I need help! Applications in Business and Economics Data Data Sources Descriptive Statistics Statistical Inference Computers & Statistical Analysis

Definition: Collection, summarization, analysis, and reporting of numerical findings

Statistics is concerned with DATA Collection; Organization; Summarization Presentation and Scientific Analysis · · drawing valid conclusions · · making informed decisions 1.1. What is Statistics? What are its Applications?

Applications of Statistics in Business and Economics

Accounting n Economics Public accounting firms use statistical sampling procedures when conducting audits for their clients. Economists use statistical information in making forecasts about the future of the economy or some aspect of it.

Applications in Business and Economics A variety of statistical quality control charts are used to monitor the output of a production process. n Production Electronic point-of-sale scanners at retail checkout counters are used to collect data for a variety of marketing research applications. n Marketing

Applications in Business and Economics Financial advisors use price-earnings ratios and dividend yields to guide their investment recommendations. Finance Finance

Data, Data Sets, Elements, Variables, and Observations

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

Stock Annual Earn/ Stock Annual Earn/ Exchange Sales($M) Share($) Data, Data Sets, Elements, Variables, and Observations 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

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

Scales of measurement determine the Scales of measurement determine the amount of information contained in the data. Scales of measurement determine the Scales of measurement determine the amount of information contained in the data. They determine the nature of data summarization They determine the nature of data summarization and statistical analyses that are most appropriate. and statistical analyses that are most appropriate. They determine the nature of data summarization They determine the nature of data summarization and statistical analyses that are most appropriate. and statistical analyses that are most appropriate.

Four commonly used Scales of measurement Nominal Ordinal Interval Ratio

Nominal Scales A nonnumeric label or numeric code may be used. A nonnumeric label or numeric code may be used. Data labels or names used to identify an Data labels or names used to identify an attribute of the element. attribute of the element. Data labels or names used to identify an Data labels or names used to identify an attribute of the element. attribute of the element.

Example: Example: Classification of University students by the Classification of University students by the school in which they are enrolled using school in which they are enrolled using labels such as Business, Humanities, labels such as Business, Humanities, Education, and so on. (Non-numeric) Education, and so on. (Non-numeric) Alternatively, a numeric code could be used for Alternatively, a numeric code could be used for the school variable (e.g. 1: denotes Business, the school variable (e.g. 1: denotes Business, 2: denotes Humanities, 3 : denotes Education, and 2: denotes Humanities, 3 : denotes Education, and so on). so on). Example: Example: Classification of University students by the Classification of University students by the school in which they are enrolled using school in which they are enrolled using labels such as Business, Humanities, labels such as Business, Humanities, Education, and so on. (Non-numeric) Education, and so on. (Non-numeric) Alternatively, a numeric code could be used for Alternatively, a numeric code could be used for the school variable (e.g. 1: denotes Business, the school variable (e.g. 1: denotes Business, 2: denotes Humanities, 3 : denotes Education, and 2: denotes Humanities, 3 : denotes Education, and so on). so on). Scales of Measurement n Nominal Scales

Ordinal Scales A nonnumeric label or numeric code may be used. A nonnumeric label or numeric code may be used. Data Measured using Ordinal scales Data Measured using Ordinal scales have the properties of nominal data. However, the order or rank of the data is meaningful. the order or rank of the data is meaningful. Data Measured using Ordinal scales Data Measured using Ordinal scales have the properties of nominal data. However, the order or rank of the data is meaningful. the order or rank of the data is meaningful.

Ordinal Scales Example: Example: Classification of University students by their Classification of University students by their class standing using a nonnumeric label such as class standing using a nonnumeric label such as Freshman, Sophomore, Junior, or Senior. Freshman, Sophomore, Junior, or Senior. Alternatively, a numeric code could be used for Alternatively, a numeric code could be used for the class standing variable (e.g. 1 denotes the class standing variable (e.g. 1 denotes Freshman, 2 denotes Sophomore, and so on). Freshman, 2 denotes Sophomore, and so on). Example: Example: Classification of University students by their Classification of University students by their class standing using a nonnumeric label such as class standing using a nonnumeric label such as Freshman, Sophomore, Junior, or Senior. Freshman, Sophomore, Junior, or Senior. Alternatively, a numeric code could be used for Alternatively, a numeric code could be used for the class standing variable (e.g. 1 denotes the class standing variable (e.g. 1 denotes Freshman, 2 denotes Sophomore, and so on). Freshman, 2 denotes Sophomore, and so on).

