Presentation on theme: "BCOR 1020 Business Statistics"— Presentation transcript:
1BCOR 1020 Business Statistics Lecture 2 – January 17, 2008
2Overview Chapter 2 – Data Collection… Key Definitions Level of MeasurementTime Series vs. Cross-Sectional DataSampling ConceptsSampling MethodsData SourcesSurvey Research
3Chapter 2 – Key Definitions Data is the plural form of the Latin datum (a “given” fact).In scientific research, data arise from experiments whose results are recorded systematically.In business, data usually arise from accounting transactions or management processes.Important decisions may depend on data.We will refer to Data as plural and data set as a particular collection of data as a whole.Observation – each data value.Subject (or individual) – an item for study (e.g., an employee in your company).Variable – a characteristic about the subject or individual (e.g., employee’s income).
4Chapter 2 – Key Definitions Three types of data sets:Data SetVariablesTypical TasksUnivariateOneHistograms, descriptive statistics, frequency tallies, estimation, hypothesis testingBivariateTwoScatter plots, correlations, simple regressionMultivariateMore than twoMultiple regression, data mining, econometric modeling
5Chapter 2 – Key Definitions Consider the multivariate data set with5 variables8 subjects5 x 8 = 40 observationsMultivariate data sets can become quite large.
6Chapter 2 – Key Definitions A data set may have a mixture of data types.Types of DataAttribute (qualitative)Numerical (quantitative)Verbal Label X = economics (your major)Coded X = 3 (i.e., economics)Discrete X = 2 (your siblings)Continuous X = 3.15 (your GPA)
7Chapter 2 – Key Definitions Attribute Data:Also called categorical, nominal or qualitative data.Values are described by words rather than numbers.For example, - Automobile style (e.g., X = full, midsize, compact, subcompact). - Mutual fund (e.g., X = load, no-load).Data Coding:Coding refers to using numbers to represent categories to facilitate statistical analysis. (We need numerical representations to perform the math.)Coding an attribute as a number does not make the data numerical.For example, 1 = Bachelor’s, 2 = Master’s, 3 = DoctorateRankings may exist (consider the above example)
8Chapter 2 – Key Definitions Binary Data – An Important Class of Attribute Data:A binary variable has only two values, 1 = presence, 0 = absence of a characteristic of interest (codes themselves are arbitrary).For example, 1 = employed, 0 = not employed 1 = married, 0 = not married 1 = male, 0 = female 1 = female, 0 = maleThe coding itself has no numerical value so binary variables are attribute data.
9Chapter 2 – Key Definitions Numerical Data – Numerical or quantitative dataarise from counting, measurement or some kind ofmathematical operation.For example,Number of auto insurance claims filed in March.Length of time between customer arrivals on a webpage.Ratio of profit to sales for last quarter.Can be broken down into two types – discrete or continuous data.
10Chapter 2 – Key Definitions Discrete Data – A numerical variable with acountable number of values that can be representedby an integer (no fractional values).For example,Number of Medicaid patients (e.g., X = 2).Number of takeoffs at O’Hare (e.g., X = 37).Continuous Data – A numerical variable that canhave any value within an interval (e.g., length,weight, time, sales, price/earnings ratios).Any continuous interval contains infinitely many possible values (e.g., 426 < X < 428).
11Clickers What type of data (attribute, discrete numerical, or continuous numerical) is yourGPA?A = attributeB = discrete numericalC = continuous numerical
12Clickers What type of data (attribute, discrete numerical, or continuous numerical) is theoccupation of a mortgage applicant?A = attributeB = discrete numericalC = continuous numerical
13Chapter 2 – Level of Measurement There are four levels of measurement for data:Level of MeasurementCharacteristicsExampleNominalCategories onlyEye color (blue, brown, green, hazel)OrdinalRank has meaningBond ratings (Aaa, Aab, C, D, F, etc.)IntervalDistance has meaningTemperature (57o Celsius)RatioMeaningful zero existsAccounts payable ($21.7 million)
14Chapter 2 – Level of Measurement Nominal Measurement – Nominal data merely identify acategory. Nominal data are qualitative, attribute, categoricalor classification data (e.g., Apple, Compaq, Dell, HP).Nominal data are usually coded numerically, codes are arbitrary (e.g., 1 = Apple, 2 = Compaq, 3 = Dell, 4 = HP).Only mathematical operations are counting (e.g., frequencies) and simple statistics.Ordinal Measurement – Ordinal data codes can be ranked(e.g., 1 = Frequently, 2 = Sometimes, 3 = Rarely, 4 = Never).Distance between codes is not meaningful (e.g., distance between 1 and 2, or between 2 and 3, or between 3 and 4 lacks meaning).Many useful statistical tests exist for ordinal data. Especially useful in social science, marketing and human resource research.
