V REVIEW OF STATISTICAL POWER

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Document Number (FOIA) /ESDN (CREST): 
CIA-RDP96-00789R003000260001-0
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RIFPUB
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U
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2
Document Creation Date: 
November 4, 2016
Document Release Date: 
September 5, 2003
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1
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Publication Date: 
January 1, 1993
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RP
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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 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