Compare Three or More Means

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Presentation Description

This is a lecture on One Way Analysis of Variance for comparing three or more means. This lecture was organized by Alemi and is part of open online course at http://openonlinecourses.com/statistics

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One way ANALYSIS OF VARIANCE (ANOVA):

One way ANALYSIS OF VARIANCE (ANOVA) Farrokh Alemi, Ph.D. 1

Purpose of ANOVA:

One-way Two-way or Factorial Purpose of ANOVA 2

Why not do repeated t-tests?:

Multiple comparison problem 5 groups, 10 comparison of means Type one error is 0.29 not .05 Why not do repeated t-tests? 3

Framework for Hypothesis Testing:

Framework for Hypothesis Testing

Framework for Hypothesis Testing:

Framework for Hypothesis Testing

Test Assumptions:

Independent samples Independent observations within samples Dependent variable normally distributed Population variances are equal Test Assumptions 6

State Hypotheses:

H o :  1 =  2 =  3 =  4 H a : Not H o Any  1   2 or  2   3 or  1  3 will reject State Hypotheses 7 Always Two Sided Test

Calculate Test Statistics:

Calculate Test Statistics 8

Logic Behind the Test Statistic:

Partitioning of variance A. Between Group Variability B. Within Group Variability Logic Behind the Test Statistic 9

Total Sum of Squares:

Total Sum of Squares 10

Between Groups Sum of Squares:

Between Groups Sum of Squares 11

Within Groups Sum of Squares:

Within Groups Sum of Squares 12

Partitioning of Variance:

Partitioning of Variance 13

Calculating Test Statistics:

Calculating Test Statistics 14

Lookup P-Value:

Lookup P-Value 15

Reject or Fail to Reject:

α = .05 If F c > F α Reject H 0 If F c > F α Can not Reject H 0 Reject or Fail to Reject 16

Example:

Group 1: Patients in 4 West Group 2: Patients in 4 East Group 3: Patients in 3 Floor Example 17

Example :

Satisfaction Rating (0-10) Treatment Conditions (3 Groups) Example 18

Observations :

Observations 19

SS Within:

SS Within 20

SS Between:

SS Between 21

Sum of Squares Total:

Sum of Squares Total 22

Components of Variance:

Components of Variance 23

Degrees of Freedom:

Degrees of Freedom 24

Test Statistic:

Test Statistic 25

Lookup Critical Value:

Lookup Critical Value 26

Conclusion:

Conclusion 27

Take home lesson:

Take home lesson 28

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