CIA-RDP96-00789R003000260001-0

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Technical Protocol for the MEG Investigation
Approved For Release 2003/09/09 : CIA-RDP96-00789R003000260001-0
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:
(x - 10)
Z
=
where x is the value of the dependent variable and po and og 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
Họ
H1
Power
0
Zc
ZAC="AC
z-score
Figure 3. Normal Representation of Statistical Power
Approved For Release 2003/09/09 : CIA-RDP96-00789R003000260001-0
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Technical Protocol for the MEG Investigation
Approved For Release 2003/09/09 : CIA-RDP96-00789R003000260001-0
In general the effect size, 8, may be defined as:
€ = 1,
(3)
where n is the sample size. Let EAC be the empirically derived effect size for anomalous cognition (AC).
Then zAC=HAC in Figure 3 is computed from Equation 3. From Figure 3 we see that power is defined by:
Power =
1
ZC
1
00
e
S(5-MAC) 2
dy .
(4)
Let
z =
5-MAC
OAC
Then Equation 4 becomes
Power
1
00
-0.522 dz,
z'c
e
where z'e = 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)
CAC
(6)
where £AC 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
ef = 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 2003/09/09 : CIA-RDP96-00789R003000260001-0
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