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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.
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.
Data -- Elements, Variables, and Observations
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
Variables
Element 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.
QualitativeQualitative Quantitative
Quantitative
NumericalNumerical NumericalNumericalNonnumericalNonnumerical
DataData
NominalNominal
OrdinalOrdinal
NominalNominal OrdinalOrdinal IntervalInterval RatioRatio
Data-- Scales of Measurement
Cross-sectional data are collected at the same or approximately the same point in time. 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
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. 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
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
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
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 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.
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 ($) Sound Quality CD Capacity FM Tuning Tape Decks
Aiwa NSX-AJ800 250 Good 3 Fair 2
JVC FS-SD1000 500 Good 1 Very Good 0
JVC MX-G50 200 Very Good 3 Excellent 2
Panasonic SC-PM11 170 Fair 5 Very Good 1
RCA RS 1283 170 Good 3 Poor 0
Sharp CD-BA2600 150 Good 3 Good 2
Sony CHC-CL1 300 Very Good 3 Very Good 1
Sony MHC-NX1 500 Good 5 Excellent 2
Yamaha GX-505 400 Very Good 3 Excellent 1
Yamaha MCR-E100 500 Very Good 1 Excellent 0
2 13
16
7
7
5
50
4 26
32
14
14
10
100
Parts Cost ($)
Parts Frequency
PercentFrequency
Descriptive Statistics – Example
2 13
16
7
7
5
50
4 26
32
14
14
10
100
Parts Cost ($)
Parts Frequency
PercentFrequency
Descriptive Statistics – Example
Numerical Descriptive Statistics
The most common numerical descriptive statistic is the average (or mean).
The average price is ?
Descriptive Statistics: Price ($) Total Sum of
Variable Count Percent CumPct Mean StDev Sum Squares Minimum
Price ($) 10 100 100 314.0 147.9 3 140.0 1182800.0 150.0
N for
Variable Median Maximum Mode Mode
Price ($) 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