zrmacc/Power

Examples of power calculations.

Linear Regression

Consider the linear model: $Y = X\beta_{X} + Z\beta_{Z} + \epsilon$. Suppose each of X, Y, and Z has been centered to have mean zero. The function PowerLinReg determines the power to reject $H_{0}:\beta_{X} = 0$ via the standard Wald test. For example:

library(Power)
PowerLinReg(
  beta_x = 1,
  cov_xz = 0.5,
  n = 10,
  t1e = 0.05,
  var_resid = 1,
  var_x = 1,
  var_z = 1
)

## [1] 0.781908

Here beta_x is the true coefficient for X, cov_xz is the covariance between X and Z, n is the sample size, t1e is the type I error, var_resid is the residual variance of $Y|(X,Z)$, i.e. the variance of $\epsilon$, var_x and var_y are the variance of X and Y. Note that when either X or Z is a vector, rather than a scalar, cov_xz, var_x, and var_z should be supplied as matrices.

To determine the necessary sample size for a target power:

SampleSizeLinReg(
  beta_x = 1,
  cov_xz = 0.5,
  max_n = 100,
  power = 0.90,
  t1e = 0.05,
  var_resid = 1,
  var_x = 1,
  var_z = 1
)

##    n     power
## 1 15 0.9183621

Here max_n is an upper bound on the sample size, and power is the target power.