statsmodels.stats.power.tt_ind_solve_power(effect_size=None, nobs1=None, alpha=None, power=None, ratio=1.0, alternative='two-sided')

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

for t-test the keywords are:

effect_size, nobs1, alpha, power, ratio

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


standardized effect size, difference between the two means divided by the standard deviation. effect_size has to be positive.

nobs1int 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

alphafloat 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.

powerfloat 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 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 ratio given the other arguments it has to be explicitly set to None.

alternativestr, ‘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’.


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


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.

Last update: Dec 14, 2023