Statistics

1. Statistics Data

2. Contents Applications in Business and Economics Data Data Sources Descriptive Statistics Statistical Inference Computers and Statistical Analysis

3. STATISTICSin PRACTICE • Most issues of Business Week provide an in-depth report on a topic of current interest. Often, the in-depth reports contain statistical facts and summaries that help the reader understand the business and economic information. • Business Week also uses statistics and statistical information in managing its own business.

4. Applications in Business and Economics • Accounting • Finance • Marketing • Production • Economics

5. Data • Data and Data Sets • Elements, Variables, and Observations • Scales of Measurement • Qualitative and Quantitative Data • Cross-Sectional and Time Series Data

6. Data —Data and data set • Dataare the facts and figures collected, summarized, analyzed, and interpreted. • The data collected in a particular study are referred to as the data set.

7. Data -- Elements, Variables, and Observations • The elements are the entities on which data are collected. • A variable is a characteristic of interest for the elements. • The set of measurements collected for a particular element is called an observation. • The total number of data values in a data set is the number of elements multiplied by the number of variables.

8. Data -- Elements, Variables, and Observations • the data set contains 8 elements. • five variables: Exchange, Ticker Symbol, Market Cap, Price/Earnings Ratio, Gross Profit Margin. • observations: the first observation (DeWolfe Companies) is AMEX, DWL, 36.4, 8.4, and 36.7.

9. Variables Observation Element Names Data Set Data -- Elements, Variables, and Observations Stock Annual Earn/ Exchange Sales($M) Share($) Company AMEX 73.10 0.86 OTC 74.00 1.67 NYSE 365.70 0.86 NYSE 111.40 0.33 AMEX 17.60 0.13 Dataram EnergySouth Keystone LandCare Psychemedics

10. Data-- Scales of Measurement • Nominal scale • When the data for a variable consist of labels or names used to identify an attribute of the element. • For example, gender, ID number, “exchange variable” in Table 1.1 • nominal data can be recorded using a numeric code. We could use “0” for female, and “1” for male.

11. Data-- Scales of Measurement • Nominal scale example: • Students of a university are classified by the school in which they are enrolled using a nonnumeric label such as Business, Humanities, Education, and so on. • Alternatively, a numeric code could be used for the school variable (e.g. 1 denotes Business, 2 denotes Humanities, 3 denotes Education, and so on).

12. Data-- Scales of Measurement • Ordinal scale • If the data exhibit the properties of nominal data and the order or rank of the data is meaningful. • For example, questionnaire: a repair service rating of excellent, good, or poor. • Ordinal data can be recorded using a numeric code. We could use 1 for excellent, 2 for good, and 3 for poor.

13. Data-- Scales of Measurement • Ordinal scale example: • Students of a university are classified by their class standing using a nonnumeric label such as Freshman, Sophomore, Junior, or Senior. • Alternatively, a numeric code could be used for the class standing variable (e.g. 1 denotes Freshman, 2 denotes Sophomore, and so on).

14. Data-- Scales of Measurement • Interval scale • The data show the properties of ordinal data and the interval between values is expressed in terms of a fixed unit of measure. • Example: SAT scores, temperature. • Interval data are always numeric.

15. Data-- Scales of Measurement • Interval data example: • Three students with SAT scores of 1120, 1050, and 970 can be ranked or ordered in terms of best performance to poorest performance. • In addition, the differences between the scores are meaningful. For instance, student 1 scored 1120 – 1050 =70 points more than student 2, while student 2 scored 1050 – 970 = 80 points more than student 3.

16. Data-- Scales of Measurement • Ratio scale • The data have all the properties of interval data and the ratio of two values is meaningful. • Ratio scale requires that a zero value be included to indicate that nothing exists for the variable at the zero point. • For example, distance, height, weight, and time use the ratio scale of measurement.

17. Data-- Scales of Measurement • Ratio scale example: • Melissa’s college record shows 36 credit hours earned, while Kevin’s record shows 72 credit hours earned. • Kevin has twice as many credit hours earned as Melissa.

18. Data --Qualitative and Quantitative Data • Data can be further classified as either qualitative or quantitative. • The statistical analysis appropriate for a particular variable depends upon whether the variable is qualitative or quantitative.

19. Data --Qualitative and Quantitative Data • If the variable is qualitative, the statistical analysis is rather limited. • In general, there are more alternatives for statistical analysis when the data are quantitative.