Interval Scales Interval data are always numeric. Interval data are always numeric. The data have the properties of ordinal data, and The data have the properties of ordinal data, and the interval between observations is expressed in the interval between observations is expressed in terms of a fixed unit of measure. terms of a fixed unit of measure. The data have the properties of ordinal data, and The data have the properties of ordinal data, and the interval between observations is expressed in the interval between observations is expressed in terms of a fixed unit of measure. terms of a fixed unit of measure.

Interval Scales Example: Example: Melissa has an SAT score of 1205, while Kevin Melissa has an SAT score of 1205, while Kevin has an SAT score of Melissa scored 115 has an SAT score of Melissa scored 115 points more than Kevin. points more than Kevin. Example: Example: Melissa has an SAT score of 1205, while Kevin Melissa has an SAT score of 1205, while Kevin has an SAT score of Melissa scored 115 has an SAT score of Melissa scored 115 points more than Kevin. points more than Kevin.

Ratio Scales The data have all the properties of interval data The data have all the properties of interval data and the ratio of two values is meaningful. and the ratio of two values is meaningful. The data have all the properties of interval data The data have all the properties of interval data and the ratio of two values is meaningful. and the ratio of two values is meaningful. Variables such as distance, height, weight, and time Variables such as distance, height, weight, and time use the ratio scale. use the ratio scale. Variables such as distance, height, weight, and time Variables such as distance, height, weight, and time use the ratio scale. use the ratio scale. Ratio scale must contain a zero value that indicates that nothing exists for the variable at the zero point. that nothing exists for the variable at the zero point. Ratio scale must contain a zero value that indicates that nothing exists for the variable at the zero point. that nothing exists for the variable at the zero point.

Ratio Scales Example: Example: Melissa’s college record shows 36 credit hours Melissa’s college record shows 36 credit hours earned, while Kevin’s record shows 72 credit earned, while Kevin’s record shows 72 credit hours earned. Kevin has twice as many credit hours earned. Kevin has twice as many credit hours earned as Melissa. hours earned as Melissa. Example: Example: Melissa’s college record shows 36 credit hours Melissa’s college record shows 36 credit hours earned, while Kevin’s record shows 72 credit earned, while Kevin’s record shows 72 credit hours earned. Kevin has twice as many credit hours earned. Kevin has twice as many credit hours earned as Melissa. hours earned as Melissa.

Data are often classified into one of the following two categories Data are often classified into one of the following two categories Quantitative Data Qualitative Data Data Types

The statistical analysis that is appropriate depends The statistical analysis that is appropriate depends on whether the data for the variable are qualitative on whether the data for the variable are qualitative or quantitative. or quantitative. The statistical analysis that is appropriate depends The statistical analysis that is appropriate depends on whether the data for the variable are qualitative on whether the data for the variable are qualitative or quantitative. or quantitative. In general, there are more alternatives for statistical In general, there are more alternatives for statistical analysis when the data are quantitative. analysis when the data are quantitative. In general, there are more alternatives for statistical In general, there are more alternatives for statistical analysis when the data are quantitative. analysis when the data are quantitative. Qualitative and Quantitative Data

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

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

Data and Scales of Measurement: Summary QualitativeQualitativeQuantitativeQuantitative NumericalNumerical NumericalNumerical NonnumericalNonnumerical DataData NominalNominalOrdinalOrdinalNominalNominalOrdinalOrdinalIntervalIntervalRatioRatio

