Blocked (Stratified) Individual Random Assignment (BIRA)¶
BIRA2_1c¶
| Assignment | Clustering Level | Treatment Assignment | Treatment Level | Cluster Effect |
|---|---|---|---|---|
| blocked | 2 | individual | 1 | constant |
[1]:
from pypowerup import effect_size, power, sample_size
[2]:
# effect size, i.e., minimum detectable effect sizes (MDES):
effect_size(design = "bira2_1c", n=80, J=14, power=0.8, alpha=0.05, two_tailed=True, p=0.5, r21=0, g=0)
[2]:
0.1675746241777643
[3]:
# sample_size, i.e., minimum required samples sizes (MRSS) for level 2 units.
sample_size(design = "bira2_1c", n=80, es=0.168, power=0.8, alpha=0.05, two_tailed=True, p=0.5, r21=0, g=0)
[3]:
14.0
[4]:
# power
power(design = "bira2_1c", n=80, J=14, es=0.168, alpha=0.05, two_tailed=True, p=0.5, r21=0, g=0)
[4]:
0.801986386400488
Parameters for BIRA2_1c:
| Parameters | effect_size |
sample_size |
power |
|---|---|---|---|
| design | ✓ | ✓ | ✓ |
| es | ✓ | ✓ | |
| n | ✓ | ✓ | ✓ |
| J | ✓ | ✓ | |
| power | ✓ | ✓ | |
| alpha | ✓ | ✓ | ✓ |
| two_tailed | ✓ | ✓ | ✓ |
| p | ✓ | ✓ | ✓ |
| r21 | ✓ | ✓ | ✓ |
| g | ✓ | ✓ | ✓ |
BIRA2_1f¶
| Assignment | Clustering Level | Treatment Assignment | Treatment Level | Cluster Effect |
|---|---|---|---|---|
| blocked | 2 | individual | 1 | fixed |
[5]:
# effect size, i.e., minimum detectable effect sizes (MDES):
effect_size(design = "bira2_1f", n=10, J=200, power=0.8, alpha=0.05, two_tailed=True, p=0.5, r21=0, g=0)
[5]:
0.1253671054395026
[6]:
# sample_size, i.e., minimum required samples sizes (MRSS) for level 2 units.
sample_size(design = "bira2_1f", n=10, es=0.125, power=0.8, alpha=0.05, two_tailed=True, p=0.5, r21=0, g=0)
[6]:
201.0
[7]:
# power
power(design = "bira2_1f", n=10, J=200, es=0.125, alpha=0.05, two_tailed=True, p=0.5, r21=0, g=0)
[7]:
0.7976961337604935
Parameters for BIRA2_1f
| Parameters | effect_size |
sample_size |
power |
|---|---|---|---|
| design | ✓ | ✓ | ✓ |
| es | ✓ | ✓ | |
| n | ✓ | ✓ | ✓ |
| J | ✓ | ✓ | |
| power | ✓ | ✓ | |
| alpha | ✓ | ✓ | ✓ |
| two_tailed | ✓ | ✓ | ✓ |
| p | ✓ | ✓ | ✓ |
| r21 | ✓ | ✓ | ✓ |
| g | ✓ | ✓ | ✓ |
BIRA2_1r¶
| Assignment | Clustering Level | Treatment Assignment | Treatment Level | Cluster Effect |
|---|---|---|---|---|
| blocked | 2 | individual | 1 | random |
[8]:
# effect size, i.e., minimum detectable effect sizes (MDES)
effect_size(design = "bira2_1r", n=80, J=480, rho2=0.35, omega2=0.1, power=0.8, alpha=0.05,
two_tailed=True, p=0.5, r21=0, r2t2=0, g=0)
[8]:
0.033290496240165834
[9]:
# sample_size, i.e., minimum required samples sizes (MRSS) for level 2 units
sample_size(design = "bira2_1r", es=0.033290496240165834, n=80, rho2=0.35, omega2=0.1, power=0.8, alpha=0.05,
two_tailed=True, p=0.5, r21=0, r2t2=0, g=0)
[9]:
480.0
[10]:
# power
power(design = "bira2_1r", es=0.033290496240165834, n=80, J=480, rho2=0.35, omega2=0.1, alpha=0.05,
two_tailed=True, p=0.5, r21=0, r2t2=0, g=0)
[10]:
0.800001211704756
Parameters for BIRA2_1r
| Parameters | effect_size |
sample_size |
power |
|---|---|---|---|
| design | ✓ | ✓ | ✓ |
| es | ✓ | ✓ | |
| n | ✓ | ✓ | ✓ |
| J | ✓ | ✓ | |
| power | ✓ | ✓ | |
