Chapter 1 Data and Statistics I need help! Applications in Economics Data Data Sources Descriptive Statistics Statistical Inference Computers and Statistical Analysis

Applications in Economics Statistics : a methodology to use data to learn the “truth.” i.e., Uncover the true data mechanism Probability : Branch of mathematics that models of the truth In economics, we estimate and test economic models and their predictions Use empirical models for prediction, forecasting, and policy analysis.

Applications in Business 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 Finance Financial advisors use statistical models to guide their investment advice. Finance Finance

Annual Earn/ Annual Earn/ Company Sales($M) Share($) Data, Data Sets, Elements, Variables, and Observations Dataram EnergySouth Keystone LandCare Psychemedics Variables Data Set Observation Element Names Names Dataram Dataram EnergySouth EnergySouth Keystone Keystone LandCare LandCare Psychemedics Psychemedics

Data and Data Sets Data are the facts and figures collected, summarized, analyzed, and interpreted. 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.

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 QualitativeQualitativeQuantitativeQuantitative NumericalNumerical NumericalNumerical NonnumericalNonnumerical DataData NominalNominalOrdinalOrdinalNominalNominalOrdinalOrdinalIntervalIntervalRatioRatio

The scale indicates the data summarization and The scale indicates the data summarization and statistical analyses that are most appropriate. statistical analyses that are most appropriate. The scale indicates the data summarization and The scale indicates the data summarization and statistical analyses that are most appropriate. statistical analyses that are most appropriate. The scale determines the amount of information The scale determines the amount of information contained in the data. contained in the data. The scale determines the amount of information The scale determines the amount of information contained in the data. contained in the data. Scales of measurement include: Scales of measurement include: Nominal Ordinal Interval Ratio

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

Example: Example: Students of a university are classified by the Students of a university are classified by the dorm that they live in using a nonnumeric label dorm that they live in using a nonnumeric label such as Farley, Keenan, Zahm, Breen-Phillips, such as Farley, Keenan, Zahm, Breen-Phillips, and so on. and so on. A numeric code can be used for A numeric code can be used for the school variable (e.g. 1: Farley, 2: Keenan, the school variable (e.g. 1: Farley, 2: Keenan, 3: Zahm, and so on). 3: Zahm, and so on). Example: Example: Students of a university are classified by the Students of a university are classified by the dorm that they live in using a nonnumeric label dorm that they live in using a nonnumeric label such as Farley, Keenan, Zahm, Breen-Phillips, such as Farley, Keenan, Zahm, Breen-Phillips, and so on. and so on. A numeric code can be used for A numeric code can be used for the school variable (e.g. 1: Farley, 2: Keenan, the school variable (e.g. 1: Farley, 2: Keenan, 3: Zahm, and so on). 3: Zahm, and so on). Scales of Measurement n Nominal

Scales of Measurement Ordinal Ordinal A nonnumeric label or numeric code may be used. A nonnumeric label or numeric code may be used. The data have the properties of nominal data and The data have the properties of nominal data and the order or rank of the data is meaningful. the order or rank of the data is meaningful. The data have the properties of nominal data and The data have the properties of nominal data and the order or rank of the data is meaningful. the order or rank of the data is meaningful.

Scales of Measurement Ordinal Ordinal Example: Example: Students of a university are classified by their Students of a university are classified 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. A numeric code can be used for A numeric code can 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: Students of a university are classified by their Students of a university are classified 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. A numeric code can be used for A numeric code can 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).

Scales of Measurement Interval Interval 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.

Scales of Measurement Interval Interval Example: Average Starting Salary Offer 2003 Example: Average Starting Salary Offer 2003 Economics/Finance: $40,084 Economics/Finance: $40,084 History: $32,108 History: $32,108 Psychology: $27,454 Psychology: $27,454 Econ & Finance majors earn $7,976 more than History majors and $12,630 more than Psychology majors. Source: National Association of Colleges and Employers Example: Average Starting Salary Offer 2003 Example: Average Starting Salary Offer 2003 Economics/Finance: $40,084 Economics/Finance: $40,084 History: $32,108 History: $32,108 Psychology: $27,454 Psychology: $27,454 Econ & Finance majors earn $7,976 more than History majors and $12,630 more than Psychology majors. Source: National Association of Colleges and Employers

Scales of Measurement Ratio Ratio 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. This scale must contain a zero value that indicates This 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. This scale must contain a zero value that indicates This 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.

