Compare the odds ratio from logistic regression to 1. The model is of a continuous explanatory variable and a binary outcome variable. This calculator takes the group sizes as the inputs and calculates the effect size that the study has (1 - β) power to detect. The effect size is expressed as the minimum detectable odds ratio per 1 SD increase in the continuous explanatory variable. Closer to 1 is better, because it means your study is powered to pick up a smaller effect size. This calculator also allows an adjustment by variance inflation factor.

Instructions: Enter parameters in the green cells. Answers will appear in the blue box below.

N₁

Sample size, group 1

N₀

Sample size, group 0

ρ²

Multiple correlation coefficient squared

VIF

Variance inflation factor (see below)

α (two-tailed)

Threshold probability for rejecting the null hypothesis. Type I error rate.

β =

Probability of failing to reject the null hypothesis under the alternative hypothesis. Type II error rate.

VIF = Variance Inflation Factor = 1/(1-ρ²) = 1

N_1Eff = Effective sample size for Group 1 = N₁/VIF =

N_0Eff = Effective sample size for Group 0 = N₀/VIF =

DF = Degrees of freedom = N_1Eff + N_0Eff -2 =

T_α =

NCP = Non-centrality parameter = ncp(β, DF, T_α) =

E = Effect = NCP * √1/N_1Eff + 1/N_0Eff =

OR = exp(E) =

Odds ratio:

Reference:

Hsieh FY, Bloch DA, Larsen MD. A simple method of sample size calculation for linear and logistic regression. Stat Med. 1998;17(14):1623-34.

Chow S-C, Shao J, Wang H. Sample size calculations in clinical research. 2nd ed. Boca Raton: Chapman & Hall/CRC; 2008. Section 3.2.1, page 58.