1. Cross-Sectional Data Cross-sectional data are collected at the same or Cross-sectional data are collected at the same or approximately the same point in time over a range of approximately the same point in time over a range of different subjects. different subjects. Cross-sectional data are collected at the same or Cross-sectional data are collected at the same or approximately the same point in time over a range of approximately the same point in time over a range of different subjects. different subjects. Example: data detailing the number of building Example: data detailing the number of building permits issued in a given year in each of the counties permits issued in a given year in each of the counties of Minnesota of Minnesota Example: data detailing the number of building Example: data detailing the number of building permits issued in a given year in each of the counties permits issued in a given year in each of the counties of Minnesota of Minnesota

2. Time Series 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 a given country of Minnesota permits issued in a given country of Minnesota during each of the last 5 years Example: data detailing the number of building Example: data detailing the number of building permits issued in a given country of Minnesota permits issued in a given country of Minnesota during each of the last 5 years

3. Panel (Longitudinal) Data Panel (longitudinal) data are data collected over the Panel (longitudinal) data are data collected over the same set of several Subjects for several time periods. Panel (longitudinal) data are data collected over the Panel (longitudinal) data are data collected over the same set of several Subjects for several time periods. Example: data detailing the number of building Example: data detailing the number of building permits issued in each county in the state of permits issued in each county in the state of Minnesota over the last 36 years Minnesota over the last 36 years Example: data detailing the number of building Example: data detailing the number of building permits issued in each county in the state of permits issued in each county in the state of Minnesota over the last 36 years Minnesota over the last 36 years

Existing Sources (Secondary 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 of America Special-interest organizations – Graduate Management Admission Council Admission Council Internet – more and more firms

Statistical Studies (Primary 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 (non-experimental) studies no In observational (non-experimental) 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 (non-experimental) studies no In observational (non-experimental) 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

Time Requirement Cost of Acquisition Data Errors Data Errors Searching for information can be time consuming. Searching for information can be time consuming. Information may no longer be useful by the time it Information may no longer be useful by the time it is available. Organizations often charge for information even Organizations often charge for information even when it is not their primary business activity. when it is not their primary business activity. Using any data that happens to be available or Using any data that happens to be available or that were acquired with little care can lead to poor that were acquired with little care can lead to poor and misleading information. and misleading information.

Data are acquired! What Next? Extracting the Information Contained in the Data. How Can we extract the information content of a data?

Three different methods: 1. Tabular Methods, 2. Graphical Methods, 3. Numerical Methods

Example: Hudson Auto Repair The manager of Hudson Auto would like to have a better understanding of the COST of PARTS used in the engine tune-ups performed at the shop. She randomly selects 50 customer invoices for which tune-ups were performed. Data in the following table refers to the costs of parts, rounded to the nearest dollar.

Example: Hudson Auto Repair Example: Hudson Auto Repair n Sample of Parts Cost for 50 Tune-ups n The data presented here contains the information the manger needs, but is not in a usable format. The information content of the data needs to be extracted. How?

(2/50)X100 Parts Cost ($) Cost ($) Parts Frequency Frequency PercentFrequency

Parts Cost ($) Parts Cost ($) Frequency 50      Tune-up Parts Cost

Hudson’s average cost of parts, based on the 50 Hudson’s average cost of parts, based on the 50 tune-ups studied, is $79 (found by summing the tune-ups studied, is $79 (found by summing the 50 cost values and then dividing by 50). 50 cost values and then dividing by 50). The most common numerical descriptive statistic The most common numerical descriptive statistic is the average (or mean). is the average (or mean).

Statistical Inference - the process of using data obtained from a sample to make estimates and test hypotheses about the characteristics of a population What do we do with Information Extracted from data?

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

1.Population (All tune-ups). Average cost of parts is unknown unknown. 2. Sample (of 50 engine tune-ups is examined.) 3. The sample data Provides an average parts cost of $79 per tune-up. 4. The sample average is used to make inference about the population average.

Statistical analysis often involves working with Statistical analysis often involves working with large amounts of data. large amounts of data. Computer software is typically used to conduct the Computer software is typically used to conduct the analysis. analysis. Statistical software packages such as Microsoft Excel Statistical software packages such as Microsoft Excel and Minitab are capable of data management, analysis, and Minitab are capable of data management, analysis, and presentation. and presentation. Instructions for using Excel in chapter appendices. Instructions for using Excel in chapter appendices.