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Msb14epptch01 (1)

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School
University of Vermont**We aren't endorsed by this school
Course
ANTH 253
Subject
Statistics
Date
Jan 14, 2025
Pages
76
Uploaded by HighnessPartridgeMaster1172
Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 1A LWAY S L E A R N I N GChapter 1Statistics, Data, and Statistical Thinking
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 2A LWAY S L E A R N I N GChapter 1 - Contents1.The Science of Statistics2.Types of Statistical Applications in Business3.Fundamental Elements of Statistics4.Types of Data5.Collecting Data: Sampling and Related Issues6.Business Analytics: Critical Thinking with Statistics
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 3A LWAY S L E A R N I N GWhere We’re Going 
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 4A LWAY S L E A R N I N G1.1The Science of Statistics
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 5A LWAY S L E A R N I N GWhat Is Statistics?Statisticsis the art and science of learning from data. It involves:•Collecting, organizing summarizing, analyzing, and interpreting information which may be:•quantitative (numeric) or •descriptive (words, like eye color). •The objective is to answer a question of interest which can be answered using data.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 6A LWAY S L E A R N I N GWhat business questions might we wish to answer? •Which of several products is a consumer more likely to purchase?•What is the estimated cost for replacement of products under warranty?•How does the average lifetime for a new composite material used in the manufacture of an artificial hip compare with the material currently in use?•What is the trend in hospital costs over the next 6 years?
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 7A LWAY S L E A R N I N G1.2Types of Statistical Applications in Business
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 8A LWAY S L E A R N I N GStatistics: Two Key Processes1)Describe data – typically using graphs, charts and summary metrics (like averages/medians etc.) 2)Draw conclusions (making estimates, decisions, predictions, etc. about the population of interest(entire collection) using a sample(a subset)
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 9A LWAY S L E A R N I N GStatistical MethodsStatisticalMethodsDescriptiveStatisticsInferentialStatisticsInferential Statistics is not always needed. If the data represents the entire population of study, inferences are not needed.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 10A LWAY S L E A R N I N GSimple Example •Suppose you want to know the proportion of yellow M & M’s in the bag of M & M’s you just bought. What is a proportion by the way??•You would simply count the yellow M & M’s and divide by the total. No inference is needed. •When might an inference be needed with regard to yellow M & M’s?
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 11A LWAY S L E A R N I N GDescriptive StatisticsDescriptive statistics - To summarize the information in a data set, and to present the information in a convenient form. •Involves graphs and charts; computations of important metrics, like average. •Consider this – Does your manager want to see a 10,000 line report that captures each individual part manufactured in the last 6 months and which country it was shipped to? Wouldn’t a simple graph be much more useful?
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 12A LWAY S L E A R N I N GInferential StatisticsInferential Statistics - Utilizes sampledata to make:•Estimates about population parameters (Parameter - A numeric value associated with the population, like population average) •Decisions, Predictions, or other generalizations about the population. •Ex: Whether two population proportions are equal; The proportion of votes Trump will receive vs. Harris. (Too close to call).
