QBA 301 Chapter Two Factor Anova, Spring 2014

Two-Factor ANOVA Dr. Jordan Srour BUS 301: Int. Bus. Stats Lebanese American University 27 November 2013 F.J.Srour (LAU) QBA 301 27 November 2013 1 / 13 Overview Today’s Lecture Case II, reminder, Due by 5pm, 28 November. Quiz 2: In-class, 9 December 2013 Assignment 5 Overview of Week Review Two-Factor ANOVA (14.5) F.J.Srour (LAU) QBA 301 27 November 2013 2 / 13 Case Study Reminder Case Study Part II, due 28 November 2013 Done as partners – each pair of two people hands in one letter. Submission is a letter...do NOT hand in reams of excel sheets. Clearly write your findings; use tables and charts as necessary. F.J.Srour (LAU) QBA 301 27 November 2013 3 / 13 Notes Notes Notes Assignment 5, Due 4 December, Start of Class Assignment 5, Due Start of Class, 4 December Assignment requires you to fill out a worksheet and solve the following four book problems: 1 13.93 2 14.9 3 14.37 4 14.75 NOTE: We will work on Problems 14.9 and 14.37 together in the lab on Friday. F.J.Srour (LAU) QBA 301 27 November 2013 4 / 13 Overview of Week Overview of Week Monday: Two-Factor ANOVA (on Quiz 2) Wednesday (Today): Two-Factor ANOVA, reviewed (on Quiz 2) Friday: In Computer Lab (Practice with ANOVA.) F.J.Srour (LAU) QBA 301 27 November 2013 5 / 13 Two-Factor ANOVA, Excel Example A survey was conducted wherein Americans aged between 37 and 45 were asked how many jobs they have held in their lifetimes. Also recorded were gender and educational attainment. Can we infer that differences exist between genders and educational levels? F.J.Srour (LAU) QBA 301 27 November 2013 6 / 13 Notes Notes Notes Two-Factor ANOVA, Excel Four Types of Hypotheses One-Way ANOVA H0: The means of all the groupings are equal. H1 : At least one mean differs. Differences between Levels of Factor A H0: The means of the a levels of factor A are equal. H1 : At least one mean differs. Differences between Levels of Factor B H0: The means of the b levels of factor B are equal. H1 : At least one mean differs. Test of Interaction between Factor A and Factor B H0: Factors A and B do not interact to affect the mean responses. H1 : Factors A and B do interact to affect the mean responses. F.J.Srour (LAU) QBA 301 27 November 2013 7 / 13 Two-Factor ANOVA, Excel One-Way ANOVA Results What can we conclude? Reject H0; There are differences. F.J.Srour (LAU) QBA 301 27 November 2013 8 / 13 Two-Factor ANOVA, Excel Overview of Two Factor Data Structure F.J.Srour (LAU) QBA 301 27 November 2013 9 / 13 Notes Notes Notes Two-Factor ANOVA, Excel Test for Differences in A and B and Interactions F.J.Srour (LAU) QBA 301 27 November 2013 10 / 13 Two-Factor ANOVA, Excel Four Test Statistics One-Way ANOVA F = MST MSE Differences between Levels of Factor A F = MS(A) MSE Differences between Levels of Factor B F = MS(B) MSE Test of Interaction between Factor A and Factor B F = MS(AB) MSE F.J.Srour (LAU) QBA 301 27 November 2013 11 / 13 Two-Factor ANOVA, Excel Example in Excel What can we conclude from the Two-Factor With Replication ANOVA in Excel? F.J.Srour (LAU) QBA 301 27 November 2013 12 / 13 Notes Notes Notes Two-Factor ANOVA, Excel Next Time In Lab F.J.Srour (LAU) QBA 301 27 November 2013 13 / 13 Notes Notes Notes