Here's a simulated data set from the reaction time experiment testing how long it takes to identify whether or not two figures are the same when one of them is rotated 0, 45 or 90 degrees. The dependent variable is the number of milliseconds to correctly press the "same" key. [The trials where the stimuli are different are not included in this analysis].
Each score can be decomposed into the sum of three components:
Subject Number

Group 1
0 deg rotation 
Group 2
45 deg rotation 
Group 3
90 deg rotation 
1

192  199  260 
2

199  211  242 
3

177  201  260 
4

202  218  244 
5

215  209  241 
6

205  211  236 
7

180  218  243 
Group Mean

195.71  209.57  246.57 
The mean of all 21 scores = 217.28. This is called the "Overall Mean"


(alpha)_{i
}aka
"Group Deviation" 
21.57  7.714  29.285 
Any score =

+ Overall Mean

+ Group Deviation

+ Error

X_{26} = 211 =

+ 217.28

+ (7.714)

+(1.485)

Any Score = 
The mean of all the scores +

How far the group mean is from the overall mean +

How far the observation is from the group mean

Note: You can download a Microsoft Excel spreadsheet that lays out this information (anovaglm.xls)
1. What are the three parts that make up an observation in an ANOVA data set?
2. In a data set the average of all the scores is 218.23. The mean of Group 2 is 209.85. One observation in Group 2 is 215.
What is the deviation of the group mean from the overall mean?
What is the deviation of the observation from the group mean?
3. In another data set the average of all the scores is 213.52. The Group mean is 29.09 units from the grand mean; the observation is 12.42 units below the group mean. What is the value of the observation?
© 20022006 by BurrtonWoodruff. All rights reserved. Modified