1/71 Statistics Data

2/71 Contents Applications in Business and Economics Data Data Sources Descriptive Statistics Statistical Inference Computers and Statistical Analysis

STATISTICS in 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.

Accounting Finance Marketing Production Economics Applications in Business and Economics

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

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

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.

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 Data -- Elements, Variables, and Observations

Stock Annual Earn/ Stock Annual Earn/ Exchange Sales($M) Share($) Company Dataram Dataram EnergySouth EnergySouth Keystone Keystone LandCare LandCare Psychemedics Psychemedics AMEX AMEX OTC OTC NYSE NYSE NYSE NYSE AMEX AMEX Variables Element Names Names Data Set Observation Data -- Elements, Variables, and Observations

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.

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). 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. 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). 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. 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. 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. 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. Data-- Scales of Measurement

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.

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.

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

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.

QualitativeQualitativeQuantitativeQuantitative NumericalNumericalNumericalNumericalNonnumericalNonnumerical DataData NominalNominalOrdinalOrdinalNominalNominalOrdinalOrdinalIntervalIntervalRatioRatio Data-- Scales of Measurement

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

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

Data Sources Existing Sources Statistical Studies Data Acquisition Errors

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

Data Sources

Statistical Studies Data Sources 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 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 In observational (nonexperimental) studies no attempt is made to control or influence the attempt is made to control or influence the variables of interest. variables of interest. In observational (nonexperimental) studies no In observational (nonexperimental) studies no attempt is made to control or influence the attempt is made to control or influence the variables of interest. variables of interest. a survey is a good example

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.

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

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

Descriptive Statistics – Example Next table is the data for different mini-systems. Brand & ModelPrice ($)Sound QualityCD CapacityFM TuningTape Decks Aiwa NSX-AJ800250Good3Fair2 JVC FS-SD Good1Very Good0 JVC MX-G50200Very Good3Excellent2 Panasonic SC-PM11170Fair5Very Good1 RCA RS Good3Poor0 Sharp CD-BA Good3Good2 Sony CHC-CL1300Very Good3Very Good1 Sony MHC-NX1500Good5Excellent2 Yamaha GX Very Good3Excellent1 Yamaha MCR-E100500Very Good1Excellent0

Parts Cost ($) Parts Frequency Percent Frequency Descriptive Statistics – Example

Parts Cost ($) Parts Frequency Percent Frequency Descriptive Statistics – Example

Numerical Descriptive Statistics The most common numerical descriptive statistic is the average (or mean). The average price is ? Descriptive Statistics: Price ($) Total Sum of Variable Count Percent CumPct Mean StDev Sum Squares Minimum Price ($) N for Variable Median Maximum Mode Mode Price ($)

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

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.