NormalIndPower.solve_power(effect_size=None, nobs1=None, alpha=None, power=None, ratio=1.0, alternative='two-sided') [source]

solve for any one parameter of the power of a two sample z-test

for z-test the keywords are:
effect_size, nobs1, alpha, power, ratio

exactly one needs to be None, all others need numeric values

  • effect_size (float) – standardized effect size, difference between the two means divided by the standard deviation. If ratio=0, then this is the standardized mean in the one sample test.
  • nobs1 (int or float) – number of observations of sample 1. The number of observations of sample two is ratio times the size of sample 1, i.e. nobs2 = nobs1 * ratio ratio can be set to zero in order to get the power for a one sample test.
  • alpha (float in interval (0,1)) – significance level, e.g. 0.05, is the probability of a type I error, that is wrong rejections if the Null Hypothesis is true.
  • power (float in interval (0,1)) – power of the test, e.g. 0.8, is one minus the probability of a type II error. Power is the probability that the test correctly rejects the Null Hypothesis if the Alternative Hypothesis is true.
  • ratio (float) – ratio of the number of observations in sample 2 relative to sample 1. see description of nobs1 The default for ratio is 1; to solve for ration given the other arguments it has to be explicitly set to None.
  • alternative (string, 'two-sided' (default), 'larger', 'smaller') – extra argument to choose whether the power is calculated for a two-sided (default) or one sided test. The one-sided test can be either ‘larger’, ‘smaller’.

value – The value of the parameter that was set to None in the call. The value solves the power equation given the remaining parameters.

Return type:



The function uses scipy.optimize for finding the value that satisfies the power equation. It first uses brentq with a prior search for bounds. If this fails to find a root, fsolve is used. If fsolve also fails, then, for alpha, power and effect_size, brentq with fixed bounds is used. However, there can still be cases where this fails.

© 2009–2012 Statsmodels Developers
© 2006–2008 Scipy Developers
© 2006 Jonathan E. Taylor
Licensed under the 3-clause BSD License.