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 13A LWAY S L E A R N I N GSummary of what we have discussed•The field of Statistics relies on data. Without data we are not able to address the underlying question of interest using statistical methods. •If the data represents the entire collection, (the population) then no inferences are needed. We can simply summarize the data and report out. •If the data represents a sample (a subset) then we will need inferential statistics to allow us to make educated guesses regarding the entire population of interest.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 14A LWAY S L E A R N I N G1.3Fundamental Elementsof Statistics
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 15A LWAY S L E A R N I N GFundamental ElementsExperimental (or observational) unitObject upon which we collect data (like a person, or a company, or a country) If we conduct an experimentwe have experimental units. If we simply observe(which includes surveys), then we have observational units. •Population•The entire set of units (subjects) we are interested in studying•* Populations are not necessarily people in the world of Statistics
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 16A LWAY S L E A R N I N GFundamental Elements•Variable - •A characteristic of the unit of study.•Values change across units. Ex: height, gender •Sample•Consists of units that are a subset of the population units •Statistical Inference•To estimate or predict or generalize about a characteristic of the population using information from a sample•Estimating, predicting and generalizing carry some amount of uncertainty
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 17A LWAY S L E A R N I N GExample- Using a Sample to draw an inference for average age •FOX News hypothesizes (educated guess) that the averageage of FOX viewers is greater than 60. To test the hypothesis, a sample of 200 FOX viewers is used and the age of each viewer is obtained. a.Describe the population. b.Describe the variable of interest.c. Describe the sample.d. Describe the inference.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 18A LWAY S L E A R N I N GExample (cont)Solutiona. The population - All FOX viewers.b. The variable of interest - The age (in years) of each viewer is the variable of interest.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 19A LWAY S L E A R N I N GExample (cont)c. The sample – The 200 FOX viewers selected for the study.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 20A LWAY S L E A R N I N GExample (cont)d. Describe the inference.The inference – To generalizethe information contained in the sample of 200 viewers to the population of all FOX viewers. Based on the average age of the 200 viewers the researcher will infer whether it is likely the average age of the population (all Fox viewers) exceeds 60 years.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 21A LWAY S L E A R N I N GFundamental ElementsMeasure of Reliability•Statement (usually qualified) about the degree of uncertainty associated with a statistical inference. •Polling results for elections are often reported as Candidate X is projected to take 52% of the vote, with a margin of error of .5%;•The margin or error captures the uncertainty in the projected amount of 52%
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 22A LWAY S L E A R N I N GFour Elements of Descriptive Statistics1.Identifying the population of interest and whether a sample will be utilized2.Identifying one or more variables that are to be investigated3.Tables, graphs, or numerical summary tools4.Identification of patterns in the data5.If a sample was used it is possible and likely to continue with inferential statistics
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 23A LWAY S L E A R N I N GFive Elements of Inferential Statistics1.Identifying the population of interest2.Identifying one or more variables that are to be investigated3.Identifying the sample 4.Make an inference about the population based on information contained in the sample5.Establishing a measure of reliability for the inference (we often use the margin of error)
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 24A LWAY S L E A R N I N GExample•A fast-food restaurant has 6,289 outlets with drive-throughs. •Problem statement – Management wishes to attract more customers to its drive-through services, and is considering giving a 50% discount to customers who wait more than a specified number of minutes between the time they place the order and the time they get it. (I wonder if they did a cost/benefit analysis on this before deciding to discount at 50%) •To help determine what the time limit should be, they have decided to estimate the average waiting time at their drive-through window in Dallas, Texas.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 25A LWAY S L E A R N I N GExample•For 7 consecutive days, times are recorded using digital clocks.•At the end of the 7-day period, 2,109 orders had been timed.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 26A LWAY S L E A R N I N GExample (cont)a. Describe the process of interest at the Dallas restaurant.b. Describe the variable of interest.c. Describe the sample.d. Describe the inference of interest.e. Describe how the reliability of the inference could be measured.Solutiona. The process of interest is the drive-through window at the selected restaurant. It is a process because it “produces,” or “generates,” meals over time—that is, it services customers over time.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 27A LWAY S L E A R N I N GExample (cont)b. Describe the variable of interest.The variable is customer wait timec. Describe the sample.The sample consists of the 2,109 orders that were processed through the drive-through during the 7-day period at a particular location (Dallas, TX).
