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Important Terminologies In Statistical Inference

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Important Terminologies In Statistical Inference

1. 1. Lessons in Business Statistics
2. 2. An Overview of Statistics
3. 3. Introduction Managers make sound decisions when they use allManagers make sound decisions when they use all relevant information in an effective and meaningfulrelevant information in an effective and meaningful manner. The principal purpose of statistics is tomanner. The principal purpose of statistics is to provide decisionprovide decision--makers with a set of techniquesmakers with a set of techniques for collecting, analyzing, and interpreting data intofor collecting, analyzing, and interpreting data into actionable recommendations. Statistical methodsactionable recommendations. Statistical methods are widely used to aid decisionare widely used to aid decision--makers in allmakers in all functional areas of management. This chapterfunctional areas of management. This chapter provides the basic ideas and concepts at a generalprovides the basic ideas and concepts at a general level.level.
4. 4. 1) Why Should I Study Statistics? Situation 1Situation 1 A company has to decide whether to introduce a new productA company has to decide whether to introduce a new product into the market or not. The company will introduce the productinto the market or not. The company will introduce the product into the market if 30% of the target audience in the relevantinto the market if 30% of the target audience in the relevant population will accept the product so that the risk of productpopulation will accept the product so that the risk of product failure is minimized. Obviously consumer acceptance isfailure is minimized. Obviously consumer acceptance is paramount in making this decision. To know about theparamount in making this decision. To know about the consumer acceptance in a reasonable manner, the company hasconsumer acceptance in a reasonable manner, the company has done a "test marketing" exercise. In the test market, 30% ofdone a "test marketing" exercise. In the test market, 30% of the sample target audience (based on a sample of 150the sample target audience (based on a sample of 150 consumers) indicate their acceptance of the product. Does theconsumers) indicate their acceptance of the product. Does the sample result at 95% confidence level suggest that 30% of thesample result at 95% confidence level suggest that 30% of the target audience in the population (entire market) will accept thtarget audience in the population (entire market) will accept thee product?product?
5. 5. 1) Why Should I Study Statistics? Continues Situation 2Situation 2 A bank which has been steadily losing customers in the lightA bank which has been steadily losing customers in the light of intense competition wants to investigate the reasons forof intense competition wants to investigate the reasons for the loss of customers on account of perceived service qualitythe loss of customers on account of perceived service quality in critical dimensions like response time, reliability, courtesyin critical dimensions like response time, reliability, courtesy of the service staff, and credibility. The bank would like toof the service staff, and credibility. The bank would like to conduct a comprehensive survey to measure the perceivedconduct a comprehensive survey to measure the perceived service quality from the customers' angle on theseservice quality from the customers' angle on these dimensions with that of competition. This would help thedimensions with that of competition. This would help the bank develop and implement effective strategies to woo itsbank develop and implement effective strategies to woo its present customers back as well as to attract new customers.present customers back as well as to attract new customers.
6. 6. 1) Why Should I Study Statistics? Continues Can you make the right decision in situation 1 andCan you make the right decision in situation 1 and situation 2 with minimum risk without the help ofsituation 2 with minimum risk without the help of statistics? The answer is clearly a "No". Informationstatistics? The answer is clearly a "No". Information based decision making using statistical analysis isbased decision making using statistical analysis is absolutely essential in the present environmentabsolutely essential in the present environment characterized by intense competition, onslaught of newcharacterized by intense competition, onslaught of new products and services, globalization, and revolution ofproducts and services, globalization, and revolution of information technology.information technology.
7. 7. 2 ) What is Statistics? By "Statistics"By "Statistics" we mean methods speciallywe mean methods specially adapted to theadapted to the collectioncollection,, classificationclassification,, analysisanalysis,, andand interpretationinterpretation of data forof data for making effective decisions in all functionalmaking effective decisions in all functional areas of management.areas of management.
