Statistics

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Statistics

Data

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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 36.7.


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

Dataram EnergySouth Keystone LandCare Psychemedics

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

VariablesElement Names

Data Set

Observation


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).


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.


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).


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.


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.


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.


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 --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.

Qualitative Quantitative

Numerical NumericalNonnumerical

Data

Nominal

Ordinal

Nominal Ordinal Interval Ratio


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

Data-- Cross-Sectional 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

Data– Time series Data

Data Sources Existing Sources Statistical Studies Data Acquisition Errors

Data Sources Existing Sources

Within a firm – almost any departmentBusiness database services – Dow Jones & Co.Government agencies - U.S. Department of LaborIndustry associations – Travel Industry Association of AmericaSpecial-interest organizations – Graduate Management Admission Council

Internet – more and more firms

Data Sources

Statistical Studies

Data Sources

In experimental studies the variables of interestare first identified. Then one or more factors arecontrolled so that data can be obtained about howthe factors influence the variables.

In observational (nonexperimental) studies no attempt is made to control or influence the variables of interest.

a survey is agood 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 & Model Price ($) Sound Quality CD Capacity FM Tuning Tape DecksAiwa NSX-AJ800 250 Good 3 Fair 2JVC FS-SD1000 500 Good 1 Very Good 0JVC MX-G50 200 Very Good 3 Excellent 2Panasonic SC-PM11 170 Fair 5 Very Good 1RCA RS 1283 170 Good 3 Poor 0Sharp CD-BA2600 150 Good 3 Good 2Sony CHC-CL1 300 Very Good 3 Very Good 1Sony MHC-NX1 500 Good 5 Excellent 2Yamaha GX-505 400 Very Good 3 Excellent 1Yamaha MCR-E100 500 Very Good 1 Excellent 0

2 13 16 7 7 5 50

4 26 32 14 14 10 100

Parts Cost ($)

Parts Frequency

PercentFrequency


2 13 16 7 7 5 50

4 26 32 14 14 10 100

Parts Cost ($)

Parts Frequency

PercentFrequency


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 ($) 10 100 100 314.0 147.9 3 140.0 1182800.0 150.0 N forVariable Median Maximum Mode ModePrice ($) 275.0 500.0 500 3

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. Averagecost of parts is

unknown.

2. A sample of 50engine tune-ups

is examined.

3. The sample data provide a sampleaverage parts costof $79 per tune-up.

4. The sample averageis 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.

Documents

Statistics