20. Data –Qualitative Data • Labels or names used to identify an attribute of each element • Qualitative data are often referred to as categorical data • Use either the nominal or ordinal scale of measurement • Can be either numeric or nonnumeric • Appropriate statistical analyses are rather limited

21. Data --Quantitative Data • Quantitative data indicate how many or how much: • discrete, if measuring how many • continuous, if measuring how much • Quantitative data are always numeric. • Ordinary arithmetic operations are meaningful for quantitative data.

22. Data-- Scales of Measurement Data Qualitative Quantitative Numerical Numerical Nonnumerical Nominal Ordinal Nominal Ordinal Interval Ratio

23. Data-- Cross-Sectional Data Cross-sectional data are collected at the same or approximately the same point in time. Example: data detailing the number of building permits issued in July 2011 in each of the districts of Tainan City

24. Data– Time series Data Time series data are collected over several time periods. Example: data detailing the number of building permits issued in Tainan City in each of the last 36 months

25. Data Sources • Existing Sources • Statistical Studies • Data Acquisition Errors

26. Data Sources • Existing Sources Within a firm – almost any department Business database services – Dow Jones & Co. Government agencies - U.S. Department of Labor Industry associations – Travel Industry Association of America Special-interest organizations – Graduate Management Admission Council Internet – more and more firms

27. Data Sources

28. a survey is a good example Data Sources • Statistical Studies • In experimental studies the variables of interest • are first identified. Then one or more factors are • controlled so that data can be obtained about how • the factors influence the variables. In observational (nonexperimental) studies no attempt is made to control or influence the variables of interest.

29. Data Sources • Time requirement • Searching for information can be time consuming. • Information may no longer be useful by the time it is available • Cost of Acquisition • Organizations often charge for information even • when it is not their primary business activity.

30. Data Sources • Data Errors • Using any data that happens to be available or • that were acquired with little care can lead to poor and misleading information

31. Descriptive Statistics • Descriptive statistics are the tabular, graphical, and numerical methods used to summarize data.

32. Descriptive Statistics – Example • Next table is the data for different mini-systems. Brand & Model Price ($) Sound Quality CD Capacity FM Tuning Tape Decks Aiwa NSX-AJ800 250 Good 3 Fair 2 JVC FS-SD1000 500 Good 1 Very Good 0 JVC MX-G50 200 Very Good 3 Excellent 2 Panasonic SC-PM11 170 Fair 5 Very Good 1 RCA RS 1283 170 Good 3 Poor 0 Sharp CD-BA2600 150 Good 3 Good 2 Sony CHC-CL1 300 Very Good 3 Very Good 1 Sony MHC-NX1 500 Good 5 Excellent 2 Yamaha GX-505 400 Very Good 3 Excellent 1 Yamaha MCR-E100 500 Very Good 1 Excellent 0

33. Descriptive Statistics – Example Parts Cost ($) Percent Frequency Parts Frequency 2 13 16 7 7 5 50 4 26 32 14 14 10 100

34. Descriptive Statistics – Example Parts Cost ($) Percent Frequency Parts Frequency 2 13 16 7 7 5 50 4 26 32 14 14 10 100

35. Numerical Descriptive Statistics • The most common numerical descriptive statistic is the average (or mean). • The average price is ? Descriptive Statistics: Price ($) Total Sum of Variable Count Percent CumPct Mean StDev Sum Squares Minimum Price ($) 10 100 100 314.0 147.9 3 140.0 1182800.0 150.0 N for Variable Median Maximum Mode Mode Price ($) 275.0 500.0 500 3

36. Statistical Inference Population - the set of all elements of interest in a particular study Sample - a subset of the population Statistical inference - the process of using data obtained from a sample to make estimates and test hypotheses about the characteristics of a population Census - collecting data for a population Sample survey - collecting data for a sample

37. Process of Statistical Inference 1. Population consists of all tune-ups. Average cost of parts is unknown. 2. A sample of 50 engine tune-ups is examined. 3. The sample data provide a sample average parts cost of $79 per tune-up. 4. The sample average is used to estimate the population average.

38. Computers and Statistical Analysis • Statistical analysis often involves working with large amounts of data. • Computer software is typically used to conduct the analysis. • Statistical software packages such as Microsoft Excel and Minitab are capable of data management, analysis, and presentation.