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 28A LWAY S L E A R N I N GExample (cont)d. Describe the inference of interest.•The company’s immediate interest is in learning about the drive-through window in Dallas.•i.e. to estimate the average waiting time at the Dallas facility using the sample average.•They may also use this to estimate the average wait time at all their locations, although this would not be a good statistical strategy. i.e. It would not be wise to randomly select only one of over 6,000 locations to make an inference about all 6,000 locations.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 29A LWAY S L E A R N I N GExample (cont)e. Describe how the reliability of the inference could be measured.At this point in the book we are not at a position to discuss how reliability is actually computed. Suppose we found that the average waiting time is 4.2 minutes, with a bound on the error of estimation of 0.5 minutes. We could then be reasonably certain that the true average waiting time for the Dallas process is between 3.7 and 4.7 minutes. (Notice how we added and subtracted the error of estimation (.5 minutes) from the average wait time of 4.2 minutes. )
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 30A LWAY S L E A R N I N GSummary of the Fundamental Elements of Statistics •Samples and populations play key roles in Statistics. You will work with either a sample or the entire population, when conducting a statistical study. •Every statistical question focuses on some population.•The major areas of Statistics are:•Descriptive Statistics (Summarize, organize, graph)•Inferential Statistics (Samples do not provide the complete picture. We must make inferences back to the population when working with a sample. )•Variables are associated with a population or sample unit. Every statistical study involves variable(s). •When making an inference, we include a level of reliability to provide insight on how far off our estimate might be.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 31A LWAY S L E A R N I N G1.5Types of Data
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 32A LWAY S L E A R N I N GTypes of DataQuantitative data:•True numbers (not like social security numbers or phone numbers but numbers that can be mathematically manipulated).•Often measurements or counts.Qualitative data•Descriptive data, like gender, hair color.•This data isclassified into one of a group of categories, for instance defect type is a possible category.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 33A LWAY S L E A R N I N GTypes of Data- all data is either quantitative or qualitative Types ofDataQuantitativeDataQualitativeData
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 34A LWAY S L E A R N I N GQuantitative Data ExamplesMeasured on a numerical scale.1.Temperature - The temperature at which each piece of heat-resistant plastic begins to melt in a sample of 202.Unemployment rate - The current unemployment rate (measured as a percentage) for your state of residence 3.GMAT Scores - The scores of a sample of 150 MBA applicants who took the GMAT exam4.Female employee count - The number of female executives in each of a sample of 75 manufacturing companies
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 35A LWAY S L E A R N I N GQualitative DataClassified into categories.1.Political Party - The political party affiliation (Democrat, Republican, or Independent) in a sample of 50 CEOs2.Defective Status - The defective status (defective or not) of each of 100 Intel computer chips3.Car Size - The size of a car (subcompact, compact, midsize, or full-size) rented by each of a sample of 30 business travelers4.A taste tester’s ranking - (best, worst, etc.) of four brands of barbecue sauce for a panel of 10 testers
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 36A LWAY S L E A R N I N GQualitative DataIs it possible for Car Size to become a numeric variable? Yes. If we think of it in terms of weight, or length, then the variable becomes numeric.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 37A LWAY S L E A R N I N GExample•Manufacturing plants sometimes discharge toxic-waste materials such as DDT into nearby rivers and streams. (My note – DDT was banned in the US in 1972 however it is a persistent environmental pollutant and may linger in the environment).•These toxins can adversely affect plants and animals living in that area. •A study of fish in the Tennessee River (in Alabama) and its three tributary creeks: Flint Creek, Limestone Creek, and Spring Creek was conducted.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 38A LWAY S L E A R N I N GExample•A total of 144 fish were captured•What do you think is the research question?•Is the 144 fish a sample or a population? •What is the unit in this study? The following variables were reported for each fish : (continued on next slide)
