Simple Individual Random Assignment (IRA)

Assignment	Clustering Level	Treatment Assignment	Treatment Level	Cluster Effect
simple	1	individual	1	NA

from pypowerup import effect_size, power, sample_size

# effect size, i.e., minimum detectable effect sizes (MDES):
effect_size(design='ira', n=787, power=0.8, alpha=0.05, two_tailed=True, p=0.5, r21=0, g=0)

0.19997988869985736

# sample size, i.e., minimum required samples sizes (MRSS):
sample_size(design='ira', es=0.2, power=0.8, alpha=0.05, two_tailed=True, p=0.5, r21=0, g=0)

787.0

# power
power(design='ira', es=0.2, n=787, alpha=0.05, two_tailed=True, p=0.5, r21=0, g=0)

0.8000799952735076

Parameters for IRA

Parameters	effect_size	sample_size	power
design	✓	✓	✓
es		✓	✓
n	✓		✓
power	✓	✓
alpha	✓	✓	✓
two_tailed	✓	✓	✓
p	✓	✓	✓
r21	✓	✓	✓
g	✓	✓	✓

Output validation with statsmodels

Here we used statsmodels with the same parameters to validate our model results. Note nobs1 in statsmodels is the sample size for treatment group, which is half of the total sample size output from our model. Thus, we define nobs1=787/2=393.5 in the models beflow.

from statsmodels.stats.power import TTestIndPower

# effect size
analysis = TTestIndPower()
analysis.solve_power(power=0.8, nobs1=393.5, ratio=1, alpha=0.05, alternative='two-sided')

0.19997768751017836

# sample size (statsmodels output treatment sample size only, which is the half of our computed total sample size)
analysis.solve_power(0.2, power=0.8, nobs1=None, ratio=1, alpha=0.05,alternative='two-sided')

393.4056989990335

# power
analysis.solve_power(0.2, nobs1=393.5, ratio=1.0, alpha=0.05, alternative='two-sided')

0.8000942129794306

With the same parameters, we get the same results as the statsmodels. However, statsmodels does not do power analysis for more complicated designs, which we will cover next.