. Stratified Sampling: The population is divided into smaller homogenous group or strata by some 17 characteristic and from each of these strata members are selected randomly. Finally from each stratum using simple random or systematic sample method is used to select final sample. www.cuidol.in Unit-9 (MBA602) All right are reserved with CU-IDOL

4. Cluster Sampling (Area Sampling): A researcher/ 18 enumerator selects sampling units at All right are reserved with CU-IDOL random and then does complete observation of all units in the group. For example, the study involves Primary schools. Select randomly 15 schools. Then study all the children of 15 schools. In cluster sampling the unit of sampling consists of multiple cases. It is also known as area sampling, as the selection of individual member is made on the basis of place residence or employment. www.cuidol.in Unit-9 (MBA602)

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Non-Probability Sampling 20 1. Purposive Sampling: In this sampling method, the researcher selects a \"typical group\" of individuals who might represent the larger population and then collects data from this group. Also known as Judgmental Sampling. www.cuidol.in Unit-9 (MBA602) All right are reserved with CU-IDOL

2. Convenience Sampling : It refers to the procedures of obtaining units or members who are most conveniently 2 1 available. It consists of units which are obtained because cases are readily available. In selecting the incidental sample, the researcher determines the required sample size and then simply collects data on that number of individuals who are available easily. www.cuidol.in Unit-9 (MBA602) All right are reserved with CU-IDOL

3. Quota Sampling: The selection of the sample is made by the researcher, who decides the quotas for selecting 2 2 sample from specified sub groups of the population. For example, an interviewer might be need data from 40 adults and 20 adolescents in order to study students’ television viewing habits. Selection will be 20 Adult men and 20 adult women 0 adolescent girls and 10 adolescent boys www.cuidol.in Unit-9 (MBA602) All right are reserved with CU-IDOL

4. Snowball Sampling: 23 All right are reserved with CU-IDOL  In snowball sampling, the researcher Identifying and selecting available respondents who meet the criteria for inclusion.  After the data have been collected from the subject, the researcher asks for a referral of other individuals, who would also meet the criteria and represent the population of concern.  Chain sampling, chain-referral, sampling referral sampling Unit-9 (MBA602) www.cuidol.in

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SAMPLING ERRORS SAMPLING ERROR: is incurred when the statistical characteristics of a population are estimated from a subset, 2 6 or sample, of that population. For example, if one measures the height of a thousand individuals from a country of one million, the average height of the thousand is typically not the same as the average height of all one million people in the country. TYPES OF SAMPLING ERRORS Random Sampling Error:- Random error is a pattern of errors that tend to cancel one another out so that the overall result still accurately reflects the true value. Every sample design will generate a certain amount of random error Bias Sampling Error:- Bias, on the other hand, is more serious because the pattern of errors is loaded in one direction or another and therefore do not balance each other out, producing a true distortion. www.cuidol.in Unit-9 (MBA602) All right are reserved with CU-IDOL

SAMPLING DISTRIBUTION- A sampling distribution represents the 27 distribution of the statistics for a particular sample. For example, a sampling distribution of the mean indicates the frequency with which specific occur. This means that the frequency of values is mapped out. You can also create distributions of other statistics, like the variance. Below is an example of a sampling distribution for the mean. The shape of the curve allows you to compare the empirical distribution of value to a theoretical distribution of values. A theoretical distribution is a distribution that is based on equations instead of empirical data. Two common theoretical distributions are Student’s t and the F-distribution. The benefit of creating distributions is that the empirical ones can be compared to theoretical ones to identify differences or goodness of fit for the model. That is the ultimate goal of statistics, to create an empirical model that explains patterns in the data that differ significantly from the theoretical model. www.cuidol.in Unit-9 (MBA602) All right are reserved with CU-IDOL

TYPES OF SAMPLING DISTRIBUTION 28 The types of sampling distribution are as follows: 1) Sampling Distribution of the Mean: Sampling distribution of means of a population data is defined as the theoretical probability distribution of the sample means which are obtained by extracting all the possible samples having the same size from the given population. Given a finite population with mean (m) and variance (s2). When sampling from a normally distributed population, it can be shown that the distribution of the sample mean will have the following properties www.cuidol.in Unit-9 (MBA602) All right are reserved with CU-IDOL

