Stats 11 (Fall 2004) Lecture Note Instructor: Hongquan XuIntroduction to Statistical Methods for Business and EconomicsChapter 1: What is Statistics?• Statistics is the science of DATA.• Statistics deals with the collection, organization and interpretation of data.• Course Goal: Learn various tools for using data to gain understanding and make sound decisions.The Subject of Statistics (Section 1.4)Statistics is concerned with the process of finding out about the world and how it operates in the face ofvariation and uncertainty by collecting and then making sense of data.The investigative process(a) Real problem: Who will be the next US President?(b) Question: Who do you vote for the President: Bush or Kerry?(c) Design method of data collection:(d) Collect data:(e) Summary and analysis of data:(f) Answers to original questions:Example: US Presidential Race 2004An in-class poll: Bush Kerry1Bush KerryIn-class pollABC/PostCBS/NYTimesCNN/USA/GallupWhich one do you trust? Why?Three fundamental kinds of statistical investigations• sampling or surveys (Section 1.1)• experiments (Section 1.2)• observational studies (Section 1.3)Section 1.1 Polls and SurveysSurveys study part to gain information about the whole.Jargon describing surveys• Target population: complete set of individuals, objects, or units that we want to information about.• Study p opulation: complete s et of units that might possibly be included in the study.• Sample: subset of units about which we actually collect info.• Census: attempt to study every individual in the entire population.• Variable: a characteristic of each unit that we measure.• Parameter: a numerical characteristic of the population• Statistic: a numerical characteristic of the sample.A census often takes a long time and is expensive.A carefully conducted survey is often more than a census.Often we don’t know the population parameter and want to it.We take a sample, compute the sample statistic and use it to the p opulation parameter.Random samplingDraw units from the study population at random, e.g., using a lottery. Every subject in the study populationhas some chance to be selected.• simple random sample (SRS): every individual has equal chance to be selected.• cluster sampling: a cluster of individuals are used as a sampling unit, rather than individuals.2• stratified sampling: divide the population into strata (groups of similar individuals) and choose a SRSfrom each strata.• multi-stage sampling: a combination of SRS, cluster sampling and stratified sampling.Why do we sample at random?• To avoid subjective and other .• To allow the calculation of (i.e., the likely size of the error in our sample estimates).Sources of error in surveys• Random sampling leads to sampling errors.• Nonsampling errors can be much larger than the sampling errors.The chance errors in survey estimates are generally smaller if we take samples.Sources of nonsampling errors• Selection bias: Arises when the population sampled is not exactly the population of interest.• Self-selection: People themselves decide whether or not to be surveyed. Results akin to severe non-response.• Non-response bias: Non-respondents often behave or think differently from respondents. Low responserates can lead to huge biases.• Question wording effects: Even slight differences in question wording can produce measurable differ-ences in how people respond.• Interviewer effects: Different interviewers asking the same questions can tend to obtain different an-swers.• Survey format effects: Factors such as question order, questionnaire layout, self-administered question-naire or interviewer, can effect the results.Dealing with errors• Statistical methods are available for estimating the likely size of errors.• All we can do with nonsampling errors is to try to minimize them at the stage.• Pilot survey: One tests a survey on a relatively small group of people to try to identify any problemswith the survey design b e fore conducting the survey properly.Some questions for thinking:Q: Why are many magazine surve ys s uspec t?A:Q: Is interviewing p e ople at random on the street a good survey? Why?A:3US Presidential Race 2004Source: http://news.bbc.co.uk/ and http://www.electoral-vote.com/Which one do you trust? Why?On September 17, 2004, the CNN/USA/Gallup Poll shows Bush (55%) and Kerry (42%) amongst likelyvoters. Read an interesting article about this poll:“Why You Should Ignore The Gallup Poll This Morning – And Maybe Other Gallup Polls As Well?”at http://www.theleftcoaster.com/archives/002806.html4Section 1.2 ExperimentationExperiments deliberately impose some treatment on individuals in order to observe their response.Principles of Experimental Design• Blocking: group or match homogenous experimental units.• Randomization: use chance to assign experimental units to treatments.• Replication: apply treatments to many experimental units.Blocking ensures comparisons with respect to factors known to be important. Random-ization tries to obtain comparability with respect to factors and allows the calculation ofestimation error.Example: Typing efficiency of two keyboards: A and B. Experiment: Six different manuscripts are randomlyassigned to numbers 1–6 and given to the same typist. Each manuscript is first typed on keyboard A thenon keyboard B in the following order:1. A, B, 2. A, B, 3. A, B, 4. A, B, 5. A, B, 6. A, B.How are the principles used?• Blocking:• Randomization:• Replication:What are the strength and weakness of this design?Consider another design:1. A, B, 2. B, A, 3. A, B, 4. B, A, 5. A, B, 6. A, B.Any weakness?Consider a third design:1. A, B, 2. A, B, 3. A, B, 4. B, A, 5. B, A, 6. B, A.Any weakness?What design do you rec omme nd?A good advice is: what you can and what you cannot.5Jargon describing experiments• Control group: group of experimental units that is given no treatment. Treatment effect is estimatedby comparing each treatment group with control group• Blinding: Preventing people involved in expe riment from knowing which experimental subjects havereceived which treatment. One may b e able to blind subjects themselves, people administering thetreatments, people measuring the results.• Double blind: Both the subjects and those administering the treatments have been blinded.• Placebo: An inert dummy treatment.• Placebo effect: Response caused in human subjects by the idea that they are being