Scales of Measurement Ratio Ratio Example: Example: Econ & Finance majors salaries are 1.24 times Econ & Finance majors salaries are 1.24 times History major salaries and are 1.46 times History major salaries and are 1.46 times Psychology major salaries Psychology major salaries Example: Example: Econ & Finance majors salaries are 1.24 times Econ & Finance majors salaries are 1.24 times History major salaries and are 1.46 times History major salaries and are 1.46 times Psychology major salaries Psychology major salaries

Data can be qualitative or quantitative. Data can be qualitative or quantitative. The appropriate statistical analysis depends The appropriate statistical analysis depends on whether the data for the variable are qualitative on whether the data for the variable are qualitative or quantitative. or quantitative. The appropriate statistical analysis depends The appropriate statistical analysis depends on whether the data for the variable are qualitative on whether the data for the variable are qualitative or quantitative. or quantitative. There are more options for statistical There are more options for statistical analysis when the data are quantitative. analysis when the data are quantitative. There are more options for statistical There are more options for statistical analysis when the data are quantitative. analysis when the data are quantitative. Qualitative and Quantitative Data

Qualitative Data Labels or names used to identify an attribute of each Labels or names used to identify an attribute of each element. E.g., Black or white, male or female. element. E.g., Black or white, male or female. Labels or names used to identify an attribute of each Labels or names used to identify an attribute of each element. E.g., Black or white, male or female. element. E.g., Black or white, male or female. Referred to as categorical data 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

Quantitative Data Quantitative data indicate how many or how much: Quantitative data indicate how many or how much: Discrete, if measuring how many. E.g., number Discrete, if measuring how many. E.g., number of 6-packs consumed at tail-gate party of 6-packs consumed at tail-gate party Discrete, if measuring how many. E.g., number Discrete, if measuring how many. E.g., number of 6-packs consumed at tail-gate party of 6-packs consumed at tail-gate party Continuous, if measuring how much. E.g., pounds Continuous, if measuring how much. E.g., pounds of hamburger consumed at tail-gate party of hamburger consumed at tail-gate party Continuous, if measuring how much. E.g., pounds Continuous, if measuring how much. E.g., pounds of hamburger consumed at tail-gate party of hamburger consumed at tail-gate party 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.

Cross-Sectional Data Cross-sectional data observations across individuals Cross-sectional data observations across individuals at the same point in time. at the same point in time. Cross-sectional data observations across individuals Cross-sectional data observations across individuals at the same point in time. at the same point in time. Example: the growth rate from 1960 to 2004 of Example: the growth rate from 1960 to 2004 of each country in the world (about 182 of them). each country in the world (about 182 of them). Example: wages for head of household in Indiana Indiana Example: the growth rate from 1960 to 2004 of Example: the growth rate from 1960 to 2004 of each country in the world (about 182 of them). each country in the world (about 182 of them). Example: wages for head of household in Indiana Indiana

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: the sequence of U.S. GDP growth each Example: the sequence of U.S. GDP growth each Year from 1960 to 2005 Example: the sequence of Professor Mark’s wage each year from 1983 to each year from 1983 to Example: the sequence of U.S. GDP growth each Example: the sequence of U.S. GDP growth each Year from 1960 to 2005 Example: the sequence of Professor Mark’s wage each year from 1983 to each year from 1983 to 2005.

Data Sources Existing 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 of America Special-interest organizations – Graduate Management Admission Council Admission Council Collect your own

Statistical Studies Statistical Studies Data Sources In experimental studies variables of interest are identified. Then additional factors are varied to obtain data that tells us how those factors influence the variables. In experimental studies variables of interest are identified. Then additional factors are varied to obtain data that tells us how those factors influence the variables. In observational (nonexperimental) studies we In observational (nonexperimental) studies we cannot control or influence the cannot control or influence the variables of interest. variables of interest. In observational (nonexperimental) studies we In observational (nonexperimental) studies we cannot control or influence the cannot control or influence the variables of interest. variables of interest. a survey is a good example

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

Example: Hudson Auto Repair The manager of Hudson Auto would like to understand the cost of parts used in the engine tune-ups performed in the shop. She examines 50 customer invoices for tune-ups. The costs of parts, rounded to the nearest dollar, are listed on the next slide.

Example: Hudson Auto Repair Example: Hudson Auto Repair n Sample of Parts Cost for 50 Tune-ups

Tabular Summary: Frequency and Percent Frequency Tabular Summary: Frequency and Percent Frequency (2/50)100 Parts Cost ($) Parts Frequency Percent Frequency

Graphical Summary: Histogram Graphical Summary: Histogram Parts Cost ($) Parts Cost ($) Frequency 50      Tune-up Parts Cost

Numerical Descriptive Statistics Numerical Descriptive Statistics 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 sample mean). is the average (or sample mean).

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

Process of Statistical Inference Process of Statistical Inference 1. Population consists of all tune-ups. Average cost of parts is unknown 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. population average.