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## Within-subjects and between-subjects variance

Hi!

I'm looking for a way to distinguish the within-subjects variance from the between-subjects variance!
My data table looks like this:

Person 1 Value1 1
Person 1 Value2 2
Person 2 Value1 1
Person 2 Value2 2
Person 2 Value3 3
Person 2 Value4 4
Person 3 Value1 1
Person 3 Value2 2
Person 3 Value3 3
Person 4 Value1 1
Person 5 Value1 1
Person 5 Value2 2

What I tried was a "MANOVA" from the "Fit model" menu with "Value" as role variable Y and the two columns "Person" and "Number" as model effects, but it didn't work...
Who can help me out?
1 ACCEPTED SOLUTION

Accepted Solutions
Solution

## Re: Within-subjects and between-subjects variance

I have to respectfully disagree with the last response. Yes, the error mean square is an estimate of the within subjects variance, but the model mean square is not the estimate of the between subject variance.

There are a few ways to obtain the variance component estimates.

1. Using Fit Model, assign Person as a model effect. Highlight it, then select Attributes>Random Effect. Run the model. The variance components are part of the output. The Person Var Component is the between subject variance, and the Residual Var Comp is the within subject variance. Person needs to be nominal.

In the Fit Model dialog, you can choose between REML and EMS. The methods will be the same for balanced data. For unbalanced data, the one to use is REML.

2. Use Variability Chart. Again, Person should be nominal. Assign Person as the X, Grouping variable. After clicking OK, select Variance components from the red triangle menu. The variance components are output.
3 REPLIES 3

## Re: Within-subjects and between-subjects variance

Steffi

Under Fit Model, your model consists of simply person, and you would select Standard Least Squares.

THe between subject variance is the Model Mean Square from the Analysis of Variance table. The within subjects variance is the Error Mean Square.
Solution

## Re: Within-subjects and between-subjects variance

I have to respectfully disagree with the last response. Yes, the error mean square is an estimate of the within subjects variance, but the model mean square is not the estimate of the between subject variance.

There are a few ways to obtain the variance component estimates.

1. Using Fit Model, assign Person as a model effect. Highlight it, then select Attributes>Random Effect. Run the model. The variance components are part of the output. The Person Var Component is the between subject variance, and the Residual Var Comp is the within subject variance. Person needs to be nominal.

In the Fit Model dialog, you can choose between REML and EMS. The methods will be the same for balanced data. For unbalanced data, the one to use is REML.

2. Use Variability Chart. Again, Person should be nominal. Assign Person as the X, Grouping variable. After clicking OK, select Variance components from the red triangle menu. The variance components are output.

## Re: Within-subjects and between-subjects variance

Thanks. You are indeed correct, Jonathan!