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Univariate StatisticsTopics for Next Four LecturesBasic Issues in StatisticsSlide 4Slide 5Slide 6Example: Training ProgramSlide 8Example: TurnoverWhat is Data?Slide 11Slide 12Slide 13Types of DataSlide 15Slide 16Summarizing DataSlide 18Slide 19Slide 20Slide 21Slide 22Measures of Central TendencyClass Age Data (Ordered)Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Measures of Central Tendency*DispersionSlide 36Slide 37Slide 38Slide 39Dispersion: PopulationSlide 41Slide 42Alternative Formula: VarianceSlide 44Standard DeviationProbability DistributionsProbability: TerminologyMore on Probability DistributionsProbability Distribution: Three CoinsExample: Charting Absences Over 30-Day PeriodSlide 51Slide 52Slide 53Probability Distributions: UniformSlide 55Slide 56Slide 57Slide 58Probability Distributions: PoissonSlide 60Slide 61Slide 62Slide 63Call Center ExampleSlide 65Probability Distributions: BinomialSlide 67Slide 68Slide 69Slide 70Slide 71Slide 72Probability Distributions: HazardSlide 74Probability Distributions: Continuous VariablesSlide 76Slide 77Slide 78Slide 79Slide 80Normal DistributionSlide 82Slide 83Slide 84Slide 85Slide 86Slide 87Slide 88Slide 89Slide 90Slide 91Slide 92Slide 93Slide 94Slide 95Slide 96Slide 97Slide 98Slide 99Slide 100Sampling Distributions / Central Limit TheoremSlide 102Samples and PopulationsSlide 104Slide 105Slide 106Slide 107Slide 108Slide 109Slide 110Slide 111Slide 112Slide 113Central Limit TheoremSlide 115Slide 116Slide 117Slide 118Slide 119Slide 120Slide 121Slide 122Slide 123Slide 124Slide 125Slide 126Slide 127Slide 128Slide 129Samples & PopulationsSlide 131Slide 132Slide 133Slide 134Slide 135Slide 136Slide 137Univariate StatisticsUnivariate StatisticsLIR 832Class #2September 15, 2008Topics for Next Four LecturesTopics for Next Four LecturesFundamental Problem in Statistics: Learning about populations from samplesDescribing Data Compactly: –How we might describe data, why compactness matters.–Measures of Central Tendency (what are they, when to use them)–Measures of dispersionProbability Distributions:–As samples are hopefully random draws from populations, we need to understand the likelihood of drawing samples. This leads us to a review of some basic probability distributions.Inference from Samples to Populations:–Sampling Distributions and the Central Limit Theorem–Estimation–Hypothesis TestingBasic Issues in StatisticsBasic Issues in StatisticsPopulations and Samples: Generally wish to know about populations–What is a population?–How do we count a population?–What types of populations would you be concerned with in your professional life?Basic Issues in StatisticsBasic Issues in StatisticsUse of Samples to Learn about PopulationsWhat is a sample?–representative sample–random sample–convenience sampleWhy use samples rather than populations?–less time consuming to collect–less expensive to collect–often more accurate than census–population may not exist at the time data is collectedBasic Issues in StatisticsBasic Issues in StatisticsSamples are affected by randomness, two samples drawn from a population are unlikely to be identical (sampling variability) and neither is an exact reproduction of the population.–What is meant by random?An event is random if, despite knowing all of the possible outcomes in advance, we are not able to exactly predict a particular outcome.experiment: M&M issueSamples are, to some degree, random –different samples produce different estimates–sample mean may be different than (but close to) population meanBasic Issues in StatisticsBasic Issues in StatisticsSince sample is not an exact reproduction of the population, we need to allow for sampling variability in using samples to tell us about populations.What types of HR/IR issues might involve the use of samples?Example: Training ProgramExample: Training ProgramWe are interested in a training program which is supposed to improve productivity. It would be very expensive to implement throughout a firm, particularly if it doesn’t work. Instead, we set up an experiment in which we try the program on a sample of employees at a single location (this may be called a pilot program).Example: Training ProgramExample: Training ProgramWe experiment with a pilot program and find that productivity rose by 2% Our problem in using the pilot (sample): if we replicate the pilot throughout the firm is it reasonable to believe that:–we will get a 2% boost in productivity, or –This could this just be the result of getting a “good” sample (Folks who happened to respond favorably to the program).Our core problem in using samples is distinguishing between systematic effects of programs and chance outcomesExample: TurnoverExample: TurnoverYou run human resources for a large low wage manufacturing plant. Your firm has established that there should be a 2.5% turnover rate per month and has a policy that turnover rates above 2.5% are evidence of ineffective human resource programs.You have kept your turnover rate at 2.4% per month for the last year and one half. Last month and this month that rate has shot up to 3.2%. Is this evidence that you are not doing your job as a human resource manager?What is Data?What is Data?Answer: The numeric representation of the characteristics of an individual, object or experiment.You, as an individual, provide multi-dimensional data:–Quantitative: AgeHeightYour pre-class views on LIR 832–Qualitative:GenderEducational AttainmentOccupation–Economic Data:IncomeDebtExpected Income on graduating from this program.What is Data?What is Data?You are multi-dimensional. We may be very interested in the relationship between your characteristics:–Gender and Educational Attainment with expected income–Blood pressure with ageData can also be collected on plants, establishments and firms as well as by political or geographic entity.–Firm: Revenue, Operating Costs, Debt to Equity Ratio, Number of Employees, Number of Locations, Distribution of Occupations, Presence of Program to Encourage Diversity in the Labor ForceWhat is Data?What is Data?We are typically interested in variables, data which vary across ‘individuals’ or ‘units of observation.–age, gender, income vary across individuals in this class–revenue, profit (and so much more) varies across divisions of General

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