V REVIEW OF STATISTICAL POWER

• Document Type: CREST
• Collection: STARGATE
• Document Number (FOIA) /ESDN (CREST): CIA-RDP96-00789R003000260001-0
• Release Decision: RIFPUB
• Original Classification: U
• Document Page Count: 2
• Document Creation Date: November 4, 2016
• Document Release Date: September 5, 2003
• Sequence Number: 1
• Publication Date: January 1, 1993
• Content Type: RP

Technical Protocol for the MEG Investigation
Approved For Release 2003/09/09 : CIA-RDP96-00789R003000260001-0
V REVIEW OF STATISTICAL POWER
z-score
Figure 3. Normal Representation of Statistical Power
The power of a statistical measure is defined as the probability of a significant observation given that an
effect hypothesis (Ht) is true. Define the value of a dependent variable asX Then, given that the null
hypothesis (Ho) is true, a significant observation, x is defined as one in which the probability of observing
x ?_ go + 1 . 645c0,
where iro 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:
(x - fro)
ao '
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 zc 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
Ht are PAC and oAC, respectively.
5% of Area
Power I
Approved For Release 2003/09/09 : CIA-RDP96-00789R003000260001-0
 Technical Protocol for the MEG Investigation
Approved For Release 2003/09/09 : CIA-RDP96-00789R003000260001-0
In general the effect size, s, may be defined as:
8 = (3)
where n is the sample size. Let EAC be the empirically derived effect size for anomalous cognition (AC).
Then zAC =IrAC in Figure 3 is computed from Equation 3. From Figure 3 we see that power is defined by:
1
e GAc d5.
Power = L=
Then Equation 4 becomes
-031 c-/'AC1
Power = - I e'- 0.5Z2 dz,
where z', _ z -/2AC
QAC
(4)
(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 Hl 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:
4z2(P)
n = EZ AC
(6)
where CAC is the estimated mean value for the effect size under Hl. 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
Approved For Release 2003/09/09 : CIA-RDP96-00789R003000260001-0 16