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