What Is Statistics - University of Texas at Dallas

1 What is Statistic?OPRE 6301In today s world.. we are constantly being bombarded with Statistics andstatistical information. For example:Customer SurveysMedical NewsDemographicsPolitical PollsEconomic PredictionsMarketing InformationSales ForecastsStock Market ProjectionsConsumer Price IndexSports StatisticsHow can we make sense out of all this data?How do we differentiate valid from flawed claims?1 What is Statistics ?! Statistics is a way to get information from data. DataStatisticsInformationData:Facts, especially numerical facts, collected together for reference or :Knowledge communicated concerning some particular is atoolfor creating anunderstandingfrom aset of Definitions:The Science of drawing a precise line between an unwar-ranted assumption and a forgone Science of stating precisely what you don t Example: Stats Anxiety.

2 A business school student is anxious about their statisticscourse, since they ve heard the course is difficult. Theprofessor provides last term s final exam marks to thestudent. What can be discerned from this list of numbers?DataStatisticsInformationList of last term s :New information about the Statistics Class average,Proportion of class receiving A sMost frequent mark,Marks distribution, Statistical Concepts..Population a population is the group ofallitems of interest to astatistics practitioner. frequently very large; sometimes All 5 million Florida voters (per Example ).Sample A sample is a set of data drawn from the population.

3 Potentially very large, but less than the a sample of 765 voters exit polled on election A descriptive measure of A descriptive measure of , we have..Populations have Parameters,Samples have Statistics .. aremethodsof organizing, summarizing, and present-ing data in a convenient and informative way. Thesemethods include:Graphical Techniques (Chapter 2), andNumerical Techniques (Chapter 4).The actual method used depends on whatinformationwe would like to extract. Are we interested in..measure(s) of central location? and/ormeasure(s) of variability (dispersion)?Descriptive Statistics helps to answer these questions.

4 6 Inferential Statistics ..Descriptive Statistics describe the data set that s beinganalyzed, but doesn t allow us to draw any conclusionsor make any interferences about the data. Hence we needanother branch of Statistics :inferential Statistics is also a set of methods, but it is usedto draw conclusions or inferences about characteristics ofpopulationsbased on data from Inference..Statistical inference is the process of making an estimate,prediction, or decision about a population based on can weinferabout a Population s Parametersbased on a Sample s Statistics ?8We usestatisticsto make inferences , we can make an estimate, prediction, or deci-sion about apopulationbased , we can apply what we know about a sample to thelarger population from which it was drawn!

5 Rationale:Large populations make investigating each member im-practical and and cheaper to take a sample and make estimatesabout the population from the :Such conclusions and estimates arenotalways going tobe correct. For this reason, we build into the statisti-cal inference measures of reliability, namelyconfi-dence levelandsignificance and Significance Levels..Theconfidence levelis the proportion of times that anestimating procedure will be a confidence level of 95% means that, estimatesbased on this form of statistical inference will be cor-rect 95% of the the purpose of the statistical inference is to drawa conclusion about a population, thesignificance levelmeasures how frequently the conclusion will be wrong inthe long a 5% significance level means that, in the long run,this type of conclusion will be wrong 5% of the we use (Greek letter alpha ) to represent signifi-cance, then our confidence level is 1.

6 This relationship can also be stated as:Confidence Level + Significance Level = 1 Consider a statement from polling data you may hearabout in the news: This poll is considered accurate within percentagepoints, 19 times out of 20. In this case, our confidence level is 95% (19/20 = ),while our significance level is 5%.11 Examples of Business Problems..Accounting: An auditor is interested in the costs of business travelOrganization Behavior: A manager is interested in why turnover ofemployees seems to have increasedMarketing: Your firm wishes to expand its product line and deter-mine which products are of interest to consumersFinance: The CEO wishes to understand what factors are affectingthe firm s stock priceEconomics: Your firm is interested in the status of the economy overthe next yearOperations Research/Management: Store managers have beenre-porting increased waiting lines at checkout countersManagement Information Systems.

7 You are contemplating replacingyour financial reporting systemInternational Management: You are interested in expanding yourfirm s services to a non-US market12