Blocked (Stratified) Cluster Randomized Assignment (BCRA)¶
BCRA3_2f¶
| Assignment | Clustering Level | Treatment Assignment | Treatment Level | Cluster Effect |
|---|---|---|---|---|
| blocked | 3 | cluster | 2 | fixed |
[1]:
from pypowerup import effect_size, sample_size, power
[2]:
# effect size, i.e., minimum detectable effect sizes (MDES)
effect_size(design='bcra3_2f', rho2=0.10, r21=0.50, r22=0.50, g=1, n=20, J=44, K=5)
[2]:
0.10219354337360606
[3]:
# sample_size, i.e., minimum required samples sizes (MRSS) for level 3 units
sample_size(design='bcra3_2f', es=0.10219354337360606, rho2=0.10, r21=0.50, r22=0.50, g=1, n=20, J=44)
[3]:
5.0
[4]:
# power
power(design='bcra3_2f', es=0.10219354337360606, rho2=0.10, r21=0.50, r22=0.50, g=1, n=20, J=44, K=5)
[4]:
0.8000016066584502
| Parameters | effect_size |
sample_size |
power |
|---|---|---|---|
| design | ✓ | ✓ | ✓ |
| es | ✓ | ✓ | |
| n | ✓ | ✓ | ✓ |
| J | ✓ | ✓ | ✓ |
| K | ✓ | ✓ | |
| power | ✓ | ✓ | |
| alpha | ✓ | ✓ | ✓ |
| two_tailed | ✓ | ✓ | ✓ |
| p | ✓ | ✓ | ✓ |
| r21 | ✓ | ✓ | ✓ |
| rho2 | ✓ | ✓ | ✓ |
| r22 | ✓ | ✓ | ✓ |
| g | ✓ | ✓ | ✓ |
BCRA3_2r¶
| Assignment | Clustering Level | Treatment Assignment | Treatment Level | Cluster Effect |
|---|---|---|---|---|
| blocked | 3 | cluster | 2 | random |
[5]:
# effect size, i.e., minimum detectable effect sizes (MDES)
effect_size(design='bcra3_2r', rho3=0.38, rho2=0.10, omega3=0.50, r21=0.37,
r22=0.53, r2t3=0, g=0, n=20, J=2, K=64)
[5]:
0.20020041517111645
[6]:
# sample_size, i.e., minimum required samples sizes (MRSS) for level 3 units
sample_size(design='bcra3_2r', es=0.20020041517111645, rho3=0.38, rho2=0.10, omega3=0.50, r21=0.37,
r22=0.53, r2t3=0, g=0, n=20, J=2)
[6]:
64.0
[7]:
# power
power(design='bcra3_2r', es=0.20020041517111645, rho3=0.38, rho2=0.10, omega3=0.50, r21=0.37,
r22=0.53, r2t3=0, g=0, n=20, J=2, K=64)
[7]:
0.8000043161361032
| Parameters | effect_size |
sample_size |
power |
|---|---|---|---|
| design | ✓ | ✓ | ✓ |
| es | ✓ | ✓ | |
| n | ✓ | ✓ | ✓ |
| J | ✓ | ✓ | ✓ |
| K | ✓ | ✓ | |
| power | ✓ | ✓ | |
| alpha | ✓ | ✓ | ✓ |
| two_tailed | ✓ | ✓ | ✓ |
| p | ✓ | ✓ | ✓ |
| r21 | ✓ | ✓ | ✓ |
| rho2 | ✓ | ✓ | ✓ |
| r22 | ✓ | ✓ | ✓ |
| r2t3 | ✓ | ✓ | ✓ |
| rho3 | ✓ | ✓ | ✓ |
| omega3 | ✓ | ✓ | ✓ |
| g | ✓ | ✓ | ✓ |
BCRA4_2r¶
| Assignment | Clustering Level | Treatment Assignment | Treatment Level | Cluster Effect |
|---|---|---|---|---|
| blocked | 4 | cluster | 2 | random |
[8]:
# effect size, i.e., minimum detectable effect sizes (MDES)
effect_size(design='bcra4_2r', rho4=0.05, rho3=0.15, rho2=0.15, omega4=0.5, omega3=0.5, r21=0.5, r22=0.5,
r2t3=0.5, r2t4=0.5, g=0, n=10, J=4, K=4, L=20)
[8]:
0.14584081061169768
[9]:
# sample_size, i.e., minimum required samples sizes (MRSS) for level 4 units
sample_size(design='bcra4_2r', es=0.14584081061169768, rho4=0.05, rho3=0.15, rho2=0.15, omega4=0.5, omega3=0.5, r21=0.5, r22=0.5,
r2t3=0.5, r2t4=0.5, g=0, n=10, J=4, K=4)
[9]:
20.0
[10]:
# power
power(design='bcra4_2r', es=0.14584081061169768, rho4=0.05, rho3=0.15, rho2=0.15, omega4=0.5, omega3=0.5, r21=0.5, r22=0.5,
