{
  "$type": "site.standard.document",
  "bskyPostRef": {
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    "uri": "at://did:plc:wwyqal4cnqhuwyacdj7rqq3n/app.bsky.feed.post/3miego2vovot2"
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  "path": "/t/sample-size-calculation-for-paired-data-using-ordinal-models/28685#post_1",
  "publishedAt": "2026-03-31T11:37:09.000Z",
  "site": "https://discourse.datamethods.org",
  "tags": [
    "Ordinal Models for Paired Data – Statistical Thinking"
  ],
  "textContent": "I came across this blog post by Prof. Harrell Ordinal Models for Paired Data – Statistical Thinking.\n\nI was trying to replicate the simulation in order to estimate the sample size for my paired study. Eveyrthing works perfectly and I am getting a reasonable sample size estimation. I just want to make sure that I am not missing any important details or doing anything wrong.\n\nHere is my code\n\n\n    # Key metrics for the simulation (dummy data)\n\n    before <- c(1.2,2.3,3.5,2.1,4.2,2.2,4.2,5.4,2.5,5.6,5.7,2.8,5.3,2.2,1.2)\n    after <- c(4.2,2.3,3.5,2.1,2.2,2.2,5.2,5.4,2.5,5.1,5.4,2.2,5.3,2.2,4.2)\n    delta_obs <- mean(before) - mean(after)\n    sd_obs    <- sd(before)\n    rho_obs   <- 0.5    # used the same rho used by prof. Harrell\n\n\n    get_paired_power <- function(n, reps = 500) {\n      p_values <- replicate(reps, {\n        y1 <- rnorm(n, mean = 0, sd = sd_obs)\n        y2 <- rnorm(n, mean = delta_obs + rho_obs * y1, sd = sqrt(1 - rho_obs^2) * sd_obs)\n        y_sim  <- c(y1, y2)\n        x_sim  <- c(rep(0, n), rep(1, n))\n        id_sim <- factor(c(1:n, 1:n))\n\n        f <- orm(y_sim ~ x_sim, x=TRUE, y=TRUE)\n        g <- robcov(f, id_sim)\n\n        anova(g)['x_sim', 'P']\n      })\n      mean(p_values < 0.05, na.rm = TRUE)\n    }\n\n    targets <- c(0.80) # here I am using 0.8 only\n    results <- data.frame(Power_Target = targets, Required_Pairs = NA)\n\n    current_n <- 140\n    for (i in 1:length(targets)) {\n      while (get_paired_power(current_n) < targets[i]) {\n        current_n <- current_n + 10 # Incrementing pairs\n        print(current_n)\n      }\n      results$Required_Pairs[i] <- current_n\n    }\n\n    print(results)\n",
  "title": "Sample size calculation for Paired Data using ordinal models"
}