15Chapter 2 – Level of Measurement Interval Measurement – Data can not only be ranked, butalso have meaningful intervals between scale points (e.g.,difference between 60F and 70F is same as differencebetween 20F and 30F).Since intervals between numbers represent distances, mathematical operations can be performed (e.g., average).Zero point of interval scales is arbitrary, so ratios are not meaningful (e.g., 60F is not twice as warm as 30F).
16Chapter 2 – Level of Measurement Likert Scales – A special case of interval (?) datafrequently used in survey research.The coarseness of a Likert scale refers to the number of scale points (typically 5 or 7).A neutral midpoint (“Neither Agree Nor Disagree”) is allowed if an odd number of scale points is used or omitted to force the respondent to “lean” one way or the other.Likert data are coded numerically (e.g., 1 to 5) but any equally spaced values will work.Careful choice of verbal anchors results in measurable intervals (e.g., the distance from 1 to 2 is “the same” as the interval, say, from 3 to 4).Ratios are not meaningful (e.g., here 4 is not twice 2).Many statistical calculations can be performed (e.g., averages, correlations, etc.).
17Chapter 2 – Level of Measurement Likert Scales – ExampleTwo variants of Likert scales…How would you rate your marketing instructor? (check one) Terrible Poor Adequate Good ExcellentHow would you rate your marketing instructor? (check one)Very BadVery Good
18Chapter 2 – Level of Measurement Ratio Measurement – Ratio data have all properties ofnominal, ordinal and interval data types and also possess ameaningful zero (absence of quantity being measured).Because of this zero point, ratios of data values are meaningful (e.g., $20 million profit is twice as much as $10 million).Zero does not have to be observable in the data, it is an absolute reference point.Changing Data by Recoding – In order to simplify data orwhen exact data magnitude is of little interest, ratio data canbe recoded downward into ordinal or nominal measurements(but not conversely).For example, recode systolic blood pressure as “normal” (under 130), “elevated” (130 to 140), or “high” (over 140).The above recoded data are ordinal (ranking is preserved) but intervals are unequal and some information is lost.
19Chapter 2 – Level of Measurement Use the following procedure to recognize data types:QuestionIf “Yes”Q1. Is there a meaningful zero point?Ratio data (all statistical operations are allowed)Q2. Are intervals between scale points meaningful?Interval data (common statistics allowed, e.g., means and standard deviations)Q3. Do scale points represent rankings?Ordinal data (restricted to certain types of nonparametric statistical tests)Q4. Are there discrete categories?Nominal data (only counting allowed, e.g. finding the mode)
20Clickers Which type of data (nominal, ordinal, interval, or ratio) is the pay of employeesin the Wal-Mart store in Hutchinson Kansas?A = nominalB = ordinalC = intervalD = ratio
21Chapter 2 – Time Series & Cross-Sectional Data Time Series Data – Each observation in the samplerepresents a different equally spaced point in time (e.g.,years, months, days).Periodicity may be annual, quarterly, monthly, weekly, daily, hourly, etc.We are interested in trends and patterns over time (e.g., annual growth in consumer debit card use from 1999 to 2006).Cross-sectional Data – Each observation represents adifferent individual unit (e.g., person) at the same point intime (e.g., monthly VISA balances).We are interested in variation among observations or in relationships.We can combine the two data types to get pooled cross-sectional and time series data.
22Clickers Which type of data (time series or cross- sectional) is Mexico’s GDP for the last 10quarters?A = time seriesB = cross-sectional
23Chapter 2 – Sampling Concepts Sample or Census?A sample involves looking only at some items selected from the population.A census is an examination of all items in a defined population.Why collect a sample rather than complete a census?
