Statistics for business and economics Measurement scales.ppt

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

Statistics
Statistics: 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 mechanism
data mechanism
Probability
Probability: Branch of mathematics that
: Branch of mathematics that
models of the truth
models of the truth
In economics, we estimate and test economic models
In economics, we estimate and test economic models
and their predictions
and 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 monitor
control charts are used to monitor
the output of a production process.
the output of a production process.
 Production
Production
Electronic point-of-sale scanners at
Electronic point-of-sale scanners at
retail checkout counters are used to
retail checkout counters are used to
collect data for a variety of marketing
collect data for a variety of marketing
research applications.
research applications.
 Marketing
Marketing

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

Annual Earn/
Annual Earn/
Company Sales($M) Share($)
Company Sales($M) Share($)
Data, Data Sets,
Data, Data Sets,
Elements, Variables, and Observations
Dataram
Dataram 73.10
73.10 0.86
0.86
EnergySouth 74.00
EnergySouth 74.00 1.67
1.67
Keystone
Keystone 365.70
365.70 0.86
0.86
LandCare
LandCare 111.40
111.40 0.33
0.33
Psychemedics 17.60
Psychemedics 17.60 0.13
0.13
Variables
Variables
Data Set
Data Set
Observation
Observation
Element
Element
Names
Names
Dataram
Dataram
EnergySouth
EnergySouth
Keystone
Keystone
LandCare
LandCare
Psychemedics
Psychemedics

Data and Data Sets
Data and Data Sets
 Data
Data 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 referred
The data collected in a particular study are referred
to as the
to as the data set
data set.
.

 The
The elements
elements are the entities on which data are
are the entities on which data are
collected.
collected.
 A
A variable
variable is a characteristic of interest for the elements.
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
element is called an observation
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.

Scales of Measurement
Qualitative
Qualitative Quantitative
Quantitative
Numerical
Numerical Numerical
Numerical
Nonnumerical
Nonnumerical
Data
Data
Nominal
Nominal Ordinal
Ordinal Nominal
Nominal Ordinal
Ordinal Interval
Interval Ratio
Ratio

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.
Scales of measurement include:
Scales of measurement include:
Nominal
Nominal
Ordinal
Ordinal
Interval
Interval
Ratio
Ratio

 Nominal
Nominal
A
A nonnumeric label
nonnumeric label or
or numeric code
numeric code may be used.
may be used.
Data are
Data are labels or names
labels 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 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
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).
 Nominal
Nominal

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

 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.
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
Interval
Interval data are
Interval data are always numeric
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.

 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
Econ & Finance majors earn $7,976 more than
History majors and $12,630 more than
History majors and $12,630 more than
Psychology majors.
Psychology majors.
Source: National Association of Colleges and Employers
Source: National Association of Colleges and Employers

 Ratio
Ratio
The data have all the properties of interval data
The data have all the properties of interval data
and the
and the ratio of two values is meaningful
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.
This
This scale must contain a zero value
scale 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.

 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

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.
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 and Quantitative Data

Qualitative Data
Qualitative Data
Labels or names
Labels 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 data
categorical data
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
Quantitative data indicate
Quantitative data indicate how many or how much:
how many or how much:
D
Discrete
iscrete, if measuring how many. E.g., number
, if measuring how many. E.g., number
of 6-packs consumed at tail-gate party
of 6-packs consumed at tail-gate party
Continuous
Continuous, if measuring how much. E.g., pounds
, if measuring how much. E.g., pounds
of hamburger consumed at tail-gate party
of hamburger consumed at tail-gate party
Quantitative data are
Quantitative data are always numeric
always numeric.
.
Ordinary arithmetic operations are meaningful for
Ordinary arithmetic operations are meaningful for
quantitative data.
quantitative data.

Cross-Sectional Data
Cross-Sectional Data
Cross-sectional data
Cross-sectional data observations across individuals
observations across individuals
at the same point in time.
at the same point in time.
Example
Example: 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).
Example
Example: wages for head of household in
: wages for head of household in
Indiana
Indiana

Time Series Data
Time Series Data
Time series data
Time series data are collected over several time
are collected over several time
periods.
periods.
Example
Example: the sequence of U.S. GDP growth each
: the sequence of U.S. GDP growth each
Year from 1960 to 2005
Year from 1960 to 2005
Example:
Example: the sequence of Professor Mark’s wage
the sequence of Professor Mark’s wage
each year from 1983 to 2005.
each year from 1983 to 2005.

Data Sources
Data Sources
 Existing Sources
Existing Sources
Within a firm
Within a firm – almost any department
– almost any department
Business database services
Business database services – Dow Jones & Co.
– Dow Jones & Co.
Government agencies
Government agencies - U.S. Department of Labor
- U.S. Department of Labor
Industry associations
Industry associations – Travel Industry Association
– Travel Industry Association
of America
of America
Special-interest organizations
Special-interest organizations – Graduate Management
– Graduate Management
Admission Council
Admission Council
Collect your own
Collect your own

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

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

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

91 78 93 57 75 52 99 80 97 62
71 69 72 89 66 75 79 75 72 76
104 74 62 68 97 105 77 65 80 109
85 97 88 68 83 68 71 69 67 74
62 82 98 101 79 105 79 69 62 73
 Sample of Parts Cost for 50 Tune-ups
Sample of Parts Cost for 50 Tune-ups

Tabular Summary:
Tabular Summary:
Frequency and Percent Frequency
Frequency and Percent Frequency
50-59
50-59
60-69
60-69
70-79
70-79
80-89
80-89
90-99
90-99
100-109
100-109
2
2
13
13
16
16
7
7
7
7
5
5
50
50
4
4
26
26
32
32
14
14
14
14
10
10
100
100
(2/50)100
(2/50)100
Parts
Parts
Cost ($)
Cost ($)
Parts
Parts
Frequency
Frequency
Percent
Percent
Frequency
Frequency

Graphical Summary: Histogram
Graphical Summary: Histogram
2
4
6
8
10
12
14
16
18
Parts
Cost ($)
Frequency
5059 6069 7079 8089 9099 100-110
Tune-up Parts Cost
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
is the average
average (or
(or sample mean
sample mean).
).

Population
Population
Sample
Sample
Statistical inference
Statistical inference
Census
Census
Sample survey
Sample survey

 the set of all elements of interest in a
the set of all elements of interest in a
particular study
particular study

 a subset of the population
a subset of the population

 the process of using data obtained
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 population

 collecting data for a sample
collecting data for a sample

Process of Statistical Inference
Process of Statistical Inference
1
1. Population
. Population
consists of all
consists of all
tune-ups. Average
tune-ups. Average
cost of parts is
cost of parts is
unknown
unknown.
2
2. A sample of 50
. A sample of 50
engine tune-ups
engine tune-ups
is examined.
is examined.
3
3. The sample data
. The sample data
provide a sample
provide a sample
average parts cost
average parts cost
of $79 per tune-up.
of $79 per tune-up.
4
4. The sample average
. The sample average
is used to estimate the
is used to estimate the
population average.
population average.

Statistics for business and economics Measurement scales.ppt

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