20220409_understanding_clt_and_ttest_part2.ipynb

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    "sample_size_n = 200\n",
    "sample_mean_from_binomial = get_sample_parameter_from_variable(400, \n",
    "                                                               sample_size_n, \n",
    "                                                               df, \n",
    "                                                               'mean', \n",
    "                                                               'binomial')\n",
    "sample_median_from_normal = get_sample_parameter_from_variable(400, \n",
    "                                                               sample_size_n, \n",
    "                                                               df, \n",
    "                                                               'median', \n",
    "                                                               'normal')\n",
    "sample_std_from_uniform = get_sample_parameter_from_variable(400, \n",
    "                                                             sample_size_n, \n",
    "                                                             df, \n",
    "                                                             'std', \n",
    "                                                             'uniform')\n",
    "#Here we compute \"manually\" the standard error\n",
    "sample_mean_from_binomial_std = np.std(sample_mean_from_binomial)\n",
    "sample_median_from_normal_std = np.std(sample_median_from_normal)\n",
    "sample_std_from_uniform_std = np.std(sample_std_from_uniform)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Here we compute standard error using the expressions\n",
    "sample_mean_from_binomial_se = df.binomial.std()/np.sqrt(sample_size_n)\n",
    "sample_median_from_normal_se = 1.2533 * (df.normal.std()/np.sqrt(sample_size_n))\n",
    "sample_std_from_uniform_se = df.uniform.std() / np.sqrt(2*(sample_size_n-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{\n",
      "    \"binomialdist_example (mean, n=200)\": {\n",
      "        \"computed_se\": 0.0504901583850754,\n",
      "        \"formula_se\": 0.05815619602703747\n",
      "    },\n",
      "    \"normaldist_example (median, n=200)\": {\n",
      "        \"computed_se\": 0.004247561325654817,\n",
      "        \"formula_se\": 0.004343732383749954\n",
      "    },\n",
      "    \"uniformdist_example (std, n=200)\": {\n",
      "        \"computed_se\": 0.013055146058296654,\n",
      "        \"formula_se\": 0.02204320895687334\n",
      "    }\n",
      "}\n"
     ]
    }
   ],
   "source": [
    "#Comparing results of computing SE \"manually\" versus formula\n",
    "se = {\n",
    "    f\"binomialdist_example (mean, n={sample_size_n})\": {\n",
    "        \"computed_se\": sample_mean_from_binomial_std,\n",
    "        \"formula_se\": sample_mean_from_binomial_se\n",
    "    },\n",
    "    f\"normaldist_example (median, n={sample_size_n})\": {\n",
    "        \"computed_se\": sample_median_from_normal_std,\n",
    "        \"formula_se\": sample_median_from_normal_se\n",
    "    },\n",
    "    f\"uniformdist_example (std, n={sample_size_n})\": {\n",
    "        \"computed_se\": sample_std_from_uniform_std,\n",
    "        \"formula_se\": sample_std_from_uniform_se\n",
    "    }\n",
    "}\n",
    "print(json.dumps(se, indent=4))"
   ]
  }
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