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Basic Business Statistics
11th Edition
Chapter 19
Data Analysis Overview
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc.
Chap 19-1
Learning Objectives
In this chapter, you learn:
The steps involved in choosing what statistical
methods to use to conduct a data analysis
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 19-2
Good Data Analysis Requires
Choosing The Proper Technique(s)

Choosing the proper technique(s) to use
requires the consideration of:
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
The purpose of the analysis
The type of variable being analyzed



Numerical
Categorical
The assumptions about the variable you are willing to
make
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 19-3
Questions To Ask When Analyzing
Numerical Variables

Do you seek to:
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




Describe the characteristics of the variable (possibly
broken into several groups)
Draw conclusions about the mean and standard
deviation of the variable in a population
Determine whether the mean and standard deviation
of the variable differs depending on the group
Determine which factors affect the value of the
variable
Predict the value of the variable based on the value
of other variables
Determine whether the values of the variable are
stable over time
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 19-4
How to Describe the Characteristics
of a Numerical Variable

Develop tables and charts and compute
descriptive statistics to describe the variable’s
characteristics:

Tables and charts


Stem-and-leaf display, percentage distribution, histogram,
polygon, boxplot, normal probability plot
Statistics

Mean, median, mode, quartiles, range, interquartile range,
standard deviation, variance, and coefficient of variation
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 19-5
How to draw conclusions about the
population mean or standard deviation

Confidence interval for the mean based on the
t-distribution
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Hypothesis test for the mean (t-test)

Hypothesis test for the variance ( 2 -test)
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 19-6
How to determine whether the mean or
standard deviation differs by group

Two independent groups studying central
tendency
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Normally distributed numerical variables
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

Pooled t-test if you can assume variances are equal
Separate-variance t-test if you cannot assume variances are
equal
 Both tests assume the variables are normally distributed
and you can examine this assumption by developing
boxplots and normal probability plots
 To decide if the variances are equal you can conduct an
F-test for the differences between two variances
Numerical variables not normally distributed

Wilcoxon rank sum test
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 19-7
How to determine whether the mean or
standard deviation differs by group
continued

Two groups of matched items or repeated
measures studying central tendency

Paired differences normally distributed
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Paired differences not normally distributed
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Paired t-test
Wilcoxon signed ranks test
Two independent groups studying variability

Numerical variables normally distributed

F-test
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 19-8
How to determine whether the mean or
standard deviation differs by group
continued

Three or more independent groups and
studying central tendency

Numerical variables normally distributed


One Way Analysis of Variance
Three or more groups of matched or repeated
measurements

Numerical variables normally distributed
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Randomized block design
Numerical variables not normally distributed

Friedman test
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 19-9
How to determine which factors
affect the value of the variable

Two factors to be examined

Two-factor factorial design
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 19-10
How to predict the value of a variable
based on the value of other variables

One independent variable

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Two or more independent variables
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Simple linear regression model
Multiple regression model
Data taken over a period of time and you want
to forecast future time periods
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Moving averages
Exponential smoothing
Least-squares forecasting
Autoregressive modeling
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 19-11
How to determine whether the values of
a variable are stable over time

Studying a process and have collected data over time
 Develop R and X charts
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 19-12
Questions To Ask When Analyzing
Categorical Variables

Do you seek to:
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


Describe the proportion of items of interest in each
category (possibly broken into several groups)
Draw conclusions about the proportion of items of
interest in a population
Determine whether the proportion of items of interest
differs depending on the group
Predict the proportion of items of interest based on
the value of other variables
Determine whether the proportion of items of interest
is stable over time
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 19-13
How to describe the proportion of
items of interest in each category
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Summary tables
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Charts
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Bar chart
Pie chart
Pareto chart
Side-by-side bar charts
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 19-14
How to draw conclusions about the
proportion of items of interest

Confidence interval for proportion of items of
interest

Hypothesis test for the proportion of items of
interest (Z-test)
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 19-15
How to determine whether the proportion of
items of interest differs depending on the group

Categorical variable has two categories
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Two independent groups
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Two groups of matched or repeated measurements
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McNemar test
More than two independent groups
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Two proportion Z-test
2 -test for the difference between two proportions
2 -test for the difference among several proportions
More than two categories and more than two
groups

