## Power<50% [Power / Sample Size]

Hi BEQool,

❝ Why do we pass the study if the power is below 50%?

Let’s dive deeper into you example:

library(PowerTOST) n   <- sampleN.scABEL(CV = 1.1, theta0 = 0.95, design = "2x2x3",                       details = FALSE, print = FALSE)[["Sample size"]] n   <- seq(n, 36, -2) res <- data.frame(n = n, lower = NA_real_, upper = NA_real_, power = NA_real_) for (j in seq_along(n)) {   res[j, 2:3] <- CI.BE(CV = 1.1, pe = 0.95, n = n[j], design = "2x2x3")   res[j, 4]   <- power.scABEL(CV = 1.1, theta0 = 0.95, n = n[j], design = "2x2x3") } print(signif(res, 4), row.names = FALSE)   n  lower upper  power  88 0.7838 1.151 0.8080  86 0.7821 1.154 0.7974  84 0.7803 1.157 0.7866  82 0.7784 1.159 0.7750  80 0.7764 1.162 0.7626  78 0.7744 1.165 0.7503  76 0.7723 1.169 0.7360  74 0.7701 1.172 0.7226  72 0.7679 1.175 0.7070  70 0.7655 1.179 0.6911  68 0.7631 1.183 0.6743  66 0.7606 1.187 0.6567  64 0.7579 1.191 0.6373  62 0.7551 1.195 0.6180  60 0.7522 1.200 0.5972  58 0.7492 1.205 0.5745  56 0.7460 1.210 0.5504  54 0.7426 1.215 0.5267  52 0.7391 1.221 0.5008  50 0.7353 1.227 0.4733  48 0.7314 1.234 0.4453  46 0.7272 1.241 0.4134  44 0.7227 1.249 0.3816  42 0.7180 1.257 0.3490  40 0.7129 1.266 0.3122  38 0.7075 1.276 0.2751  36 0.7016 1.286 0.2372

Strange. I have to think about it…
CI.BE() gives us the realized results (i.e., the values observed in a particular study), whereas power.scABEL() the results of 105 simulations. Both the CV and PE are skewed to the right and, therefore, I would expect that simulated power is lower than assessing whether a particular study passes. However, such a large discrepancy is surprising for me.

Dif-tor heh smusma 🖖🏼 Довге життя Україна!
Helmut Schütz

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