Calculating Power and Determining a Required Sample Size
I. t - tests and Power
Step 1 (Regardless of the type of t-test) find t, n (overall sample size), mean difference (X1-X2).
s
Step 2 Find the standard deviation.
 X1  X 2
d' 
s 

Step 3 Find d’ :
X
1
 X2 n
t
d'
Or
t
n
Step 4 Find the Noncentrality Parameter (Delta):   d ' n (for single sample and repeated measures t)
n
  d'
For Independent Sample t
4
Step 5 Find the Power estimate (1- Beta) on the appropriate chart. (Rows = Delta, Columns = Alpha)
II. Any Statistic and N desired
Step 1 Determine the Power desired (e.g. between .80 and .90) and the alpha desired (typically .05)
Step 2 Find the Delta with respect to the desired power at a given alpha level.
Step 3 Find d’, either based on previous studies or your pilot data.
2

N desired   
Step 4 Calculate N desired :
(For Single Sample and Repeated Measures t)
 d '
:
2
   (For Independent Sample t & Anova, k = # of groups)
N desired  2( k ) 
 d '
III. Correlations and Power
Step 1 Find r and square it (r2) = represents the % variance in DV attributable to the IV
Step 2 Convert r2 to d’ :
2r
d'
1 r2


 N
 1 r 
 
Step 3 Calculate Delta (noncentrality parameter). :
2r
2
Step 4 Find the Power estimate (1- Beta) on the appropriate chart. (Rows = Delta, Columns = Alpha)
IV. Chi Square and Power
Step 1 Find X2 and n
Step 2 Compute the appropriate Phi Square Coefficient :
X2
If 2x3 or larger:  
N  K  1
X2
If 2x2 matrix :  
N
2
2
Step 3 Compute the noncentrality parameter :
 2 
 N
  
2 
1




Step 4 Find the Power estimate (1- Beta) on the appropriate chart. (Rows = Delta, Columns = Alpha)
V. Anova and Power
Step 1 Find F and n
Step 2 Convert to d’
d'
:
F
N
because
Step 3 Convert d’ to R2 (eta squared) :
F  t 2 (when you have 2 groups only)
 d' 

R2  
 d '2  4 
If more than 2 group R 2 
2
(Represents the % variance accounted for)
F ( df between )
( F ( df between )  ( df within )
 2r 

Step 4 Compute the noncentrality parameter:   
 1 r2 
k = # of groups
N
2( k )
Step 5 Find the Power estimate (1- Beta) on the appropriate chart. (Rows = Delta, Columns = Alpha)