Compare Three or More Means

Category: Education

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


Presentation Transcript


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


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 27

Take home lesson:

Take home lesson 28

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