CENTRAL LIMIT THEOREM The central limit theorem, first introduced by De Moive during the early eighteenth century, happens to be the most2 9 important theorem in statistics. According to this theorem, if we select a large number of simple random samples, for example, from any population distribution and determine the mean of each sample, the distribution of these sample means will tend to be described by the normal probability distribution with a mean µ and variance σ������/n. Or in other words, we can say that, the sampling distribution of sample means approaches to a normal distribution. Symbolically, the theorem can be explained as following : www.cuidol.in Unit-9 (MBA602) All right are reserved with CU-IDOL

UTILITY 30  The utility of this theory is that it requires virtually no conditions on distribution patterns of the individual random variable being summed. As a result, it furnishes a practical method of computing approximate probability values associated with sums of arbitrarily distributed independent random variables.  This theorem helps to explain why a vast number of phenomena show approximately a normal distribution. Because of its theoretical and practical significance, this theorem is considered as most remarkable theoretical formulation of all probability laws.  However, most of hypothesis testing and sampling theory is based on this theorem. So the central limit theorem is perhaps the most fundamental result in all of statistics. www.cuidol.in Unit-9 (MBA602) All right are reserved with CU-IDOL

SUMMARY 31 All right are reserved with CU-IDOL  Sampling  Terminology  Need of Sampling  Advantages and Disadvantages of Sampling  Characteristics of a Good Sample  Classificationof Sampling Techniques  Types of Samples  Probability Sampling  Non-Probability methods www.cuidol.in Unit-9 (MBA602)

MULTIPLE CHOICE QUESTIONS 1) In which of the following types of sampling the information is carried out under the opinion of an 32 expert? A) Quota Sampling C) Convenience Sampling B) purposive Sampling D) Judgement Sampling 2) Sampling error is defined as the difference between ............... A) population and parameter C) Population and sample B) sample and parameter D) parameter and sample 3) Selection of a cricket team for cricket world cup is called as............. A) Random Sampling C) Purposive B) Systematic Sampling D) Cluster 4) Whatdoesthe central limit theorem state? A) if the sample size increases sampling distribution must approach normal distribution B) if the sample size decreases sampling distribution must approach normal distribution C) if the sample size increases sampling distribution must approach an exponential distribution D) if the sample size decreases sampling distribution must approach an exponential distribution Ans. 1. (a) 2. (d) 3. (c) 4. (a) Unit-9 (MBA602) All right are reserved with CU-IDOL www.cuidol.in

FREQUENTLY ASKED QUESTIONS 33 Q1. What is sampling? Ans. In statistics, quality assurance, and survey methodology, sampling is the selection of a subset of individuals from within a statistical population to estimate characteristics of the whole population. For further detail please Refer SLM Q2. Why is there a need for sampling? Ans. Sampling is needed because: - Large population can be conveniently covered - Time, money and energy is saved - Helpful when units of area are homogenous - Used when percent accuracy is not acquired - Used when the data is unlimited For further detail please Refer SLM Q3. What arethe types of sampling errors? Random Sampling Error:- Random error is a pattern of errors that tend to cancel one another out so that the overall result still accurately reflects the true value. Every sample design will generate a certain amount of random error Bias Sampling Error:- Bias, on the other hand, is more serious because the pattern of errors is loaded in one direction or another and therefore do not balance each other out, producing a true distortion. For further detail please Refer SLM www.cuidol.in Unit-9 (MBA602) All right are reserved with CU-IDOL

REFERENCES 34 All right are reserved with CU-IDOL  Stigler, Cambridge M.A., “The History of Statistics”, 1986, Belknap Press  Grant, L.E. and R.C. Leavenworth, “Statistical Quality Control” 1996 McGraw Hill - Book Co.  Tufte, E.R.,”The Visual display of Quantitative Information”, 1983, Graphics Press.  Rowntree, D., “Probability” 1984, Charles Scribner's Sons.  Levin, R.I., and D.S. Rubin, “Statistics for Management”, 1997, Prentice Hall (India)  Gupta, S.C., “Fundamentals of Statistics”, Himalaya Publishing House, Mumbai. www.cuidol.in Unit-9 (MBA602)

35 THANK YOU For queries Email: [email protected] www.cuidol.in Unit-9 (MBA602) All right are reserved with CU-IDOL