2 -test of independence
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 19-16
How to predict the proportion of items of interest
based on the value of other variables

Logistic regression
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 19-17
How to determine whether the proportion of
items of interest is stable over time

Studying a process and data is taken over time

Collected items of interest over time

p-chart
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 19-18
Data Analysis Tree
Numerical & Categorical Variables
Possible Questions
How to describe the characteristics of the variable (possibly broken into several groups)?
How to draw conclusions about the mean and standard deviation of the variable in the population?
Numerical
Variables
How to determine whether the mean and standard deviation of the variable differs depending on the
group?
How to determine which factors affect the value of the variable?
How to predict the value of the variable based on the value of other variables?
How to determine whether the values of the variable are stable over time?
How to describe the proportion of items of interest in each category (possibly broken into several
groups)?
How to draw conclusions about the proportion of items of interest in a population?
Categorical
Variables
How to determine whether the proportion of items of interest differs depending on the group?
How to predict the proportion of items of interest based on the value of other variables?
How to determine whether the proportion of items of interest is stable over time?
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 19-19
Data Analysis Tree
Numerical Variables
continued
Create Tables & Charts
How to describe the
characteristics of the
variable (possibly broken
into several groups)?
Calculate Statistics
How to draw conclusions
about the mean and
standard deviation of the
variable in the population?
How to determine whether
the mean and standard
deviation of the variable
differs depending on the
group?
Variance / Standard
Deviation
Mean
Variance
2 matched
groups
>2 independent
groups
Mean, median, mode, quartiles, range,
interquartile range, standard deviation, variance,
coefficient of variation
Confidence interval for mean (t or z)
Hypothesis test for mean (t or z)
Mean
2 independent
groups
Stem-and-leaf display, percentage distribution,
histogram, polygon, boxplot, normal probability plot
Hypothesis test for variance (2 -test)
Pooled t test (both variables must be normal, variances equal)
Separate variance t test (both variables must be normal)
Wilcoxon rank sum test (variables do not have to be normal)
F-test (both variables must be normal)
Paired t test (differences must be normal)
Wilcoxon signed ranks test (differences do not have to be normal)
One Way Anova (variable must be normal)
>2 matched
groups
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Randomized Block Design (variable must be normal)
Friedman test (variable does not have to be normal)
Chap 19-20
Data Analysis Tree
Numerical Variables
continued
How to determine which
factors affect the value of
the variable?
Two factors
to be examined
One independent
variable
How to predict the value of
the variable based on the
value of other variables?
Two or more
Independent variables
Data taken over time to
forecast the future
How to determine whether
the values of the variable
are stable over time?
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Studied a process and
taken data over time
Two factor factorial design
Simple linear regression
Multiple regression model
Moving averages
Exponential smoothing
Least squares forecasting
Autoregressive modeling
Develop
X and R charts
Chap 19-21
Data Analysis Tree
Categorical Variables
continued
Summary tables
How to describe the
proportion of items of
interest in each category
(possibly broken into
several groups)
Bar charts
Pie charts
Pareto charts
Side-by-side charts
Confidence interval for the proportion of items of interest
How to draw conclusions
about the proportion of
items of interest in a
population
Hypothesis test for the proportion of items of interest
Two categories & two
independent groups
Two categories & two
matched groups
How to determine
whether the proportion of
items of interest differs
depending on the group
Two proportion Z test
χ2
test for the difference between two proportions
McNemar test
Two categories & more
than two independent
groups
χ 2 test for the difference among several proportions
More than two
categories & more than
two groups
χ 2 test of independence
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 19-22
Data Analysis Tree
Categorical Variables
continued
How to predict the
proportion of items of
interest based on the
value of other variables
How to determine
whether the proportion of
items of interest is stable
over time
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Logistic Regression
Studying a process
and collected items of
interest over time
p-chart
Chap 19-23
Chapter Summary


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Discussed how to choose the appropriate
technique(s) for data analysis for both
numerical and categorical variables
Discussed potential questions and the
associated appropriate techniques for
numerical variables
Discussed potential questions and the
associated appropriate techniques for
categorical variables
Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..
Chap 19-24