Technical Protocol for the MEG Investigation
Approved For Release 2001/03/07 : CIA-RDP96-00789ROO3000180010-9
V REVIEW OF STATISTICAL POWER
The power of a statistical measure is defined as the probability of a significant observation given that an
effect hypothesis (HI) is true. Define the value of a dependent variable as X Then, given that the null
hypothesis (HO) is true, a sigiiificant observation, Y, is defined as one in which the probability of observing
x 2: go + I . 645or.,
where V0 and ao are the mean and standard deviation of the parent Ho distribution, is less than or equal
to 0.05.
Figure 3 shows these definitions in graphical form under the assumption of normality. The Z-Score is a
normalized representation of the dependent variable and is given by:
Z = @ - g 0)
ao
where x is the value of the dependent variable and [Lo and oo are the mean and standard deviation, re-
spectively, of the parent distribution under H0, and z, is the minimum value (i.e., 1.645) required for
significance (one-tailed). The mean oft under Ho is zero. The mean and standard deviation of z under
H, are ttAC and aAC, respectively.
Approved For Release 2001/03/07 : CIA-RDP96-00789ROO3000180010-9
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Figure 3. Normal Representation of Statistical Power
Technical Protocol for the MEG Investigation
Approved For Release 2001/03/07 : CIA-RDP96-00789ROO3000180010-9
In general the effect size, F, may be defined as:
Z (3)
Fn
where n is the sample size. Let FAC be the empirically derived effect size for anomalous cognition (AC).
ThenzAC =lAAC in Figure 3 is computed from Equation 3. From Figure 3 we see that power is defined by:
1 00-0.5 _JUAC 2
Power - CA C F2 7-r fe aAc dg. (4)
ZC
Let
Z YAC
aAC
Then Equation 4 becomes
00
Power e - 0.5Z2 dz9 where z', - ZC - YAC (5)
f aAC
ZPC
For planning purposes, it is convenient to invert Equation 5 to determine the number of trials that are
necessary to achieve a given power under the H1 hypothesis. If we define z.(P) to be the z-score asso-
ciated with a powe4 P, then the number of trials required is given by:
n 4z2(P) (6)
E2
AC
where FAC is the estimated mean value for the effect size under HI. Figure 4 shows the power, calcu-
lated from Equation 5, for various effect sizes for z, 1. 645.
1.0 - zc 1.645
P 0.05
0.8
0.6-
of 0.80 0.50 0.25 0.10 0.05
0.4-
0.2
0.0----.
1 10 100 1000
I Trials I
Figure 4. Statistical Power for Various Effect Sizes
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Approved For Release 2001/03/07 : CIA-RDP96-00789ROO3000180010-9