Example 5: Power Calculation in a 1Way Repeated Measures ANOVA
In a 1way repeated measures ANOVA, you have the choice of analyzing
the data with a univariate or multivariate approach. In this example,
we show how to calculate power for the univariate Ftest.
Suppose that a group of N = 10 subjects are observed performing a task
on p = 6 different occasions. In this subjects by trials design, the degrees
of freedom are p 1 and (N  1)(p  1). However, the noncentrality parameter
δ must be adjusted, because the repeated measures are generally correlated.
Estimation, a priori, of this
noncentrality parameter requires that you specify a value for the RMSSE,
assume a common correlation between the various trial occasions as well
as a common variance, and provide an estimate of this common correlation,
ρ.
The noncentrality parameter is then given by
δ = (N(p
1)RMSSE2) / 1  r 

(6) 
Suppose that, in this case, the RMSSE is assumed to be .30, and the
common correlation is .50. Then δ
may be computed easily as
δ = (10(6
1).302) / 1  .50 = 4.5 / .50 = 9
Ribbon
bar. Select the Statistics
tab. In the Advanced/Multivariate
group, click Power Analysis to
display the Power Analysis and Interval
Estimation Startup Panel.
Classic
menus. From the Statistics
menu, select Power Analysis to
display the Power Analysis and Interval
Estimation Startup Panel.
In the Startup Panel, select Probability
Distributions and Noncentral F
Distribution.
Click the OK button to display
the Noncentral F Probability
Calculator dialog box.
First, compute the critical value of F
used for the significance test. The degrees of freedom are 5 and 45; therefore,
enter 5 in the Numerator
df field and 45 in the
Denom. df field. Then select the
(1  Cumulative p) check box,
and enter a value of .05
in the 1  Cum. p field. This
is the significance level for the Ftest.
Next, in the Compute group box,
select the F option button as
the quantity to compute. The dialog box should now look like this:
Click the Compute button to
calculate the critical value of F.
A value of 2.422085 is produced
as the Observed F.
To compute power, we need to compute the probability of obtaining a
value higher than the critical value of F,
when the degrees of freedom are 5 and 45, and the Delta
is the previously calculated value of 9. Simply enter 9
in the Delta
field, and select 1  p
as the quantity to compute in the Compute group box. The dialog box should look
like this:
To compute power, click the Compute
button and observe the value for 1 
Cum. p.
In this case, it seems the power is somewhat less than adequate, only
about .56.
See also, Power Analysis
 Index.