8. 8. AMEX Gained by Statistical Analysis American Express Company (AMEX), the pioneer in personalAmerican Express Company (AMEX), the pioneer in personal charge cards during the eighties used to systematically collectcharge cards during the eighties used to systematically collect customer feedback data from the marketplace on a continuouscustomer feedback data from the marketplace on a continuous basis. AMEX is well known for its caring attitude towardsbasis. AMEX is well known for its caring attitude towards customers.customers. The Analysis and Interpretation of the customer data revealedThe Analysis and Interpretation of the customer data revealed that the customers wanted the new card to be processed withinthat the customers wanted the new card to be processed within three weeks where as AMEX was taking around 5 weeks.three weeks where as AMEX was taking around 5 weeks. AMEX decided to issue new cards within two weeks.AMEX decided to issue new cards within two weeks. Similarly another analysis revealed that the customers wantedSimilarly another analysis revealed that the customers wanted the stolen/lost cards to be replaced within two days where asthe stolen/lost cards to be replaced within two days where as AMEX was taking two or more weeks to issue replacementAMEX was taking two or more weeks to issue replacement cards. AMEX decided to replace the lost cards within twocards. AMEX decided to replace the lost cards within two days. As a result of these two decisions, AMEX could generatedays. As a result of these two decisions, AMEX could generate \$1.4million additional profit per year.\$1.4million additional profit per year.
9. 9. 3) Typical Application Areas MarketingMarketing Marketing ResearchMarketing Research Demand ProjectionsDemand Projections FinanceFinance Financial Ratio AnalysisFinancial Ratio Analysis Cash ForecastingCash Forecasting Materials ManagementMaterials Management Inventory ControlInventory Control Incoming Quality AssessmentIncoming Quality Assessment Quality ManagementQuality Management SQC TechniquesSQC Techniques Process CapabilityProcess Capability
10. 10. 4) Types of Statistics Descriptive StatisticsDescriptive Statistics isis concerned with Dataconcerned with Data Summarization,Summarization, Graphs/Charts, andGraphs/Charts, and TablesTables Inferential StatisticsInferential Statistics is ais a method used to talk aboutmethod used to talk about a Population Parametera Population Parameter from a Sample. It involvesfrom a Sample. It involves Point Estimation, IntervalPoint Estimation, Interval Estimation, andEstimation, and Hypothesis TestingHypothesis Testing
11. 11. Descriptive Statistics Example 0 5 10 15 20 25 30 35 40 45 50 1st Qtr 3rd Qtr Machine 1 Machine 2 Machine 3 Machine 4 The Quality Control Department of aThe Quality Control Department of a large manufacturing company wouldlarge manufacturing company would like to compute summary measureslike to compute summary measures such as the mean production per shiftsuch as the mean production per shift for a particular item. The departmentfor a particular item. The department would also like to get a comparativewould also like to get a comparative picture of performance of the meanpicture of performance of the mean production across the four machines inproduction across the four machines in the plant by tabulation. Further thethe plant by tabulation. Further the company might like to graph thecompany might like to graph the comparative performance of the fourcomparative performance of the four machines by a bar chart depicting themachines by a bar chart depicting the mean production per shift.mean production per shift.
12. 12. Inferential Statistics -Example Suppose you, as a marketing manager would like to identify aSuppose you, as a marketing manager would like to identify a niche market for your product. You know from your experienceniche market for your product. You know from your experience that an accurate assessment of the income of a typical family isthat an accurate assessment of the income of a typical family is crucial. The average income of this type of families in thecrucial. The average income of this type of families in the population is estimated by you to be Rs. 320000 based on figurespopulation is estimated by you to be Rs. 320000 based on figures obtained from a sample. In this example, average income based onobtained from a sample. In this example, average income based on sample is asample is a Point EstimatePoint Estimate of the population. The average incomeof the population. The average income that falls with in a statistically formed interval of 320000 pluthat falls with in a statistically formed interval of 320000 plus ors or minus 40000 is called anminus 40000 is called an Interval EstimateInterval Estimate. Any statement such. Any statement such as the average income in the population is more than Rs. 300000as the average income in the population is more than Rs. 300000 per year is aper year is a HypothesisHypothesis. As a manager, the interval estimate may. As a manager, the interval estimate may be much more important to you than the rest!be much more important to you than the rest! Caution: Inferential Statistics assumes that the samplingCaution: Inferential Statistics assumes that the sampling methodology is random (i.e. based on probability sampling)!methodology is random (i.e. based on probability sampling)!
13. 13. 5) Some Key Terms Used in Statistics PopulationPopulation is the collection of allis the collection of all possible observations of apossible observations of a specified characteristic of interest.specified characteristic of interest. An example is all the students inAn example is all the students in the Quantitative Methods coursethe Quantitative Methods course in an MBA program.in an MBA program. SampleSample is a subset of theis a subset of the population. Suppose you want topopulation. Suppose you want to select a team of 20 students fromselect a team of 20 students from 200 students in an MBA program200 students in an MBA program for participating in a managementfor participating in a management quiz. The total students 200 is thequiz. The total students 200 is the population. 20 students selectedpopulation. 20 students selected for the quiz is the sample.for the quiz is the sample. ParameterParameter is the populationis the population characteristic of interest. Forcharacteristic of interest. For example, you are interested in theexample, you are interested in the average income of a particular classaverage income of a particular class of people. The average income ofof people. The average income of this entire class of people is called athis entire class of people is called a parameter.parameter. StatisticStatistic is based on a sample tois based on a sample to make inferences about themake inferences about the population parameter. If you look atpopulation parameter. If you look at the previous example, the averagethe previous example, the average income in the population can beincome in the population can be estimated by the average incomeestimated by the average income based on the sample. This samplebased on the sample. This sample average is called a statistic.average is called a statistic.
