Chapter 1Chapter 1 Data and Statistics Data and StatisticsI need I need

help!help!Applications in Economics

Data

Data Sources

Descriptive Statistics

Statistical Inference

Computers and Statistical Analysis

Applications in Applications in EconomicsEconomics

StatisticsStatistics: a methodology to use data to : a methodology to use data to learn the “truth.” i.e., Uncover the true learn the “truth.” i.e., Uncover the true data mechanismdata mechanism

ProbabilityProbability: Branch of mathematics that : Branch of mathematics that models of the truthmodels of the truth

In economics, we estimate and test economic models In economics, we estimate and test economic models

and their predictionsand their predictions

Use empirical models for prediction,Use empirical models for prediction,

forecasting, and policy analysis.forecasting, and policy analysis.

Applications in Business Applications in Business

Statistical quality Statistical quality

control charts are used to monitorcontrol charts are used to monitor

the output of a production process.the output of a production process.

ProductionProduction

Electronic point-of-sale scanners atElectronic point-of-sale scanners at

retail checkout counters are used toretail checkout counters are used to

collect data for a variety of marketingcollect data for a variety of marketing

research applications.research applications.

MarketingMarketing

Applications in FinanceApplications in Finance

Financial advisors use statistical modelsFinancial advisors use statistical models

to guide their investment advice.to guide their investment advice.

FinanceFinance

Annual Earn/Annual Earn/Company Sales($M) Share($)Company Sales($M) Share($)

Data, Data Sets, Data, Data Sets, Elements, Variables, and ObservationsElements, Variables, and Observations

DataramDataram 73.10 73.10 0.86 0.86

EnergySouth 74.00EnergySouth 74.00 1.67 1.67

KeystoneKeystone 365.70365.70 0.86 0.86

LandCareLandCare 111.40111.40 0.33 0.33

Psychemedics 17.60Psychemedics 17.60 0.13 0.13

VariableVariabless

Data SetData Set

ObservatioObservationnElemenElemen

tt NamesNames

DataramDataram

EnergySouthEnergySouth

KeystoneKeystone

LandCareLandCare

PsychemedicsPsychemedics

Data and Data SetsData and Data Sets DataData are the facts and figures collected, are the facts and figures collected,

summarized, analyzed, and interpreted.summarized, analyzed, and interpreted.

The data collected in a particular study are referredThe data collected in a particular study are referred to as the to as the data setdata set..

The The elementselements are the entities on which data are are the entities on which data are collected.collected. A A variablevariable is a characteristic of interest for the elements. is a characteristic of interest for the elements.

The set of measurements collected for a particularThe set of measurements collected for a particular element is called an element is called an observationobservation..

The total number of data values in a data set is theThe total number of data values in a data set is the number of elements multiplied by the number ofnumber of elements multiplied by the number of variables.variables.

Elements, Variables, and ObservationsElements, Variables, and Observations

Scales of MeasurementScales of Measurement

QualitativeQualitativeQualitativeQualitative QuantitativQuantitativee

QuantitativQuantitativee

NumericalNumericalNumericalNumerical NumericalNumericalNumericalNumericalNonnumericalNonnumericalNonnumericalNonnumerical

DataDataDataData

NominaNominallNominaNominall

OrdinaOrdinallOrdinaOrdinall

NominalNominalNominalNominal OrdinalOrdinalOrdinalOrdinal IntervalIntervalIntervalInterval RatioRatioRatioRatio

Scales of MeasurementScales of Measurement

The scale indicates the data summarization andThe scale indicates the data summarization and statistical analyses that are most appropriate.statistical analyses that are most appropriate. The scale indicates the data summarization andThe scale indicates the data summarization and statistical analyses that are most appropriate.statistical analyses that are most appropriate.

The scale determines the amount of informationThe scale determines the amount of information contained in the data.contained in the data. The scale determines the amount of informationThe scale determines the amount of information contained in the data.contained in the data.

Scales of measurement include:Scales of measurement include: Scales of measurement include:Scales of measurement include:

NominalNominal

OrdinalOrdinal

IntervalInterval

RatioRatio

Scales of MeasurementScales of Measurement NominalNominal

A A nonnumeric labelnonnumeric label or or numeric codenumeric code may be used. may be used. A A nonnumeric labelnonnumeric label or or numeric codenumeric code may be used. may be used.

