Technical Protocol for the MEG Investigation
    Approved For Release 2001/03/07 : CIA-RDP96-00789ROO3000180010-9
    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 (HI) is true. Define the value of a dependent variable as X Then, given that the null
    hypothesis (HO) is true, a sigiiificant observation, Y, is defined as one in which the probability of observing
    x 2: go + I . 645or.,
    where V0 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:
     Z = @ - g 0)
    ao
    where x is the value of the dependent variable and [Lo 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 oft under Ho is zero. The mean and standard deviation of z under
    H, are ttAC and aAC, respectively.
    Approved For Release 2001/03/07 : CIA-RDP96-00789ROO3000180010-9
    15
    Figure 3. Normal Representation of Statistical Power

    
   Technical Protocol for the MEG Investigation
   Approved For Release 2001/03/07 : CIA-RDP96-00789ROO3000180010-9
   In general the effect size, F, may be defined as:
   Z (3)
   Fn
        where n is the sample size. Let FAC be the empirically derived effect size for anomalous cognition (AC).
        ThenzAC =lAAC in Figure 3 is computed from Equation 3. From Figure 3 we see that power is defined by:
        1 00-0.5 _JUAC 2
                 Power - CA C F2 7-r fe aAc dg. (4)
   ZC
   Let
       Z YAC
   aAC
   Then Equation 4 becomes
                    00
   Power e - 0.5Z2 dz9 where z', - ZC - YAC (5)
   f aAC
   ZPC
   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 powe4 P, then the number of trials required is given by:
                          n 4z2(P) (6)
   E2
   AC
   where FAC 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 z, 1. 645.
        1.0 - zc 1.645
        P 0.05
        0.8
   0.6-
   of 0.80 0.50 0.25 0.10 0.05
   0.4-
   0.2
   0.0----.
   1 10 100 1000
   I Trials I
   Figure 4. Statistical Power for Various Effect Sizes
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   Approved For Release 2001/03/07 : CIA-RDP96-00789ROO3000180010-9