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 39A LWAY S L E A R N I N GExample (cont)1. River/creek where each fish was captured2. Species (channel catfish, largemouth bass, or smallmouth buffalo fish)3. Length (centimeters)4. Weight (grams)5. DDT concentration (parts per million)These data are saved in the DDT file. Classify each of the five variables measured as quantitative or qualitative.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 40A LWAY S L E A R N I N GExample (cont)SolutionQuantitative variables – LengthWeightDDT concentration Qualitative variables – river/creekspeciesPossible research question – What is the average concentration of DDT by species, in each river, where the 144 fish represent a sample. Each fish is a unit.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 41A LWAY S L E A R N I N GSummary of Data TypesData comes in two flavors:•Quantitative(numbers that can be mathematically manipulated •Think about it - there is no meaningful definition of an ‘average social security number but your average grade in this class does have meaning •Qualitative– Consists of categories, like eye color, stages of a disease, mood (happy/sad)
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 42A LWAY S L E A R N I N G1.6Collecting Data – Data Collection strategies
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 43A LWAY S L E A R N I N GHow do we obtain Data1.Obtain data from a published source2.Obtain Data from running a designed experiment3.Obtain Data using a survey 4.Obtain Data from conducting an observational study
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 44A LWAY S L E A R N I N GObtaining Data1. Published sources include: Books, journals, newspapers, & Web sites Some popular social survey web sites include:•General Social Survey (GSS)Contains a core set of demographic, behavioral, and attitudinal questions, as well as topics of special interest. Many of the core questions have remained unchanged since 1972, which allows for time-trend studies and replication of earlier findings.•Data.govProvides public access to machine-readable datasets generated by the Executive Branch of the Federal Government.•Harvard DataverseA searchable and downloadable repository for research data on many subjects.Pew Research CenterA popular platform for gathering data through polls and surveys, primarily
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 45A LWAY S L E A R N I N GObtaining Data•Pew Research CenterA popular platform for gathering data through polls and surveys, primarily focusing on politics, demographics, trends, and social issues.•International Social Survey Programme (ISSP)A cross-national survey program that conducts annual surveys in a broad group of countries, asking questions on a variety of topics.•National Center for Education Statistics (NCHS)Contains much data on various health indicators at both national and state levels, including public-use microdata from surveys such as the National Health Interview
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 46A LWAY S L E A R N I N GObtaining Data2. Designed experimentResearcher applies a ‘treatment’ to units in the treatment group, and often uses a placebo with the control group. Randomization ensures both groups are well balanced across all other variables (What are they talking about??) 3. SurveyA group of people are surveyed and their responses are recorded4. Observation studyUnits are observed in natural setting and variables of interest are recorded – For instance observing second graders in their classroom
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 47A LWAY S L E A R N I N GDesigned ExperimentIn a designed experiment we typically have a group of experimental units that are assigned the treatment and an untreated (or control) group.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 48A LWAY S L E A R N I N GObservational StudyAn observational study is a data-collection method where the experimental units sampled are observed in their natural setting. No attempt is made to control the characteristics of the experimental units sampled. (Examples include opinion polls and surveys.)
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 49A LWAY S L E A R N I N GSummary of Data Collection Strategies •Using existing data sources•Conducting a designed experiment•Conducting an observational study•Utilizing a survey •Bottom Line – Any statistical study requires data, how you obtain it depends on:•The research question and what data is currently available
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 50A LWAY S L E A R N I N GTypes of SamplesBefore discussing the types of Samples that are possible, we should ask:“WHY DO WE NEED TO SAMPLE?”•When it is not possible to work with the entire population, often for one or more of the following reasons:•Population is too large•The costs are prohibitive•Too time consuming•The entire population is not easily accessible •It would be too dangerous (consider a new drug or vaccine)