| alpha | ✓ | ✓ | ✓ |
| two_tailed | ✓ | ✓ | ✓ |
| p | ✓ | ✓ | ✓ |
| r21 | ✓ | ✓ | ✓ |
| g | ✓ | ✓ | ✓ |
| rho2 | ✓ | ✓ | ✓ |
| omega2 | ✓ | ✓ | ✓ |
| r2t2 | ✓ | ✓ | ✓ |
BIRA3_1r¶
| Assignment | Clustering Level | Treatment Assignment | Treatment Level | Cluster Effect |
|---|---|---|---|---|
| blocked | 3 | individual | 1 | random |
[11]:
# effect size, i.e., minimum detectable effect sizes (MDES)
effect_size(design = "bira3_1r", n=80, J=10, K=100, rho3=0.2, rho2=0.15, omega3=0.1, omega2=0.1,
power=0.8, alpha=0.05, two_tailed=True, p=0.5, r21=0, r2t2=0, r2t3=0, g=0)
[11]:
0.04451381756409839
[12]:
# sample_size, i.e., minimum required samples sizes (MRSS) for level 3 units
sample_size(design = "bira3_1r", es=0.04451381756409839, n=80, J=10, rho3=0.2, rho2=0.15, omega3=0.1, omega2=0.1,
power=0.8, alpha=0.05, two_tailed=True, p=0.5, r21=0, r2t2=0, r2t3=0, g=0)
[12]:
100.0
[13]:
# power
power(design = "bira3_1r", es=0.04451381756409839, n=80, J=10, K=100, rho3=0.2, rho2=0.15, omega3=0.1, omega2=0.1,
alpha=0.05, two_tailed=True, p=0.5, r21=0, r2t2=0, r2t3=0, g=0)
[13]:
0.8000026614774113
Parameters for BIRA3_1r
| Parameters | effect_size |
sample_size |
power |
|---|---|---|---|
| design | ✓ | ✓ | ✓ |
| es | ✓ | ✓ | |
| n | ✓ | ✓ | ✓ |
| J | ✓ | ✓ | ✓ |
| K | ✓ | ✓ | |
| power | ✓ | ✓ | |
| alpha | ✓ | ✓ | ✓ |
| two_tailed | ✓ | ✓ | ✓ |
| p | ✓ | ✓ | ✓ |
| r21 | ✓ | ✓ | ✓ |
| g | ✓ | ✓ | ✓ |
| rho2 | ✓ | ✓ | ✓ |
| omega2 | ✓ | ✓ | ✓ |
| r2t2 | ✓ | ✓ | ✓ |
| rho3 | ✓ | ✓ | ✓ |
| omega3 | ✓ | ✓ | ✓ |
| r2t3 | ✓ | ✓ | ✓ |
BIRA4_1r¶
| Assignment | Clustering Level | Treatment Assignment | Treatment Level | Cluster Effect |
|---|---|---|---|---|
| blocked | 4 | individual | 1 | random |
[14]:
# effect size, i.e., minimum detectable effect sizes (MDES)
effect_size(design = "bira4_1r", n=10, J=4, K=4, L=20, rho4=0.05, rho3=0.15, rho2=0.15,
omega4=0.5, omega3=0.5, omega2=0.5, r21=0.5, r2t2=0.5, r2t3=0.5, r2t4=0.5, g=1,
power=0.8, alpha=0.05, two_tailed=True
)
[14]:
0.1191537036343213
[15]:
# sample_size, i.e., minimum required samples sizes (MRSS) for level 4 units
sample_size(design = "bira4_1r", es=0.1191537036343213, n=10, J=4, K=4, rho4=0.05, rho3=0.15, rho2=0.15,
omega4=0.5, omega3=0.5, omega2=0.5, r21=0.5, r2t2=0.5, r2t3=0.5, r2t4=0.5, g=1,
power=0.8, alpha=0.05, two_tailed=True)
[15]:
20.0
[16]:
# power
power(design = "bira4_1r", es=0.1191537036343213, n=10, J=4, K=4, L=20, rho4=0.05, rho3=0.15, rho2=0.15,
omega4=0.5, omega3=0.5, omega2=0.5, r21=0.5, r2t2=0.5, r2t3=0.5, r2t4=0.5, g=1,
alpha=0.05, two_tailed=True)
[16]:
0.8000404338335202
Parameters for BIRA4_1r
| Parameters | effect_size |
sample_size |
power |
|---|---|---|---|
| design | ✓ | ✓ | ✓ |
| es | ✓ | ✓ | |
| n | ✓ | ✓ | ✓ |
| J | ✓ | ✓ | ✓ |
| K | ✓ | ✓ | ✓ |
| L | ✓ | ✓ | |
| power | ✓ | ✓ | |
| alpha | ✓ | ✓ | ✓ |
| two_tailed | ✓ | ✓ | ✓ |
| p | ✓ | ✓ | ✓ |
| r21 | ✓ | ✓ | ✓ |
| g | ✓ | ✓ | ✓ |
| rho2 | ✓ | ✓ | ✓ |
| omega2 | ✓ | ✓ | ✓ |
| r2t2 | ✓ | ✓ | ✓ |
| rho3 | ✓ | ✓ | ✓ |
| omega3 | ✓ | ✓ | ✓ |
| r2t3 | ✓ | ✓ | ✓ |
| rho4 | ✓ | ✓ | ✓ |
| omega4 | ✓ | ✓ | ✓ |
| r2t4 | ✓ | ✓ | ✓ |