Data are Data are labels or nameslabels or names used to identify an used to identify an attribute of the element.attribute of the element. Data are Data are labels or nameslabels or names used to identify an used to identify an attribute of the element.attribute of the element.

Example:Example: Students of a university are classified by theStudents 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 forA 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 theStudents 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 forA 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 MeasurementScales of Measurement

NominalNominal

Scales of MeasurementScales of Measurement OrdinalOrdinal

A A nonnumeric labelnonnumeric label or or numeric codenumeric code may be used. may be used. A A nonnumeric labelnonnumeric label or or numeric codenumeric code may be used. may be used.

The data have the properties of nominal data andThe data have the properties of nominal data and the the order or rank of the data is meaningfulorder or rank of the data is meaningful.. The data have the properties of nominal data andThe data have the properties of nominal data and the the order or rank of the data is meaningfulorder or rank of the data is meaningful..

Scales of MeasurementScales of Measurement

OrdinalOrdinal

Example:Example: Students of a university are classified by theirStudents 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 forA numeric code can be used for the class standing variable (e.g. 1 denotesthe 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 theirStudents 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 forA numeric code can be used for the class standing variable (e.g. 1 denotesthe class standing variable (e.g. 1 denotes Freshman, 2 denotes Sophomore, and so on).Freshman, 2 denotes Sophomore, and so on).

Scales of MeasurementScales of Measurement

IntervalInterval

Interval data are Interval data are always numericalways numeric.. Interval data are Interval data are always numericalways numeric..

The data have the properties of ordinal data, andThe data have the properties of ordinal data, and the interval between observations is expressed inthe 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, andThe data have the properties of ordinal data, and the interval between observations is expressed inthe interval between observations is expressed in terms of a fixed unit of measure.terms of a fixed unit of measure.

Scales of MeasurementScales of Measurement

IntervalInterval

Example: Average Starting Salary Offer 2003Example: Average Starting Salary Offer 2003 Economics/Finance: $40,084Economics/Finance: $40,084 History: $32,108History: $32,108 Psychology: $27,454Psychology: $27,454

Econ & Finance majors earn $7,976 more thanEcon & Finance majors earn $7,976 more thanHistory majors and $12,630 more thanHistory majors and $12,630 more thanPsychology majors.Psychology majors.

Source: National Association of Colleges and EmployersSource: National Association of Colleges and Employers

Example: Average Starting Salary Offer 2003Example: Average Starting Salary Offer 2003 Economics/Finance: $40,084Economics/Finance: $40,084 History: $32,108History: $32,108 Psychology: $27,454Psychology: $27,454

Econ & Finance majors earn $7,976 more thanEcon & Finance majors earn $7,976 more thanHistory majors and $12,630 more thanHistory majors and $12,630 more thanPsychology majors.Psychology majors.

Source: National Association of Colleges and EmployersSource: National Association of Colleges and Employers

Scales of MeasurementScales of Measurement RatioRatio

The data have all the properties of interval dataThe data have all the properties of interval data and the and the ratio of two values is meaningfulratio of two values is meaningful.. The data have all the properties of interval dataThe data have all the properties of interval data and the and the ratio of two values is meaningfulratio of two values is meaningful..

Variables such as distance, height, weight, and timeVariables such as distance, height, weight, and time use the ratio scale.use the ratio scale. Variables such as distance, height, weight, and timeVariables such as distance, height, weight, and time use the ratio scale.use the ratio scale.

This This scale must contain a zero valuescale must contain a zero value that indicates that indicates that nothing exists for the variable at the zero point.that nothing exists for the variable at the zero point. This This scale must contain a zero valuescale must contain a zero value that indicates that indicates that nothing exists for the variable at the zero point.that nothing exists for the variable at the zero point.

Scales of MeasurementScales of Measurement

RatioRatio

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 timesHistory major salaries and are 1.46 times Psychology major salariesPsychology 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 timesHistory major salaries and are 1.46 times Psychology major salariesPsychology major salaries

Data can be qualitative or quantitative.Data can be qualitative or quantitative. Data can be qualitative or quantitative.Data can be qualitative or quantitative.