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 51A LWAY S L E A R N I N GTypes of SamplesA representative sampleexhibits characteristics typical of those possessed by the population of interest. A biasedsample DOES NOT Our goal should always be to obtain a representative sample. Consider a study of all COVID patients. You select a sample with only adults whose BMI is greater than 30. This is clearly a biased sample as there are many individuals in the population with BMI’s less than 30.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 52A LWAY S L E A R N I N GTypes of Random Samples – Simple Random SampleI. Simple random sample - A simple random sample of n(where n represents some positive integer value like 500) experimental units is a sample selected from the population in such a way that:•Every different sample of size n is equally likely to be selected. •Note - This is the theoretical definition of a simple random sample. It is almost impossible to select the sample in such a way to ensure this.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 53A LWAY S L E A R N I N GRandom Number Generators can be useful when selecting simple random samples •Researchers often rely on random number generatorsto generate the numbers that will be used to select the random sample.•Most software packages and calculators have this feature•Notice this assumesyou are able to obtain a list of the population, that is sequentially numbered.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 54A LWAY S L E A R N I N GExampleProblem Statement – You wish to assess the feasibility of building a new high school and wish to gauge the opinions of people living close to the proposed building site. The neighborhood adjacent to the site has 711 homes. Use a random number generator to select a simple random sample of 20 households from the neighborhood to participate in the study
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 55A LWAY S L E A R N I N GExample (cont)SolutionThe population consists of the 711 households. To obtain a simple random sample we can use Excel:•Assign a number from 1 to 711 to each of the households in the population. These numbers are entered into an Excel worksheet. •Next apply the random number generator of Excel or XLSTAT (statistical software package for Excel), requesting that 20 households be selected without replacement (meaning you cannot be given the same value twice). One possible set of random numbers generated is 40, 63, 108, . . . , 636 and these are the households to be included in your sample.•The Excel command would be:•=RANDARRAY(1,20,1,711,TRUE)
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 56A LWAY S L E A R N I N GImportance of SelectionHow well a sample is selected from a population is of vital importance in statistical inferenceas the sample will be used to infer the characteristics of the associated population.Suppose you selected the men’s basketball team at NCSU as your sample to make an inference of average male undergraduate height.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 57A LWAY S L E A R N I N GTypes of Random Samples – Stratified Random Sample2. Stratified random sampling- used when:•The experimental units can be separated into groups that are thought to respond differently to the research question AND•It is important that their proportion in the sample mirrors that in the populationExample– Testing a COVID vaccine in adults. Elderly often have a suppressed immune response which may affect vaccine efficacy. If 25% of the population is “elderly”, we would like the sample to reflect that. Using a simple random sample may not achieve that target but stratified sampling will.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 58A LWAY S L E A R N I N GTypes of Random Samples – Stratified Random Sample contd. •Key challenge – Obtaining a reasonable approximation regarding the proportion of each group within the population of interest.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 59A LWAY S L E A R N I N GTypes of Random Samples – Cluster sample3. Cluster sampling– Designed to save time and money, but the results will not be as accurate as a simple random sample or a stratified sample. This methodology can be used when: •The population can be grouped into clusters, where each cluster resembles the underlying population. •The researcher will randomly select one or more clusters and and collect data from all experimental units within each cluster
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 60A LWAY S L E A R N I N GTypes of Random Samples – Systematic Sample4. Systematic sampling- systematically selects every kth experimental unit, typically from a list of all experimental units. •This is often used when sampling from an assembly line. (Clearly there is no official list of all experimental units in this scenario).
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 61A LWAY S L E A R N I N GNonrandom Sample ErrorsSelection biasresults when a subset of the experimental units in the population is excluded so that these units have no chance of being selected for the sample.Nonresponse biasresults when the researchers conducting a survey or study are unable to obtain data on all experimental units selected for the sample but continue with the study anyways.Measurement errorrefers to inaccuracies in the values of the data recorded. In surveys, the error may be due to ambiguous or leading questions and the interviewer’s effect on the respondent.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 62A LWAY S L E A R N I N GExample•Mobile Marketer hopes to find out what is the most popular device used by online shoppers. •They hire the mobile video ad network AdColony to conduct a nationwide survey of 1,000 US online shoppers. •The most popular device a smartphone, used by 56% of the online shoppers. 28% used a desktop or laptop computer, and 16% used a tablet.a. Identify the data-collection method.b. Identify the target population.c. Are the sample data representative of the population?
