CIA-RDP96-00789R003000180010-9

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Technical Protocol for the MEG Investigation
Approved For Release 2001/03/07 : CIA-RDP96-00789R003000180010-9
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 (H1) is true. Define the value of a dependent variable as X. Then, given that the null
hypothesis (Ho) is true, a significant observation, x, is defined as one in which the probability of observing
x ≥ 10 + 1.64500,
where po and og 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
(x - Mo)
where x is the value of the dependent variable and po and oo are the mean and standard deviation, re-
spectively, of the parent distribution under Ho, and z is the minimum value (i.e., 1.645) required for
significance (one-tailed). The mean of z under Ho is zero. The mean and standard deviation of z under
H1 are HAC and OAC, respectively.
5% of Area
Ho
H1
Power
0
Zc
ZAC=PAC
z-score
Figure 3. Normal Representation of Statistical Power
Approved For Release 2001/03/07 : CIA-RDP96-00789R003000180010-9
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Technical Protocol for the MEG Investigation
Approved For Release 2001/03/07 : CIA-RDP96-00789R003000180010-9
In general the effect size, E, may be defined as:
€ = 7,
n
(3)
where n is the sample size. Let &AC be the empirically derived effect size for anomalous cognition (AC).
ThenzAC="AC in Figure 3 is computed from Equation 3. From Figure 3 we see that power is defined by:
Power = 1
GAC V2x
e
zc
8
-0.5 (5-MAC)2
O AC
dç .
(4)
Let
z = 5 - MAC
GAC
Then Equation 4 becomes
Power = 1
/2TL
1.
z'c
e
00
-0.5z"dz,
where z'a = OAC
Za- MAC
(5)
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 power, P, then the number of trials required is given by:
n = 42(P)
4z2(P)
E AC
(6)
where EAC is the estimated mean value for the effect size under H1. 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
Probability of Significant Result
0.8
0.6
0.80
0.50
0.25
0.10
0.05
0.4
0.2
0.0
1
10
100
1000
Trials
Figure 4. Statistical Power for Various Effect Sizes
Approved For Release 2001/03/07 : CIA-RDP96-00789R003000180010-9
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