Basic Business Statistics 11 th Edition Chapter 19

Learning Objectives In this chapter, you learn: n. The steps involved in choosing what statistical methods to use to conduct a data analysis Basic Business Statistics, 11 e © 2009 Prentice-Hall, Inc. . Chap 19 -2

Good Data Analysis Requires Choosing The Proper Technique(s) n Choosing the proper technique(s) to use requires the consideration of: n n The purpose of the analysis The type of variable being analyzed n n n Numerical Categorical The assumptions about the variable you are willing to make Basic Business Statistics, 11 e © 2009 Prentice-Hall, Inc. . Chap 19 -3

Questions To Ask When Analyzing Numerical Variables n Do you seek to: n n n 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, 11 e © 2009 Prentice-Hall, Inc. . Chap 19 -4

How to Describe the Characteristics of a Numerical Variable n Develop tables and charts and compute descriptive statistics to describe the variable’s characteristics: n Tables and charts n n Stem-and-leaf display, percentage distribution, histogram, polygon, boxplot, normal probability plot Statistics n Mean, median, mode, quartiles, range, interquartile range, standard deviation, variance, and coefficient of variation Basic Business Statistics, 11 e © 2009 Prentice-Hall, Inc. . Chap 19 -5

How to draw conclusions about the population mean or standard deviation n Confidence interval for the mean based on the tdistribution n Hypothesis test for the mean (t-test) n Hypothesis test for the variance ( 2 -test) Basic Business Statistics, 11 e © 2009 Prentice-Hall, Inc. . Chap 19 -6

How to determine whether the mean or standard deviation differs by group n Two independent groups studying central tendency n Normally distributed numerical variables n n n Pooled t-test if you can assume variances are equal Separate-variance t-test if you cannot assume variances are equal n Both tests assume the variables are normally distributed and you can examine this assumption by developing boxplots and normal probability plots n To decide if the variances are equal you can conduct an F-test for the differences between two variances Numerical variables not normally distributed n Wilcoxon rank sum test Basic Business Statistics, 11 e © 2009 Prentice-Hall, Inc. . Chap 19 -7

How to determine whether the mean or standard deviation differs by group continued n Two groups of matched items or repeated measures studying central tendency n Paired differences normally distributed n n Paired differences not normally distributed n n Paired t-test Wilcoxon signed ranks test Two independent groups studying variability n Numerical variables normally distributed n F-test Basic Business Statistics, 11 e © 2009 Prentice-Hall, Inc. . Chap 19 -8

How to determine whether the mean or standard deviation differs by group continued n Three or more independent groups and studying central tendency n Numerical variables normally distributed n n One Way Analysis of Variance Three or more groups of matched or repeated measurements n Numerical variables normally distributed n n Randomized block design Numerical variables not normally distributed n Friedman test Basic Business Statistics, 11 e © 2009 Prentice-Hall, Inc. . Chap 19 -9

How to determine which factors affect the value of the variable n Two factors

How to predict the value of a variable based on the value of other variables n One independent variable n n Two or more independent variables n n Simple linear regression model Multiple regression model Data taken over a period of time and you want to forecast future time periods n n Moving averages Exponential smoothing Least-squares forecasting Autoregressive modeling Basic Business Statistics, 11 e © 2009 Prentice-Hall, Inc. . Chap 19 -11

How to determine whether the values of a variable are stable over time n Studying a process and have collected data over time n Develop R and Basic Business Statistics, 11 e © 2009 Prentice-Hall, Inc. . charts Chap 19 -12

Questions To Ask When Analyzing Categorical Variables n Do you seek to: n n n 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, 11 e © 2009 Prentice-Hall, Inc. . Chap 19 -13

How to describe the proportion of items of interest in each category n Summary tables n Charts n n Bar chart Pie chart Pareto chart Side-by-side bar charts Basic Business Statistics, 11 e © 2009 Prentice-Hall, Inc. . Chap 19 -14

How to draw conclusions about the proportion of items of interest n n Confidence interval for proportion of items of interest Hypothesis test for the proportion of items of interest (Z-test) Basic Business Statistics, 11 e © 2009 Prentice-Hall, Inc. . Chap 19 -15

How to determine whether the proportion of items of interest differs depending on the group n Categorical variable has two categories n Two independent groups n n n Two groups of matched or repeated measurements n n Mc. Nemar test More than two independent groups n n 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 n 2 -test of independence Basic Business Statistics, 11 e © 2009 Prentice-Hall, Inc. . Chap 19 -16

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

How to determine whether the proportion of items of interest is stable over time n Studying a process and data is taken over time n Collected items of interest over time n p-chart Basic Business Statistics, 11 e © 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, 11 e © 2009 Prentice-Hall, Inc. . Chap 19 -19

Data Analysis Tree Numerical Variables 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? Mean Variance / Standard Deviation 2 independent groups Mean Variance 2 matched groups continued 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 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) >2 independent groups Wilcoxon signed ranks test (differences do not have to be normal) >2 matched groups Randomized Block Design (variable must be normal) Basic Business Statistics, 11 e © 2009 Prentice-Hall, Inc. . One Way Anova (variable must be normal) Friedman test (variable does not have to be normal) Chap 19 -20

Data Analysis Tree Numerical Variables 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? Two factors to be examined One independent variable 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, 11 e © 2009 Prentice-Hall, Inc. . Studied a process and taken data over time continued Two factorial design Simple linear regression Multiple regression model Moving averages Exponential smoothing Least squares forecasting Autoregressive modeling Develop 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 for the difference between two proportions Mc. Nemar test Two categories & more than two independent groups test for the difference among several proportions More than two categories & more than two groups test of independence Basic Business Statistics, 11 e © 2009 Prentice-Hall, Inc. . Chap 19 -22

Data Analysis Tree Categorical Variables 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, 11 e © 2009 Prentice-Hall, Inc. . continued Logistic Regression Studying a process and collected items of interest over time p-chart Chap 19 -23

Chapter Summary n n n 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, 11 e © 2009 Prentice-Hall, Inc. . Chap 19 -24