include sample size in sigma passed to univariate simulations

simulations.ipynb

@@ -53,14 +53,14 @@
     "    # generate data from given distribution, calculate sample_mean, sample_sd\n",
     "    data = distribution_func(size=sample_size, **distribution_params)\n",
     "    x_bar = np.mean(data)\n",
-    "    sigma_hat = np.std(data)\n",
+    "    sigma_hat = np.std(data) / np.sqrt(sample_size)\n",
     "\n",
     "    # run delta method transformation for transformed_mean and transformed_sd\n",
     "    mu_txs[i], sigma_tx = transform_univariate(x_bar, sigma_hat, transform_func, \"delta\")\n",
     "\n",
     "    # calculate CI bounds with transformed_mean + Q * transformed_sd / sqrt(sample_size)\n",
-    "    ci_uppers[i] = mu_txs[i] + Q * sigma_tx / np.sqrt(sample_size)\n",
-    "    ci_lowers[i] = mu_txs[i] - Q * sigma_tx / np.sqrt(sample_size)\n",
+    "    ci_uppers[i] = mu_txs[i] + Q * sigma_tx\n",
+    "    ci_lowers[i] = mu_txs[i] - Q * sigma_tx\n",
     "\n",
     "    # indicate coverage success when transformed mean lies between CI bounds as described above\n",
     "    if (ci_lowers[i] < truth and truth < ci_uppers[i]):\n",