r2t3=0.5, r2t4=0.5, g=0, n=10, J=4, K=4, L=20)
[10]:
0.8000357933435768
| Parameters | effect_size |
sample_size |
power |
|---|---|---|---|
| design | ✓ | ✓ | ✓ |
| es | ✓ | ✓ | |
| n | ✓ | ✓ | ✓ |
| J | ✓ | ✓ | ✓ |
| K | ✓ | ✓ | ✓ |
| L | ✓ | ✓ | |
| power | ✓ | ✓ | |
| alpha | ✓ | ✓ | ✓ |
| two_tailed | ✓ | ✓ | ✓ |
| p | ✓ | ✓ | ✓ |
| r21 | ✓ | ✓ | ✓ |
| rho2 | ✓ | ✓ | ✓ |
| r22 | ✓ | ✓ | ✓ |
| rho3 | ✓ | ✓ | ✓ |
| omega3 | ✓ | ✓ | ✓ |
| r2t3 | ✓ | ✓ | ✓ |
| rho4 | ✓ | ✓ | ✓ |
| omega4 | ✓ | ✓ | ✓ |
| r2t4 | ✓ | ✓ | ✓ |
| g | ✓ | ✓ | ✓ |
BCRA4_3f¶
| Assignment | Clustering Level | Treatment Assignment | Treatment Level | Cluster Effect |
|---|---|---|---|---|
| blocked | 4 | cluster | 3 | fixed |
[11]:
# effect size, i.e., minimum detectable effect sizes (MDES)
effect_size(design='bcra4_3f', rho3=0.15, rho2=0.15, r21=0.5, r22=0.5,
r23=0.5, g=2, n=10, J=4, K=4, L=15)
[11]:
0.2399780453218905
[12]:
# sample_size, i.e., minimum required samples sizes (MRSS) for level 4 units
sample_size(design='bcra4_3f', es=0.2399780453218905, rho3=0.15, rho2=0.15, r21=0.5, r22=0.5,
r23=0.5, g=2, n=10, J=4, K=4)
[12]:
15.0
[13]:
# power
power(design='bcra4_3f', es=0.2399780453218905, rho3=0.15, rho2=0.15, r21=0.5, r22=0.5,
r23=0.5, g=2, n=10, J=4, K=4, L=15)
[13]:
0.8000158353898167
| Parameters | effect_size |
sample_size |
power |
|---|---|---|---|
| design | ✓ | ✓ | ✓ |
| es | ✓ | ✓ | |
| n | ✓ | ✓ | ✓ |
| J | ✓ | ✓ | ✓ |
| K | ✓ | ✓ | ✓ |
| L | ✓ | ✓ | |
| power | ✓ | ✓ | |
| alpha | ✓ | ✓ | ✓ |
| two_tailed | ✓ | ✓ | ✓ |
| p | ✓ | ✓ | ✓ |
| r21 | ✓ | ✓ | ✓ |
| rho2 | ✓ | ✓ | ✓ |
| r22 | ✓ | ✓ | ✓ |
| rho3 | ✓ | ✓ | ✓ |
| r23 | ✓ | ✓ | ✓ |
| g | ✓ | ✓ | ✓ |
BCRA4_3r¶
| Assignment | Clustering Level | Treatment Assignment | Treatment Level | Cluster Effect |
|---|---|---|---|---|
| blocked | 4 | cluster | 3 | random |
[14]:
# effect size, i.e., minimum detectable effect sizes (MDES)
effect_size(design='bcra4_3r', rho4=0.05, rho3=0.15, rho2=0.15, omega4=0.5,
r21=0.5, r22=0.5, r23=0.5, r2t4=0.5, g=3, n=10, J=4, K=20, L=20)
[14]:
0.12100407246925271
[15]:
# sample_size, i.e., minimum required samples sizes (MRSS) for level 4 units
sample_size(design='bcra4_3r', es=0.12100407246925271, rho4=0.05, rho3=0.15, rho2=0.15, omega4=0.5,
r21=0.5, r22=0.5, r23=0.5, r2t4=0.5, g=3, n=10, J=4, K=20)
[15]:
20.0
[16]:
# power
power(design='bcra4_3r', es=0.12100407246925271, rho4=0.05, rho3=0.15, rho2=0.15, omega4=0.5,
r21=0.5, r22=0.5, r23=0.5, r2t4=0.5, g=3, n=10, J=4, K=20, L=20)
[16]:
0.800053034680572
| Parameters | effect_size |
sample_size |
power |
|---|---|---|---|
| design | ✓ | ✓ | ✓ |
| es | ✓ | ✓ | |
| n | ✓ | ✓ | ✓ |
| J | ✓ | ✓ | ✓ |
| K | ✓ | ✓ | ✓ |
| L | ✓ | ✓ | |
| power | ✓ | ✓ | |
| alpha | ✓ | ✓ | ✓ |
| two_tailed | ✓ | ✓ | ✓ |
| p | ✓ | ✓ | ✓ |
| r21 | ✓ | ✓ | ✓ |
| rho2 | ✓ | ✓ | ✓ |
| r22 | ✓ | ✓ | ✓ |
| rho3 | ✓ | ✓ | ✓ |
| r23 | ✓ | ✓ | ✓ |
| rho4 | ✓ | ✓ | ✓ |
| omega4 | ✓ | ✓ | ✓ |
| r2t4 | ✓ | ✓ | ✓ |
| g | ✓ | ✓ | ✓ |