REVIEW OF STATISTICAL POWER

• Document Type: CREST
• Collection: STARGATE
• Document Number (FOIA) /ESDN (CREST): CIA-RDP96-00789R003000180010-9
• Release Decision: RIFPUB
• Original Classification: U
• Document Page Count: 2
• Document Creation Date: November 4, 2016
• Document Release Date: October 20, 1998
• Sequence Number: 10
• Publication Date: June 1, 1993
• Content Type: RP

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 (Hl) is true. Define the value of a dependent variable asx Then, given that the null
hypothesis (Hp) is true, a significant observation, Y, is defined as one in which the probability of observing
x ? u0 + 1 . 645c0,
where z0 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:
where x is the value of the dependent variable and ?o and oo are the mean and standard deviation, re-
spectively, of the parent distribution under H0, and .zz 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 ItAC and 0AC, respectively.
H1
5%ofArea
Power I
Figure 3. Normal Representation of Statistical Power
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Approved For Release 2001/03/07 : CIA-RDP96-00789R003000180010-9
 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:
(3)
where n is the sample size. Let EAC be the empirically derived effect size for anomalous cognition (AC).
ThenzAC =IAAC in Figure 3 is computed from Equation 3. From Figure 3 we see that power is defined by:
r I -0.5(5 I AC)z
Power = aAC e o'AC dg. (4)
1 1
zC
Z = 5 - 'UAC
CTAC
Then Equation 4 becomes
00
1 e -0.5i dz'
+.,Lo- a' ZC - /LAC
(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 powel P, then the number of trials required is given by:
4z2(P)
Ez
AC
(6)
where sAC 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 zz = 1.645.
Figure 4. Statistical Power for Various Effect Sizes
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Approved For Release 2001/03/07 : CIA-RDP96-00789R003000180010-9