Simple Cluster Random Assignment (CRA)¶

CRA2_2r¶

Assignment	Clustering Level	Treatment Assignment	Treatment Level	Cluster Effect
simple	2	cluster	2	random

[1]:

from pypowerup import effect_size, sample_size, power

[2]:

# effect size, i.e., minimum detectable effect sizes (MDES):
effect_size(design='cra2_2r', rho2=0.15, r21=0.40, r22=0.53, g=1, n=100, J=40,
           alpha=0.05, power=0.8, p=0.5)

[2]:

0.2502054873913746

[3]:

# sample_size, i.e., minimum required samples sizes (MRSS) for level 2 units.
sample_size(design='cra2_2r', es=0.2502054873913746, rho2=0.15, r21=0.40, r22=0.53,
            g=1, n=100, alpha=0.05, power=0.8, p=0.5)

[3]:

40.0

[4]:

# power
power(design='cra2_2r', es=0.2502054873913746, rho2=0.15, r21=0.40,
      r22=0.53, g=1, n=100, J=40, alpha=0.05, p=0.5)

[4]:

0.8000094900703394

Parameters for CRA2_2r

Parameters	`effect_size`	`sample_size`	`power`
design	✓	✓	✓
es		✓	✓
n	✓	✓	✓
J	✓		✓
power	✓	✓
alpha	✓	✓	✓
two_tailed	✓	✓	✓
p	✓	✓	✓
r21	✓	✓	✓
r22	✓	✓	✓
rho2	✓	✓	✓
g	✓	✓	✓

CRA3_3r¶

Assignment	Clustering Level	Treatment Assignment	Treatment Level	Cluster Effect
simple	3	cluster	3	random

[5]:

# effect size, i.e., minimum detectable effect sizes (MDES):
effect_size(design='cra3_3r', rho3=0.38, rho2=0.10, r21=0.37, r22=0.53,
            r23=0.87, g=1, n=20, J=2, K=66, alpha=0.05, power=0.8, p=0.5)

[5]:

0.19949475029929953

[6]:

# sample_size, i.e., minimum required samples sizes (MRSS) for level 3 units.
sample_size(design='cra3_3r', es=0.19949475029929953, rho3=0.38,
            rho2=0.10, r21=0.37, r22=0.53, r23=0.87, g=1, n=20, J=2,
            alpha=0.05, power=0.8, p=0.5)

[6]:

66.0

[7]:

# power
power(design='cra3_3r', es=0.19949475029929953, rho3=0.38, rho2=0.10, r21=0.37,
      r22=0.53, r23=0.87, g=1, n=20, J=2, K=66, alpha=0.05, p=0.5)

[7]:

0.8000043161361032

Parameters for CRA3_3r

Parameters	`effect_size`	`sample_size`	`power`
design	✓	✓	✓
es		✓	✓
n	✓	✓	✓
J	✓	✓	✓
K	✓		✓
power	✓	✓
alpha	✓	✓	✓
two_tailed	✓	✓	✓
p	✓	✓	✓
r21	✓	✓	✓
r22	✓	✓	✓
rho2	✓	✓	✓
r23	✓	✓	✓
rho3	✓	✓	✓
g	✓	✓	✓

CRA4_4r¶

Assignment	Clustering Level	Treatment Assignment	Treatment Level	Cluster Effect
simple	4	cluster	4	random

[8]:

# effect size, i.e., minimum detectable effect sizes (MDES):
effect_size(design='cra4_4r', rho4=0.05, rho3=0.05, rho2=0.10, r21=0.50, r22=0.50,
            r23=0.50, r24=0.50, g=1, n=10, J=2, K=3, L=20,
            alpha=0.05, power=0.8, p=0.5)

[8]:

0.29231230598875796

[9]:

# sample_size, i.e., minimum required samples sizes (MRSS) for level 4 units.
sample_size(design='cra4_4r', es=0.29231230598875796, rho4=0.05, rho3=0.05, rho2=0.10, r21=0.50, r22=0.50,
            r23=0.50, r24=0.50, g=1, n=10, J=2, K=3, alpha=0.05, power=0.8, p=0.5)

[9]:

20.0

[10]:

# power
power(design='cra4_4r', es=0.29231230598875796, rho4=0.05, rho3=0.05, rho2=0.10, r21=0.50, r22=0.50,
            r23=0.50, r24=0.50, g=1, n=10, J=2, K=3, L=20, alpha=0.05, p=0.5)

[10]:

0.800046080238779

Parameters for CRA4_4r

Parameters	`effect_size`	`sample_size`	`power`
design	✓	✓	✓
es		✓	✓
n	✓	✓	✓
J	✓	✓	✓
K	✓	✓	✓
L	✓		✓
power	✓	✓
alpha	✓	✓	✓
two_tailed	✓	✓	✓
p	✓	✓	✓
r21	✓	✓	✓
r22	✓	✓	✓
rho2	✓	✓	✓
r23	✓	✓	✓
rho3	✓	✓	✓
r24	✓	✓	✓
rho4	✓	✓	✓
g	✓	✓	✓