Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Chap 18-1Chap 18-1Chap 18-1
Chapter 18
A Roadmap for Analyzing Data
Basic Business Statistics12th Edition
Chap 18-2Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Chap 18-2Chap 18-2
Learning Objectives
In this chapter, you learn: The steps involved in choosing what statistical
methods to use to conduct a data analysis
Chap 18-3Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Chap 18-3
Good Data Analysis Requires Choosing The Proper Technique(s)
Choosing the proper technique(s) to use requires the consideration of: The purpose of the analysis The type of variable being analyzed
Numerical Categorical
The assumptions about the variable you are willing to make
Chap 18-3
Chap 18-4Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Chap 18-4
Questions To Ask When Analyzing Numerical Variables
Do you seek to: Describe the characteristics of the variable (possibly
broken into several groups)? Reach 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?
Chap 18-4
Chap 18-5Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Chap 18-5
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
Chap 18-5
Chap 18-6Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Chap 18-6
How To Draw Conclusions About The Population Mean Or Standard Deviation
Confidence interval for the mean based on the t-distribution
Hypothesis test for the mean (t-test)
Hypothesis test for the variance (χ2–test)
Chap 18-6
Chap 18-7Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Chap 18-7
How To Determine Whether The Mean Or Standard Deviation Differs By Group
Two independent groups studying central tendency Normally distributed numerical variables
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 ratio of two variances
Numerical variables not normally distributed Wilcoxon rank sum test
Chap 18-7
Chap 18-8Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Chap 18-8
How To Determine Whether The Mean Or Standard Deviation Differs By Group
Two groups of matched items or repeated measures studying central tendency Paired differences normally distributed
Paired t-test Paired differences not normally distributed
Wilcoxon signed ranks test
Two independent groups studying variability Numerical variables normally distributed
F-test
Chap 18-8
continued
Chap 18-9Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Chap 18-9
How To Determine Whether The Mean Or Standard Deviation Differs By Group
Three or more independent groups and studying central tendency Numerical variables normally distributed
One- Way Analysis of Variance Numerical variables not normally distributed
Kruskal-Wallis Rank Test
Three or more groups of matched or repeated measurements Numerical variables normally distributed
Randomized block design Numerical variables not normally distributed
Friedman rank test
Chap 18-9
continued
Chap 18-10Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Chap 18-10
How To Determine Which Factors Affect The Value Of The Variable
Two factors to be examined Two-factor factorial design
Chap 18-10
Chap 18-11Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Chap 18-11
How To Predict The Value Of A Variable Based On The Value Of Other Variables
One independent variable Simple linear regression model
Two or more independent variables Multiple regression model
Data taken over a period of time and you want to forecast future time periods Moving averages Exponential smoothing Least-squares forecasting Autoregressive modeling
Chap 18-11
Chap 18-12Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Chap 18-12
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 charts
Chap 18-12
X
Chap 18-13Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Chap 18-13
Questions To Ask When Analyzing Categorical Variables
Do you seek to: Describe the proportion of items of interest in each
category (possibly broken into several groups)? Reach 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?
Chap 18-13
Chap 18-14Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Chap 18-14
How To Describe The Proportion Of Items Of Interest In Each Category
Summary tables
Charts Bar chart Pie chart Pareto chart Side-by-side bar charts
Chap 18-14
Chap 18-15Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Chap 18-15
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)
Chap 18-15
Chap 18-16Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Chap 18-16
How To Determine Whether The Proportion Of Items Of Interest Differs Depending On The Group
Categorical variable has two categories Two independent groups
Two proportion Z-test for the difference between two proportions
Two groups of matched or repeated measurements McNemar test
More than two independent groups for the difference among several proportions
More than two categories and more than two groups
of independence
Chap 18-16
2 -test
2 -test
2 -test
Chap 18-17Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall
How To Predict The Proportion Of Items Of Interest Based On The Value Of Other Variables
Logistic regression
Chap 18-18Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Chap 18-18
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
Chap 18-18
Chap 18-19Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall
Data Analysis TreeNumerical & Categorical Variables
NumericalVariables
CategoricalVariables
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?
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?
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?
Chap 18-20Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall
Data Analysis TreeNumerical Variables
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?
How to determine whether the mean and standard deviation of the variable differs depending on the group?
continued
Create Tables & Charts
Calculate Statistics
Mean
Variance / StandardDeviation
Mean
Variance
Stem-and-leaf display, percentage distribution,histogram, polygon, boxplot, normal probability plot
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)
Hypothesis test for variance
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)
Randomized Block Design (variable must be normal)
Friedman rank test (variable does not have to be normal)
(2 -test)
2 independentgroups
2 matchedgroups
>2 independentgroups
>2 matchedgroups
Chap 18-21Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Chap 19-21Chap 19-21
Data Analysis TreeNumerical Variables
continued
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?
Two factorsto be examined
One independentvariable
Two or moreIndependent variables
Data taken over time toforecast the future
Studied a process andtaken data over time
Two-factor factorial design
Simple linear regression
Multiple regression model
Moving averagesExponential smoothingLeast-squares forecastingAutoregressive modeling
Develop and R chartsX
Chap 18-22Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall
Data Analysis TreeCategorical Variables
2χ
continued
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
How to determine whether the proportion of items of interest differs depending on the group
Summary tables
Bar charts
Pie charts
Pareto charts
Side-by-side charts
Confidence interval for the proportion of items of interest
Hypothesis test for the proportion of items of interest
Two proportion Z test
test for the difference between two proportions
McNemar test
test for the difference among several proportions
test of independence
Two categories & two independent groups
Two categories & two matched groups
Two categories & more than two independent groups
More than two categories & more than two groups
2χ
2χ
Chap 18-23Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall
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
Data Analysis TreeCategorical Variables
continued
Logistic Regression
p-chartStudying a process and collected items of interest over time
Chap 18-24Copyright ©2012 Pearson Education, Inc. publishing as Prentice Hall Chap 18-24
Chapter Summary
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
Chap 18-24
Top Related