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General Linear Model


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:

General Linear Model Decomposition of Scores

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
X26 = 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)


Comprehension Check

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?


© 2002-2006 by BurrtonWoodruff. All rights reserved. Modified Tuesday, September 26, 2006