24Chapter 2 – Sampling Concepts Situations Where A Sample May Be Preferred:Infinite Population – Destructive TestingTimely Results – CostAccuracy – Sensitive InformationSituations Where A Census May Be Preferred:Small Population – Large Sample SizeDatabase Exists – Legal Requirements
25Chapter 2 – Sampling Concepts Parameters and Statistics:Parameters – Any measurement that describes an entire population. Usually, the parameter value is unknown since we rarely can observe the entire population. Parameters are often (but not always) represented by Greek letters.Statistics – Any measurement computed from a sample. Usually, the statistic is regarded as an estimate of a population parameter. Sample statistics are often (but not always) represented by Roman letters.Sample (Size = n):Statistics are computed and estimate parameterse.g., = sample mean, S = sample std. dev.Population (Size = N):Characterized by Parameterse.g., m = pop. Mean, s = pop. Std. dev.
26Chapter 2 – Sampling Concepts Population – The population must be carefully specifiedand the sample must be drawn scientifically so that thesample is representative.Target Population:The target population is the population we are interested in (e.g., U.S. gasoline prices).The sampling frame is the group from which we take the sample (e.g., 115,000 stations).The frame should not differ from the target population.Finite or Infinite?A population is finite if it has a definite size, even if its size is unknown.A population is infinite if it is of arbitrarily large size.Rule of Thumb: A population may be treated as infinite when N is at least 20 times n (i.e., when N/n > 20).
27Chapter 2 – Sampling Methods Probability Samples:Simple Random Sample – Use random numbers to select items from a list (e.g., VISA cardholders).Systematic Sample – Select every kth item from a list or sequence (e.g., restaurant customers).Stratified Sample – Select randomly within defined strata (e.g., by age, occupation, gender).Cluster Sample – Like stratified sampling except strata are geographical areas (e.g., zip codes).Nonprobability Samples:Judgment Sample – Use expert knowledge to choose “typical” items (e.g., which employees to interview).Convenience Sample – Use a sample that happens to be available (e.g., ask co-worker opinions at lunch).
28Chapter 2 – Sampling Methods Simple Random Sample:Every item in the population of N items has the same chance of being chosen in the sample of n items.Clicker Example….On your clicker, select either A, B, C, or D “at random”.Collect and look at the results.Discuss whether these results look random.
29Chapter 2 – Sampling Methods With or Without Replacement:If we allow duplicates when sampling, then we are sampling with replacement.Duplicates are unlikely when n is much smaller than N.If we do not allow duplicates when sampling, then we are sampling without replacement.Sample Size:Sample size depends on the inherent variability of the quantity being measured and on the desired precision of the estimate.
30Clickers Suppose you want to know the ages of moviegoers who attend Juno. Whatkind of sample is it if you survey the first 20people who emerge from the theater?A = simple random sampleB = systematic sampleC = stratified sampleD = convenience sample
31Chapter 2 – Data Sources Useful Data Sources: Type of Data Examples U.S. general dataStatistical Abstract of the U.S.U.S. economic dataEconomic Report of the PresidentAlmanacsWorld Almanac, Time AlmanacPeriodicalsEconomist, Business Week, FortuneIndexesNew York Times, Wall Street JournalDatabasesCompuStat, Citibase, U.S. CensusWorld dataCIA World FactbookWebGoogle, Yahoo, msnIn many instances, you will collect data specific to a specific question of interest through research or survey.
32Chapter 2 – Survey Research Basic Steps of Survey Research:Step 1: State the goals of the researchStep 2: Develop the budget (time, money, staff)Step 3: Create a research design (target population, frame, sample size)Step 4: Choose a survey type and method of administrationStep 5: Design a data collection instrument (questionnaire)Step 6: Pretest the survey instrument and revise as neededStep 7: Administer the survey (follow up if needed)Step 8: Code the data and analyze it
33Chapter 2 – Survey Research Survey Types (You should acquaint yourselveswith the characteristics of each – Table 2.12).MailTelephoneInterviewsWebDirect Observation
34Chapter 2 – Survey Research Survey Guidelines:Plan – What is the purpose of the survey? Consider staff expertise, needed skills, degree of precision, budget.Design – Invest time and money in designing the survey. Use books and references to avoid unnecessary errors.Quality – Take care in preparing a quality survey so that people will take you seriously.Pilot Test – Pretest on friends or co-workers to make sure the survey is clear.Buy-in – Improve response rates by stating the purpose of the survey, offering a token of appreciation or paving the way with endorsements.Expertise – Work with a consultant early on.