Introduction to Analysis of Variance: The LOGIC of ANOVA Suppose an employer wants to evaluate how long it takes his employees to perform a typing task. He knows that his company has three levels of training: Beginner, Intermediate, and Advanced Typing. He would like to know if these groups differ in the amount of time it takes them to type a paragraph of text. Below are the results. BEGINNER INTERMEDIATE ADVANCED 16 sec 15 sec 14 sec

Introduction to Analysis of Variance: The LOGIC of ANOVA Suppose an employer wants to evaluate how long it takes his employees to perform a typing task. He knows that his company has three levels of training: Beginner, Intermediate, and Advanced Typing. He would like to know if these groups differ in the amount of time it takes them to type a paragraph of text. Below are the results. BEGINNER INTERMEDIATE ADVANCED 16 sec 8 sec 2 sec

Calculation of ANOVA (The F statistic):

Experimental example Student Mean performance Effect of stress on measured intelligence. Or performance on an intelligence test. (a=.05) The Data With Alone 2 3 Help tasks tasks 110 109 101 111 121 119 112 121 115 114 113 116 IQ scores

H1: There is an effect of stress on measured intelligence. H0: There is no effect of stress on measured intelligence. Critical Value: ANOVA has TWO degrees of freedom terms. dfnumerator = k-1 dfdenominator= N-k Where k = the number of groups and N = total number of people in whole experiment Critical Value: From F-table: Fcrit(3,8) = 4.07 (alpha=.05) Obtained Statistic:

Calculation example X =115.33 SS1 114.00 108.67 60.67 SS2 50.00 116.00 With Alone 2 3 Help tasks tasks 110 109 101 111 121 119 112 121 115 114 113 116   With Alone 2 3 Help tasks tasks 110 109 101 111 121 119 112 121 115 114 113 116 108.67 116.00 SS2 50.00 SS3 88.67 SS4 50.00 X =115.33 114.00 SS1 60.67

Calculation example X =115.33 SS1 114.00 108.67 60.67 SS2 50.00 116.00 With Alone 2 3 Help tasks tasks 110 109 101 111 121 119 112 121 115 114 113 116   With Alone 2 3 Help tasks tasks 110 109 101 111 121 119 112 121 115 114 113 116 108.67 116.00 SS2 50.00 SS3 88.67 SS4 50.00 X =115.33 114.00 SS1 60.67

Calculation example Fcrit(3,8) = 4.07 With Alone 2 3 Help tasks tasks 110 109 101 111 121 119 112 121 115 114 113 116   With Alone 2 3 Help tasks tasks 110 109 101 111 121 119 112 121 115 114 113 116 Fcrit(3,8) = 4.07 Decision: Retain the null hypothesis.

“Unplanned comparisons” One-Way ANOVA: POST-HOC tests “Unplanned comparisons” If and only if our ANOVA is significant, we conduct a post-hoc test. In this class, we will use Tukey’s post-hoc test. Example Data: Splenda Equal Sweet & Low 3 6 4 1 2 5 7