Power Formula

Power is implemented as follows:

To calculate base size for one mean

Variables input:

Z_α/2	Confidence level
Z_β	Power
σ	Standard Deviation
diff	Difference to detect

Compute the base size needed:

To calculate base size for two dependent means

Variables input:

Z_α/2	Confidence level
Z_β	Power
σ	Standard Deviation
diff	Difference to detect

Compute the base size needed:

To calculate base size for two independent means

Variables input:

Z_α/2	Confidence level
Z_β	Power
σ₁	Standard Deviation for Group 1
σ₂	Standard Deviation for Group 2
diff	Difference to detect

Compute the base size needed:

To calculate base size for one proportion

Variables input:

Z_α/2	Confidence level
Z_β	Power
p	Proportion selecting
Difference	Difference to detect

Compute the base size needed:

Note that the statistical procedure that estimates sample size for one proportion for a given beta uses the normal approximation of the binomial, and not the exact binomial test.

To calculate base size for two proportions

Variables input:

Z_α/2	Confidence level
Z_β	Power
p₁	Proportion selecting Group 1
p₂	Proportion selecting Group 2
k	Relative size of Base 2 to Base 1