Pessimistic: We reach 66% of treatment and control group.
## Year 1, pessimistic projections
ith n-treatment=20, n-control = 20, power = 0.9,sig.level= 0.05, power = 0.9, minimal detectable effect in standard deviations (d) = ?
t test power calculation
n1 = 20
n2 = 20
d = 1.051997
sig.level = 0.05
power = 0.9
alternative = two.sided
## Year 1, optimistic projections
With n_treatment=30, n_control = 60, power = 0.9,sig.level= 0.05, minimal detectable effect = ?
t test power calculation
n1 = 30
n2 = 60
d = 0.7328756
sig.level = 0.05
power = 0.9
alternative = two.sided
With n = ?, power = 0.9,sig.level= 0.05, power = 0.9, minimal detectable effect = 0.5
Two-sample t test power calculation
n = 85.03128
d = 0.5
sig.level = 0.05
power = 0.9
alternative = two.sided
NOTE: n is number in *each* group
## Year 2, pessimistic projections
With n_treatment=40, n_control = 40, power = 0.9,sig.level= 0.05, minimal detectable effect = ?
t test power calculation
n1 = 40
n2 = 40
d = 0.7339255
sig.level = 0.05
power = 0.9
alternative = two.sided
## Year 2, optimistic projections
With n_treatment=60, n_control = 120, power = 0.9,sig.level= 0.05, minimal detectable effect = ?
t test power calculation
n1 = 60
n2 = 120
d = 0.5153056
sig.level = 0.05
power = 0.9
alternative = two.sided
## Year 3, pessimistic projections
With n_treatment=60, n_control = 60, power = 0.9,sig.level= 0.05, minimal detectable effect = ?
t test power calculation
n1 = 60
n2 = 60
d = 0.5967207
sig.level = 0.05
power = 0.9
alternative = two.sided
## Year 3, optimistic projections
With n_treatment=90, n_control = 180, power = 0.9,sig.level= 0.05, minimal detectable effect = ?
t test power calculation
n1 = 90
n2 = 180
d = 0.4200132
sig.level = 0.05
power = 0.9
alternative = two.sided
## Year 4, pessimistic projections
With n_treatment=80, n_control = 80, power = 0.9,sig.level= 0.05, minimal detectable effect = ?
t test power calculation
n1 = 80
n2 = 80
d = 0.5156619
sig.level = 0.05
power = 0.9
alternative = two.sided
## Year 4, optimistic projections
With n_treatment=120, n_control = 240, power = 0.9,sig.level= 0.05, minimal detectable effect = ?
t test power calculation
n1 = 120
n2 = 240
d = 0.3633959
sig.level = 0.05
power = 0.9
alternative = two.sided
## Population necessary to detect an effect size of 0.2 with significance level = 0.05 and power = 0.9
Here the free variable was d= minimal detectable effect
With n = ?, power = 0.9,sig.level= 0.05, power = 0.9, minimal detectable effect = 0.2
Two-sample t test power calculation
n = 526.3332
d = 0.2
sig.level = 0.05
power = 0.9
alternative = two.sided
NOTE: n is number in *each* group
here the free variable was n, the population of the treatment group
son = population of the treatmente group = population of the control group
necessary to detect an effect of 0.2
## Population necessary to detect an effect size of 0.5 with significance level = 0.05 and power = 0.9
Two-sample t test power calculation
n = 85.03128
d = 0.5
sig.level = 0.05
power = 0.9
alternative = two.sided
NOTE: n is number in *each* group
## Population necessary to detect an effect size of 0.2 with significance level = 0.10 and power = 0.9
Two-sample t test power calculation
n = 428.8664
d = 0.2
sig.level = 0.1
power = 0.9
alternative = two.sided
NOTE: n is number in *each* group
## Population necessary to detect an effect size of 0.5 with significance level = 0.10 and power = 0.9
Two-sample t test power calculation
n = 69.19719
d = 0.5
sig.level = 0.1
power = 0.9
alternative = two.sided
NOTE: n is number in *each* group
## Conclusions.
Even after 4 years, under the most optimistic population projections (i.e., every participant answers our surveys every year, and 60 students who didn't get selected also do), we wouldn't have enough power to detect an effect size of 0.2 standard deviations with significance level = 0.05. However, it seems feasible to detect the kinds of effects which would justify the upward of $150.000 / year costs of ESPR within 3 years. The minimum effect which justifies the costs of ESPR should be determined beforehand, as should the axis along which we measure. I would also suggest to expand the RCT to SPARC once its feasibility has been tested at ESPR.