The appropriate statistical analysis dependsThe appropriate statistical analysis depends on whether the data for the variable are qualitativeon whether the data for the variable are qualitative or quantitative.or quantitative.

The appropriate statistical analysis dependsThe appropriate statistical analysis depends on whether the data for the variable are qualitativeon whether the data for the variable are qualitative or quantitative.or quantitative.

There are more options for statisticalThere are more options for statistical analysis when the data are quantitative.analysis when the data are quantitative. There are more options for statisticalThere are more options for statistical analysis when the data are quantitative.analysis when the data are quantitative.

Qualitative and Quantitative DataQualitative and Quantitative Data

Qualitative DataQualitative Data Labels or namesLabels or names used to identify an attribute of each 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 namesLabels or names used to identify an attribute of each 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 Referred to as categorical datacategorical data Referred to as Referred to as categorical datacategorical data

Use either the nominal or ordinal scale ofUse either the nominal or ordinal scale of measurementmeasurement Use either the nominal or ordinal scale ofUse either the nominal or ordinal scale of measurementmeasurement

Can be either numeric or nonnumericCan be either numeric or nonnumeric Can be either numeric or nonnumericCan be either numeric or nonnumeric

Appropriate statistical analyses are rather limitedAppropriate statistical analyses are rather limited Appropriate statistical analyses are rather limitedAppropriate statistical analyses are rather limited

Quantitative DataQuantitative Data

Quantitative data indicate Quantitative data indicate how many or how much:how many or how much: Quantitative data indicate Quantitative data indicate how many or how much:how many or how much:

DDiscreteiscrete, if measuring how many. E.g., number, if measuring how many. E.g., number of 6-packs consumed at tail-gate partyof 6-packs consumed at tail-gate party DDiscreteiscrete, if measuring how many. E.g., number, if measuring how many. E.g., number of 6-packs consumed at tail-gate partyof 6-packs consumed at tail-gate party

ContinuousContinuous, if measuring how much. E.g., pounds , if measuring how much. E.g., pounds of hamburger consumed at tail-gate partyof hamburger consumed at tail-gate party ContinuousContinuous, if measuring how much. E.g., pounds , if measuring how much. E.g., pounds of hamburger consumed at tail-gate partyof hamburger consumed at tail-gate party

Quantitative data are Quantitative data are always numericalways numeric.. Quantitative data are Quantitative data are always numericalways numeric..

Ordinary arithmetic operations are meaningful forOrdinary arithmetic operations are meaningful for quantitative data.quantitative data. Ordinary arithmetic operations are meaningful forOrdinary arithmetic operations are meaningful for quantitative data.quantitative data.

Cross-Sectional DataCross-Sectional Data

Cross-sectional dataCross-sectional data observations across individuals observations across individuals at the same point in time.at the same point in time. Cross-sectional dataCross-sectional data observations across individuals observations across individuals at the same point in time.at the same point in time.

ExampleExample: the growth rate from 1960 to 2004 of: 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). ExampleExample: wages for head of household in : wages for head of household in IndianaIndiana

ExampleExample: the growth rate from 1960 to 2004 of: 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). ExampleExample: wages for head of household in : wages for head of household in IndianaIndiana

Time Series DataTime Series Data

Time series dataTime series data are collected over several time are collected over several time periods.periods. Time series dataTime series data are collected over several time are collected over several time periods.periods.

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

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

Data SourcesData Sources Existing SourcesExisting Sources

Within a firmWithin a firm – almost any department – almost any department

Business database servicesBusiness database services – Dow Jones & Co. – Dow Jones & Co.

Government agenciesGovernment agencies - U.S. Department of Labor - U.S. Department of Labor

Industry associationsIndustry associations – Travel Industry Association – Travel Industry Association of Americaof America

Special-interest organizationsSpecial-interest organizations – Graduate Management – Graduate Management Admission CouncilAdmission Council

Collect your ownCollect your own

Statistical StudiesStatistical StudiesData SourcesData Sources

In In experimental studiesexperimental studies variables of interest variables of interestare identified. Then additional factors areare identified. Then additional factors arevaried to obtain data that tells us howvaried to obtain data that tells us howthose factors influence the variables.those factors influence the variables.

