• alpha is likelihood of making a type I error (usually = 0.05)
• etasq is partial eta-squared/100 so, for example, 5.9% = 0.059
• num(erator) is product over factors comprising term of interest of (numer of levels of factor -1)

• d1 is sum over the factors of (number of levels of between subject factor - 1)

• d2 is product over the factors of (number of levels of within subject factor - 1)

• ntot is the total sample size

Power can also be computed using a [attachment:aov.xls spreadsheet.]

[ COPY AND PASTE THE BOXED BELOW SYNTAX BELOW INTO A SPSS SYNTAX WINDOW AND RUN; ADJUST INPUT DATA AS REQUIRED]

DATA LIST free
/alpha etasq num d1 d2 ntot. 
BEGIN DATA.
.05 0.02 2 3 2 58 
.05 0.12 2 3 2 58
END DATA.
set errors=none. 
matrix.
get m /variables=alpha etasq num d1 d2 ntot /missing=omit.
compute alpha=make(1,1,0).
compute etasq=make(1,1,0).
compute num=make(1,1,0).
compute d1=make(1,1,0).
compute d2=make(1,1,0).
compute ntot=make(1,1,0).
compute alpha=m(:,1).
compute etasq=m(:,2).
compute num=m(:,3).
compute d1=m(:,4).
compute d2=m(:,5).
compute ntot=m(:,6).
end matrix.
compute denom=(ntot-d1-1)*d2.
COMPUTE power = 1 - NCDF.F(IDF.F(1-ALPHA,num,denom),num,denom,denom*etasq/(1-etasq)).
EXE.
formats alpha (f5.2) num (f5.2) denom (f5.2) etasq (f5.2) power (f5.2).
variable labels ntot 'Total Sample' /alpha 'Alpha' /num 'Numerator F' /denom 'Denominator F' /etasq 'Partial Eta-Sq' /power 'Power'.
report format=list automatic align(center)
  /variables=ntot alpha num denom etasq power 
  /title "ANOVA power (any anova)" .