statsmodels.stats.power.TTestIndPower.solve_power#

TTestIndPower.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 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

Parameters:

effect_sizeNone or float: standardized effect size, difference between the two means divided by the standard deviation. effect_size has to be positive.
nobs1None or 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
alphaNone or 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.
powerNone or 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.
ratioNone or float, optional: ratio of the number of observations in sample 2 relative to sample 1. see description of nobs1. ratio must be non-negative and not NaN. ratio can be set to zero in order to get the power of the one sample t-test with nobs1 observations (df = nobs1 - 1). This is a convention and not the limit of ratio going to zero: a ratio close to zero, e.g. 1e-9, means that sample 2 has almost no observations and the power is close to alpha. The default for ratio is 1; to solve for ratio given the other arguments it has to be explicitly set to None.
alternative{‘two-sided’, ‘larger’, ‘smaller’}, optional: 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’.

Returns:

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

Raises:

ValueError: If ratio is negative or NaN.

Notes

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. If these also fail to find a solution of the power equation, for example because it has no solution, a ConvergenceWarning is issued and nan is returned.

Changed in version 0.15.1: ratio=0 solves the power equation of the one sample t-test, it used to raise a ZeroDivisionError or to give wrong results. A negative or NaN ratio raises a ValueError, it used to return nan with a ConvergenceWarning.