Chap 19-1 Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc. Chap 19-1 Chapter 19 Data...

Chap 19-1Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc. Chap 19-1

Chapter 19

Data Analysis Overview

Basic Business Statistics11th Edition

Chap 19-2Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc.. Chap 19-2

Learning Objectives

In this chapter, you learn:

The steps involved in choosing what statistical methods to use to conduct a data analysis

Chap 19-3

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

Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc.. Chap 19-3

Chap 19-4

Questions To Ask When Analyzing Numerical Variables

Do you seek to: 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


Chap 19-5

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 19-6

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 (


test)

Chap 19-7

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 differences between two variances

Numerical variables not normally distributed Wilcoxon rank sum test


Chap 19-8


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


continuedcontinued

Chap 19-9


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

Randomized block design Numerical variables not normally distributed

Friedman test


continuedcontinued

Chap 19-10

How to determine which factors affect the value of the variable

Two factors to be examined Two-factor factorial design


Chap 19-11

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 19-12

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


X

Chap 19-13

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) 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


Chap 19-14

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 19-15

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 19-16

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


test

test

test

Chap 19-17

How to predict the proportion of items of interest based on the value of other variables

Logistic regression


Chap 19-18

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 19-19Chap 19-19

Data Analysis TreeNumerical & Categorical Variables

NumericalVariablesNumericalVariables

CategoricalVariablesCategoricalVariables

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?

Possible Questions







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?

Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..


Data Analysis TreeNumerical Variables







continuedcontinued

Create Tables & Charts

Calculate Statistics

Mean

Variance / StandardDeviation

Mean

Variance

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 test (variable does not have to be normal)

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 test (variable does not have to be normal)

test)

2 independentgroups

2 matchedgroups

>2 independentgroups

>2 matchedgroups



Data Analysis TreeNumerical Variables

continuedcontinued







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 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 charts

Two factor factorial design

Simple linear regression

Multiple regression model

Moving averagesExponential smoothingLeast squares forecastingAutoregressive modeling

Develop and R chartsX


Chap 19-22

Data Analysis TreeCategorical Variables

2χ

continuedcontinued

Chap 19-22Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

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 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


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

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

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 19-23





Data Analysis TreeCategorical Variables

continuedcontinued

Chap 19-23Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc..

Logistic Regression

p-chart

Logistic Regression

p-chartStudying a process and collected items of interest over time

Studying a process and collected items of interest over time

Chap 19-24

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 19-1 Basic Business Statistics, 11e © 2009 Prentice-Hall, Inc. Chap 19-1 Chapter 19 Data...

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