Technical Protocol for the MEG investigation
Approved For Release 2003/09/09 : CIA-RDP96-00789ROO3000260001-0
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 (141) is true. Define the value of a dependent variable as X Then, given that the null
hypothesis (HO) is true, a significant observation, Y, is defined as one in which the probability of observing
x ;@- po + 1 . 645co,
where V0 andoo 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 - U 0)
Z Oro
where x is the value of the dependent variable and go 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 ofz under Ho is zero. The mean and standard deviation of z under'
H, are tLAC and oAG respectively.
Approved For Release 2003/09/09: CIA-RDP96-00789ROO3000260001-0 15
Figure 3. Normal Representation ot Statistical rower
Technical Protocol for the MEG Investigation
Approved For Release 2003/09/09 : CIA-RDP96-00789ROO3000260001-0
In general the effect size, F, may be defined as:
Z (3)
where n is the sample size. Let eAC be the empirically derived effect size for anomalous cognition (AC).
Then zAC =ItAc in Figure 3 is computed from Equation 3. From Figure 3 we see that power is defined by:
1 00 - 0_5 97 - YAC2
Power = aAC Fa- f e aAC (4)
ZC
Let
Z PAC
OAC
Then Equation 4 becomes
OD
Power e'- 0_5Z2 dz, where z', = ZC JUAC (5)
f O'AC
Z1C
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 HI 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 CAC 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 zc 1. 645.
1.0 zc 1.645
p 0.05
W '0.8
0.6
CO
"6
-&I ef 0.80 0.25 0.10
0.50 0.05
0.4
0.2
0.0 E_
10 100 1000
Trials
Figure 4. Statistical Power for Various Effect Sizes
Approved For Release 2003/09/09 : CIA-RDP96-00789ROO3000260001-0 16