In In experimental studiesexperimental studies variables of interest variables of interestare identified. Then additional factors areare identified. Then additional factors arevaried to obtain data that tells us howvaried to obtain data that tells us howthose factors influence the variables.those factors influence the variables.

In In observationalobservational (nonexperimental) (nonexperimental) studiesstudies we we cannot control or influence thecannot control or influence the variables of interest.variables of interest.

In In observationalobservational (nonexperimental) (nonexperimental) studiesstudies we we cannot control or influence thecannot control or influence the variables of interest.variables of interest.

a survey is aa survey is agood good

exampleexample

Descriptive StatisticsDescriptive Statistics

Descriptive statisticsDescriptive statistics are the tabular, are the tabular, graphical, and numerical methods graphical, and numerical methods used to used to summarizesummarize data. data.

Example: Hudson Auto RepairExample: Hudson Auto Repair

The manager of Hudson AutoThe manager of Hudson Auto

would like to understand the costwould like to understand the cost

of parts used in the engineof parts used in the engine

tune-ups performed in thetune-ups performed in the

shop. She examines 50shop. She examines 50

customer invoices for tune-ups. The costs of customer invoices for tune-ups. The costs of parts,parts,

rounded to the nearest dollar, are listed on the rounded to the nearest dollar, are listed on the nextnext

slide.slide.

91 78 93 57 75 52 99 80 97 6271 69 72 89 66 75 79 75 72 76104 74 62 68 97 105 77 65 80 10985 97 88 68 83 68 71 69 67 7462 82 98 101 79 105 79 69 62 73

91 78 93 57 75 52 99 80 97 6271 69 72 89 66 75 79 75 72 76104 74 62 68 97 105 77 65 80 10985 97 88 68 83 68 71 69 67 7462 82 98 101 79 105 79 69 62 73

Example: Hudson Auto RepairExample: Hudson Auto Repair

Sample of Parts Cost for 50 Tune-upsSample of Parts Cost for 50 Tune-ups

Tabular Summary:Tabular Summary: Frequency and Percent Frequency and Percent

FrequencyFrequency

50-5950-59

60-6960-69

70-7970-79

80-8980-89

90-9990-99

100-109100-109

22

1313

1616

77

77

55

5050

44

2626

3232

1414

1414

1010

100100

(2/50)10(2/50)1000

PartsParts Cost ($)Cost ($)

PartsParts FrequencyFrequency

PercentPercentFrequencyFrequency

Graphical Summary: Graphical Summary: HistogramHistogram

22

44

66

88

1010

1212

1414

1616

1818

PartsCost ($) PartsCost ($)

Fre

qu

en

cy

Fre

qu

en

cy

5059 6069 7079 8089 9099 100-1105059 6069 7079 8089 9099 100-110

Tune-up Parts CostTune-up Parts Cost

Numerical Descriptive Numerical Descriptive StatisticsStatistics

Hudson’s average cost of parts, based on the 50Hudson’s average cost of parts, based on the 50 tune-ups studied, is $79 (found by summing thetune-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 statisticThe most common numerical descriptive statistic is the is the averageaverage (or (or sample meansample mean).).

Statistical InferenceStatistical Inference

PopulationPopulation

SampleSample

Statistical inferenceStatistical inference

CensusCensus

Sample surveySample survey

the set of all elements of interest in athe set of all elements of interest in a particular studyparticular study

a subset of the populationa subset of the population

the process of using data obtainedthe process of using data obtained from a sample to make estimatesfrom a sample to make estimates and test hypotheses about theand test hypotheses about the characteristics of a populationcharacteristics of a population

collecting data for a populationcollecting data for a population

collecting data for a samplecollecting data for a sample

Process of Statistical Process of Statistical InferenceInference

11. Population . Population consists of allconsists of all

tune-ups. Averagetune-ups. Averagecost of parts iscost of parts is

unknownunknown.

22. A sample of 50. A sample of 50engine tune-ups engine tune-ups

is examined.is examined.

33. The sample data . The sample data provide a sampleprovide a sample

average parts costaverage parts costof $79 per tune-up.of $79 per tune-up.

44. The sample average. The sample averageis used to estimate theis used to estimate the population average.population average.