181 lines
4.8 KiB
Markdown
181 lines
4.8 KiB
Markdown
# Power calculations
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Using R we will do some power calculations
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Necessary library pwr, loads with library(pwr)
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Necessary function: pwr.t2n.test
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See: https://www.statmethods.net/stats/power.html
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Optimistic: We reach everyone
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Pessimistic: We reach 66% of treatment and control group.
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## Year 1, pessimistic projections
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ith n-treatment=20, n-control = 20, power = 0.9,sig.level= 0.05, power = 0.9, minimal detectable effect in standard deviations (d) = ?
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t test power calculation
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n1 = 20
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n2 = 20
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d = 1.051997
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sig.level = 0.05
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power = 0.9
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alternative = two.sided
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## Year 1, optimistic projections
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With n_treatment=30, n_control = 60, power = 0.9,sig.level= 0.05, minimal detectable effect = ?
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t test power calculation
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n1 = 30
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n2 = 60
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d = 0.7328756
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sig.level = 0.05
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power = 0.9
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alternative = two.sided
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With n = ?, power = 0.9,sig.level= 0.05, power = 0.9, minimal detectable effect = 0.5
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Two-sample t test power calculation
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n = 85.03128
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d = 0.5
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sig.level = 0.05
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power = 0.9
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alternative = two.sided
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NOTE: n is number in *each* group
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## Year 2, pessimistic projections
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With n_treatment=40, n_control = 40, power = 0.9,sig.level= 0.05, minimal detectable effect = ?
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t test power calculation
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n1 = 40
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n2 = 40
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d = 0.7339255
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sig.level = 0.05
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power = 0.9
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alternative = two.sided
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## Year 2, optimistic projections
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With n_treatment=60, n_control = 120, power = 0.9,sig.level= 0.05, minimal detectable effect = ?
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t test power calculation
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n1 = 60
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n2 = 120
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d = 0.5153056
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sig.level = 0.05
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power = 0.9
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alternative = two.sided
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## Year 3, pessimistic projections
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With n_treatment=60, n_control = 60, power = 0.9,sig.level= 0.05, minimal detectable effect = ?
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t test power calculation
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n1 = 60
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n2 = 60
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d = 0.5967207
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sig.level = 0.05
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power = 0.9
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alternative = two.sided
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## Year 3, optimistic projections
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With n_treatment=90, n_control = 180, power = 0.9,sig.level= 0.05, minimal detectable effect = ?
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t test power calculation
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n1 = 90
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n2 = 180
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d = 0.4200132
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sig.level = 0.05
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power = 0.9
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alternative = two.sided
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## Year 4, pessimistic projections
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With n_treatment=80, n_control = 80, power = 0.9,sig.level= 0.05, minimal detectable effect = ?
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t test power calculation
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n1 = 80
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n2 = 80
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d = 0.5156619
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sig.level = 0.05
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power = 0.9
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alternative = two.sided
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## Year 4, optimistic projections
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With n_treatment=120, n_control = 240, power = 0.9,sig.level= 0.05, minimal detectable effect = ?
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t test power calculation
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n1 = 120
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n2 = 240
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d = 0.3633959
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sig.level = 0.05
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power = 0.9
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alternative = two.sided
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## Population necessary to detect an effect size of 0.2 with significance level = 0.05 and power = 0.9
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Here the free variable was d= minimal detectable effect
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With n = ?, power = 0.9,sig.level= 0.05, power = 0.9, minimal detectable effect = 0.2
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Two-sample t test power calculation
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n = 526.3332
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d = 0.2
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sig.level = 0.05
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power = 0.9
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alternative = two.sided
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NOTE: n is number in *each* group
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here the free variable was n, the population of the treatment group
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son = population of the treatmente group = population of the control group
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necessary to detect an effect of 0.2
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## Population necessary to detect an effect size of 0.5 with significance level = 0.05 and power = 0.9
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Two-sample t test power calculation
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n = 85.03128
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d = 0.5
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sig.level = 0.05
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power = 0.9
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alternative = two.sided
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NOTE: n is number in *each* group
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## Population necessary to detect an effect size of 0.2 with significance level = 0.10 and power = 0.9
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Two-sample t test power calculation
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n = 428.8664
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d = 0.2
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sig.level = 0.1
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power = 0.9
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alternative = two.sided
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NOTE: n is number in *each* group
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## Population necessary to detect an effect size of 0.5 with significance level = 0.10 and power = 0.9
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Two-sample t test power calculation
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n = 69.19719
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d = 0.5
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sig.level = 0.1
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power = 0.9
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alternative = two.sided
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NOTE: n is number in *each* group
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## Conclusions.
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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.
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