pingouin.power_ttest

pingouin.
power_ttest
(d=None, n=None, power=None, alpha=0.05, contrast='twosamples', tail='twosided')[source] Evaluate power, sample size, effect size or significance level of a onesample Ttest, a paired Ttest or an independent twosamples Ttest with equal sample sizes.
 Parameters
 dfloat
Cohen d effect size
 nint
Sample size In case of a twosample Ttest, sample sizes are assumed to be equal. Otherwise, see the
power_ttest2n()
function. powerfloat
Test power (= 1  type II error).
 alphafloat
Significance level (type I error probability). The default is 0.05.
 contraststr
Can be “onesample”, “twosamples” or “paired”. Note that “onesample” and “paired” have the same behavior.
 tailstr
Indicates whether the test is “twosided” or “onesided”.
Notes
Exactly ONE of the parameters
d
,n
,power
andalpha
must be passed as None, and that parameter is determined from the others.For a paired Ttest, the sample size
n
corresponds to the number of pairs. For an independent twosample Ttest with equal sample sizes,n
corresponds to the sample size of each group (i.e. number of observations in one group). If the sample sizes are unequal, please use thepower_ttest2n()
function instead.Notice that
alpha
has a default value of 0.05 so None must be explicitly passed if you want to compute it.This function is a mere Python translation of the original pwr.t.test function implemented in the pwr package. All credit goes to the author, Stephane Champely.
Statistical power is the likelihood that a study will detect an effect when there is an effect there to be detected. A high statistical power means that there is a low probability of concluding that there is no effect when there is one. Statistical power is mainly affected by the effect size and the sample size.
The first step is to use the Cohen’s d to calculate the noncentrality parameter \(\delta\) and degrees of freedom \(v\). In case of paired groups, this is:
\[\delta = d * \sqrt n\]\[v = n  1\]and in case of independent groups with equal sample sizes:
\[\delta = d * \sqrt{\frac{n}{2}}\]\[v = (n  1) * 2\]where \(d\) is the Cohen d and \(n\) the sample size.
The critical value is then found using the percent point function of the T distribution with \(q = 1  alpha\) and \(v\) degrees of freedom.
Finally, the power of the test is given by the survival function of the noncentral distribution using the previously calculated critical value, degrees of freedom and noncentrality parameter.
scipy.optimize.brenth()
is used to solve power equations for other variables (i.e. sample size, effect size, or significance level). If the solving fails, a nan value is returned.Results have been tested against GPower and the R pwr package.
References
 1
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale,NJ: Lawrence Erlbaum.
 2
Examples
Compute power of a onesample Ttest given
d
,n
andalpha
>>> from pingouin import power_ttest >>> print('power: %.4f' % power_ttest(d=0.5, n=20, contrast='onesample')) power: 0.5645
Compute required sample size given
d
,power
andalpha
>>> print('n: %.4f' % power_ttest(d=0.5, power=0.80, tail='onesided')) n: 50.1508
Compute achieved
d
givenn
,power
andalpha
level
>>> print('d: %.4f' % power_ttest(n=20, power=0.80, alpha=0.05, ... contrast='paired')) d: 0.6604
Compute achieved alpha level given
d
,n
andpower
>>> print('alpha: %.4f' % power_ttest(d=0.5, n=20, power=0.80, alpha=None)) alpha: 0.4630