14. 14. 6) Types of Data Qualitative DataQualitative Data are nonnumeric inare nonnumeric in nature and can't be measured.nature and can't be measured. Examples are gender, religion, andExamples are gender, religion, and place of birth.place of birth. Quantitative DataQuantitative Data are numerical inare numerical in nature and can be measured.nature and can be measured. Examples are balance in yourExamples are balance in your savings bank account, and numbersavings bank account, and number ofof members in your family.members in your family. Quantitative data can be classifiedQuantitative data can be classified into discrete type or continuousinto discrete type or continuous typetype.. Discrete typeDiscrete type can take onlycan take only certain values, and there arecertain values, and there are discontinuities between values,discontinuities between values, such as the number of rooms in asuch as the number of rooms in a hotel, which cannot be in fraction.hotel, which cannot be in fraction. Continuous typeContinuous type can take anycan take any value within a specific interval,value within a specific interval, such as the production quantity of asuch as the production quantity of a particular type of paper (measuredparticular type of paper (measured in kilograms).in kilograms).
15. 15. 7) Types of Data Measurements-Picture  NominalNominal  OrdinalOrdinal  IntervalInterval  RatioRatio InformationContentIncreases
16. 16. 7) Types of Data Measurements Nominal Data:Nominal Data: The weakest dataThe weakest data measurement. Numbers are used tomeasurement. Numbers are used to label an item or characteristic.label an item or characteristic. Categorization is the main purposeCategorization is the main purpose of this measurement. Examples: Aof this measurement. Examples: A business school may designatebusiness school may designate subject specialization by numbers,subject specialization by numbers, i.e., MBA in Finance =1, MBA ini.e., MBA in Finance =1, MBA in Systems = 2. Various brands ofSystems = 2. Various brands of toothpaste; savings bank accounttoothpaste; savings bank account numbers are other examples ofnumbers are other examples of nominal data. Note that nominalnominal data. Note that nominal data cannot be manipulated in adata cannot be manipulated in a numerical fashion.numerical fashion. Ordinal or Rank Data:Ordinal or Rank Data: NumbersNumbers are used to rank. An example isare used to rank. An example is Customer Preference for your brand.Customer Preference for your brand. An average preference is rated at 3,An average preference is rated at 3, a strong preference at 5. Simplea strong preference at 5. Simple arithmetic operations are notarithmetic operations are not possible for ordinal data. Ordinalpossible for ordinal data. Ordinal data can also be verbalized on adata can also be verbalized on a continuum like excellent, good, faircontinuum like excellent, good, fair and poor. In ordinal data, distanceand poor. In ordinal data, distance between objects cannot bebetween objects cannot be measured.measured.
17. 17. 7) Types of Data Measurements Continues Interval Data:Interval Data: If you have dataIf you have data with ordinal properties and can alsowith ordinal properties and can also measure the distance betweenmeasure the distance between objects, you have an intervalobjects, you have an interval measurement. Interval data aremeasurement. Interval data are superiorsuperior to ordinal data because,to ordinal data because, with them, decision makers canwith them, decision makers can measure the distances betweenmeasure the distances between objects. For example, frozenobjects. For example, frozen--foodfood distributors are concerned withdistributors are concerned with temperature, which is an intervaltemperature, which is an interval measurement. Interval data havemeasurement. Interval data have arbitrary zero point. Basicarbitrary zero point. Basic arithmetic operations are possiblearithmetic operations are possible with interval datawith interval data Ratio DataRatio Data:: It is the highest level ofIt is the highest level of measurement and allows you tomeasurement and allows you to perform all basic arithmeticperform all basic arithmetic operations, including division andoperations, including division and multiplication. Data measured on amultiplication. Data measured on a ratio scale have a fixed zero point.ratio scale have a fixed zero point. Examples include business data,Examples include business data, such as cost, revenue, market sharesuch as cost, revenue, market share and profit.and profit.