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Some notes on power/sample size calculation from the pwr tutorial and prior experience. Before jumping into the calculation, things-to-do are listed in the following:
Assuming an effect size of 1, we’ll need at least 17 subjects in each group to detect the difference with at least 80% power using \(\alpha\)=0.05 and two-sided testing.
# assume same sizes per group
pwr.t.test(d = 1, power = 0.8)
Two-sample t test power calculation
n = 16.71472
d = 1
sig.level = 0.05
power = 0.8
alternative = two.sided
NOTE: n is number in *each* groupWhen the sample sizes in the two groups are 198 and 37 respectively, we are able to detect a mean difference of 9.029, assuming the common standard deviation is 17.92, with at least 80% power using \(\alpha\)=0.05 and two-sided testing.
# assume different sizes per group
pwr.t2n.test(n1 = 198, n2 = 37, power = 0.8)
t test power calculation
n1 = 198
n2 = 37
d = 0.5038656
sig.level = 0.05
power = 0.8
alternative = two.sidedpwr.2p2n.test is not applicable since we assume certain
proportion of group 1 based on literature review. Assuming that roughly
35% of group 1 will develop the outcome, with the observed samples
sizes, we are able to detect a difference in proportions of 9.3% (35% in
group 1 vs. 44.3% in group 2) with 80% power using \(\alpha\)=0.05 and two-sided testing.
With an overall sample size of 30 and 5 per skin type, only a difference between 0% and 100% could be detected with 80% power using \(\alpha\)=0.05 and two-sided testing. Under same assumption, the differences between 0% and 80% or 20% and 100% could be detected with power between 70% and 80%. Those are large differences which may not be observed in the study with small sample size per group.
power.exact.test(0, 1, 5, 5, method = 'fisher')
Fisher's Exact Test
n1, n2 = 5, 5
p1, p2 = 0, 1
alpha = 0.05
power = 1
alternative = two.sided
delta = 0# equivalent: c(0.2, 1, 5, 5)
power.exact.test(0, 0.8, 5, 5, method = 'fisher')
Fisher's Exact Test
n1, n2 = 5, 5
p1, p2 = 0.0, 0.8
alpha = 0.05
power = 0.73728
alternative = two.sided
delta = 0
sessionInfo()R version 4.4.0 (2024-04-24)
Platform: aarch64-apple-darwin20
Running under: macOS 15.1.1
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.4-arm64/Resources/lib/libRlapack.dylib; LAPACK version 3.12.0
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
time zone: America/Detroit
tzcode source: internal
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] Exact_3.3 pwr_1.3-0 workflowr_1.7.1
loaded via a namespace (and not attached):
[1] jsonlite_1.8.9 compiler_4.4.0 promises_1.3.0 Rcpp_1.0.13
[5] stringr_1.5.1 git2r_0.33.0 callr_3.7.6 later_1.3.2
[9] jquerylib_0.1.4 yaml_2.3.10 fastmap_1.2.0 R6_2.5.1
[13] knitr_1.48 tibble_3.2.1 rprojroot_2.0.4 bslib_0.8.0
[17] pillar_1.9.0 rlang_1.1.4 utf8_1.2.4 cachem_1.1.0
[21] stringi_1.8.4 httpuv_1.6.15 xfun_0.47 getPass_0.2-4
[25] fs_1.6.4 sass_0.4.9 cli_3.6.3 magrittr_2.0.3
[29] ps_1.7.6 digest_0.6.37 processx_3.8.4 rootSolve_1.8.2.4
[33] rstudioapi_0.16.0 ExactData_2.0 lifecycle_1.0.4 vctrs_0.6.5
[37] evaluate_1.0.0 glue_1.8.0 whisker_0.4.1 fansi_1.0.6
[41] rmarkdown_2.28 httr_1.4.7 tools_4.4.0 pkgconfig_2.0.3
[45] htmltools_0.5.8.1