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 63A LWAY S L E A R N I N GExample (cont)Solutiona.Identify the data-collection method.The data-collection method is a survey: 1,000 US online shoppers participated in the study.b. Identify the target population.Presumably, Mobile Marketer is interested in the devices used by all US online shoppers. Consequently, the target population is all USconsumers who use the Internet for online shopping.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 64A LWAY S L E A R N I N GExample (cont)c.Are the sample data representative of the population?Because the 1,000 respondents clearly make up a subset of the target population, they do form a sample, but is it representative of the population? It is not clear how the sample was obtained. If the respondents were obtained using, say, random-digit telephone dialing, then the sample is likely to be representative because it is a random sample.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 65A LWAY S L E A R N I N GExample (cont)However, if the questionnaire was made available to anyone surfing the Internet, then the respondents are self-selected, also known as a volunteer sample. Such a survey often suffers from nonresponse bias. i.e. Those who chose not to respond or who never saw the questionnaire might have answered the questions differently, leading to a lower (or higher) sample percentage.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 66A LWAY S L E A R N I N GSummary of Types of Random Samples•Simple Random Sample – Facilitated through the use of a random number generator; each possible sample has the same chance of being selected •Cluster Sample – When the population can be broken down into sub-groups (clusters) that are representative of the population. The researcher will select one or more clusters and collect data from each unit. •Stratified Sample – When the research question may be sensitive to the response of different subgroups within the population. Requires knowledge of the proportion associated with each sub-group.•Systematic sample – Often used in manufacturing where we sample every kth unit from a list or assembly line
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 67A LWAY S L E A R N I N GSummary of NonRandom sample errors•Selection Bias – Excluding some subset of the population from the sampling process. This subset will then have no representation in the sample. •Non Response Bias – some of the units selected for the sample are unwilling to provide responses. The sample becomes biased •Measurement Error – Inaccuracies in the values recorded Could be related to how the question was worded, or a simple transcription error, or a question the participant does not want to answer truthfully. This will result in bias in the sample. Very difficult to quantify in terms of its magnitude •
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 68A LWAY S L E A R N I N G1.7Critical Thinking with Statistics
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 69A LWAY S L E A R N I N GStatistical ThinkingBusiness analytics refers to methodologies (e.g. statistical methods) that extract useful information from data in order to make better business decisions.Statistical thinkinginvolves applying rational thought and the science of statistics to critically assess data and inferences. Fundamental to the thought process is that variationexists in populations and process data.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 70A LWAY S L E A R N I N GStatistics in Business AnalyticsA good analyst must be able to reformulate the business problem into a statistical question
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 71A LWAY S L E A R N I N GKey IdeasTypes of Statistical Applications – Descriptive and Inferential Descriptive Statistics involves - 1. Identify populationand sample(collection of experimental units)2. Identify variable(s)3. Collect data4.Describe data
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 72A LWAY S L E A R N I N GKey IdeasTypes of Statistical ApplicationsInferential Statistics involves 1. Identify population(i.e. describe the collection of all experimentalunits of interest) 2. Identify variable(s)3. Collect sample data (subsetof population)4.Inference about population based on sample5. Measure of reliabilityfor inference
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 73A LWAY S L E A R N I N GKey IdeasTypes of Data1. Quantitative(numerical in nature)2.Qualitative(categorical in nature)
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 74A LWAY S L E A R N I N GKey IdeasData-Collection Methods1. Observational (e.g. survey)2.Published source3.Designed experiment
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 75A LWAY S L E A R N I N GKey IdeasTypes of Random Samples1. Simple Random Sample2.Stratified random sample3. Cluster sample4.Systematic sample.
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Copyright © 2022, 2018, and 2014 Pearson Education, Inc.Slide - 76A LWAY S L E A R N I N GKey IdeasProblems with Nonrandom Samples1. Selection bias – If you deliberately exclude a specific subset of the population from the sampling process the sample is no longer random. 2.Nonresponse bias – If the manner in which the survey is made available can result in certain sub-groups having reduced participation the sample is no longer random3.Measurement error – Results from multiple conditions, including misleading/ambiguous questions,
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