FAQ/power/rmPow - CBU statistics Wiki

Upload page content

You can upload content for the page named below. If you change the page name, you can also upload content for another page. If the page name is empty, we derive the page name from the file name.

File to load page content from
Page name
Comment
Finzd thee wrang lelters ino eacuh wosrd

location: FAQ / power / rmPow

Spreadsheet and SPSS macro inputs

  • alpha is the likelihood of making a type I error (usually = 0.05)
  • etasq is partial $$\eta^text{2}$$/100 so, for example, 5.9% = 0.059

Partial $$\eta^text{2}$$ = $$ \frac{\mbox{SS(effect)}}{\mbox{SS(effect) + SS(its error)}}$$ where SS represents the sum of squares associated with a particular term in the anova.

In other words, partial $$\eta^text{2}$$ represents the proportion of variance in outcome predicted by the effect after adjusting for other terms in the anova. Click here for further details on partial $$\eta^text{2}$$ and here.

If the Sums of Squares are not available you canconstruct eta-squared.

  • num(erator) = df of term of interest = the product of the (number of levels of each factor -1) in term of interest

  • sum (B-1) = sum of dfs involving only between subject factors in the anova or zero otherwise. df = Product of number of levels minus 1 of each between subject factor in term of interest. e.g. For a three way interaction involving three between subject factors, abc, we sum the dfs of the six lower order combinations: ab, ac and bc, a, b and c to that of abc

  • Prod (W-1) = df of within subject effect if in term of interest or 1 otherwise. df = Product of number of levels minus 1 of each within subject factor in term of interest
  • Prod W = The product of all the ithin subject levels in term of interest
  • corr is the average correlation between levels of the repeated measures (=0 if no within subjects factors)
  • Total sample size

Example input

Power can be computed using an EXCEL spreadsheet or the SPSS syntax below. Power analysis software using Winer (1991, pp 136-138) for balanced anovas may be downloaded from here with details of how to compute inputs here.

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

DATA LIST free
/alpha num bsum wdf corr ntot rsq. 
BEGIN DATA. 
.05 2 1 2 0.0 60 0.0588
.05 2 1 2 0.3 67 0.0588
END DATA.
set errors=none. 
matrix.
get m /variables=alpha num bsum wdf corr ntot rsq  /missing=omit.
compute alpha=make(1,1,0).
compute num=make(1,1,0).
compute bsum=make(1,1,0).
compute wdf=make(1,1,0).
compute corr=make(1,1,0).
compute ntot=make(1,1,0).
compute rsq=make(1,1,0).
compute alpha=m(:,1).
compute num=m(:,2).
compute bsum=m(:,3).
compute wdf=m(:,4).
compute corr=m(:,5).
compute ntot=m(:,6).
compute rsq=(m:,7).  
end matrix.
compute denom = (ntot-1-bsum)*wdf.
COMPUTE power = 1 - NCDF.F(IDF.F(1-ALPHA,num,denom),num,denom,((NTOT-1-bsum)*wdf*RSQ/(1-RSQ))/(1-corr)).
EXE.
formats ntot (f7.0) alpha (f5.2) num (f5.2) denom (f5.2) corr
 (f5.2)rsq (f5.2) power (f5.2).
variable labels ntot 'Total Sample Size' /alpha 'Alpha' /num 'Numerator F' /denom 'Denominator F' /corr 'Correlation' /rsq 'R-squared' /power 'Power'.
report format=list automatic align(center)
  /variables=ntot alpha num denom corr rsq power 
  /title "ANOVA power, between subjects factor possibly in a mixed design for given total sample size" .

Reference

Doncaster CP and Davey AJH (2007) Analysis of covariance. How to choose and construct models for the life sciences. CUP:Cambridge.

Winer BJ, Brown DR and Michels KM (1991) Statistical principles in experimental design, 3rd edition. McGraw-Hill:New York.