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carlthome/welch-s-t-test-for-independent-samples.ipynb

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welch-s-t-test-for-independent-samples.ipynb
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welch-s-t-test-for-independent-samples.ipynb
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"<a href=\"https://colab.research.google.com/gist/carlthome/0ca8e2624654358c3e9442dd9d089a1d/welch-s-t-test-for-independent-samples.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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"data": {
"text/plain": [
" Degree of freedom 1 Degree of freedom 2 T-test p-value\n",
"0 8 29 1.556304 0.136493"
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" <th></th>\n",
" <th>Degree of freedom 1</th>\n",
" <th>Degree of freedom 2</th>\n",
" <th>T-test</th>\n",
" <th>p-value</th>\n",
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"summary": "{\n \"name\": \"pd\",\n \"rows\": 1,\n \"fields\": [\n {\n \"column\": \"Degree of freedom 1\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": null,\n \"min\": 8,\n \"max\": 8,\n \"num_unique_values\": 1,\n \"samples\": [\n 8\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"Degree of freedom 2\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": null,\n \"min\": 29,\n \"max\": 29,\n \"num_unique_values\": 1,\n \"samples\": [\n 29\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"T-test\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": null,\n \"min\": 1.556304247842829,\n \"max\": 1.556304247842829,\n \"num_unique_values\": 1,\n \"samples\": [\n 1.556304247842829\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n },\n {\n \"column\": \"p-value\",\n \"properties\": {\n \"dtype\": \"number\",\n \"std\": null,\n \"min\": 0.13649272437710608,\n \"max\": 0.13649272437710608,\n \"num_unique_values\": 1,\n \"samples\": [\n 0.13649272437710608\n ],\n \"semantic_type\": \"\",\n \"description\": \"\"\n }\n }\n ]\n}"
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"source": [
"import numpy as np\n",
"import pandas as pd\n",
"import scipy.stats as stats\n",
"\n",
"\n",
"def compute_t_test():\n",
" # Create synthetic data for testing.\n",
" group1 = np.random.normal(0.7, 0.4, size=9)\n",
" group2 = np.random.normal(0.5, 0.4, size=30)\n",
"\n",
" # Compute mean, variance and size of groups.\n",
" variance1 = np.var(group1, ddof=1)\n",
" variance2 = np.var(group2, ddof=1)\n",
"\n",
" df1 = len(group1) - 1\n",
" df2 = len(group2) - 1\n",
"\n",
" mean1 = np.mean(group1)\n",
" mean2 = np.mean(group2)\n",
"\n",
" size1 = len(group1)\n",
" size2 = len(group2)\n",
"\n",
" # T-test for means of two independent samples from descriptive statistics.\n",
" # This is a test for the null hypothesis that two independent samples have identical average (expected) values.\n",
" t_test, p_value = stats.ttest_ind_from_stats(\n",
" mean1=mean1, std1=np.sqrt(variance1), nobs1=size1,\n",
" mean2=mean2, std2=np.sqrt(variance2), nobs2=size2,\n",
" equal_var=False,\n",
" )\n",
"\n",
" # Collect results.\n",
" scores = {\n",
" \"Degree of freedom 1\": df1,\n",
" \"Degree of freedom 2\": df2,\n",
" \"T-test\": t_test,\n",
" \"p-value\": p_value,\n",
" }\n",
" return scores\n",
"\n",
"\n",
"scores = compute_t_test()\n",
"pd.DataFrame(scores, index=[0])"
]
},
{
"cell_type": "code",
"source": [
"%timeit compute_t_test()"
],
"metadata": {
"id": "9kb8JmaP_WwW",
"outputId": "3bc961e6-6d53-4791-d595-013f7976157a",
"colab": {
"base_uri": "https://localhost:8080/"
}
},
"execution_count": 2,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"186 µs ± 16.4 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)\n"
]
}
]
},
{
"cell_type": "code",
"source": [
"n = 0\n",
"m = 10000\n",
"for _ in range(m):\n",
" scores = compute_t_test()\n",
" n += int(scores[\"p-value\"] < 0.05)\n",
"n/m"
],
"metadata": {
"id": "JtlHWmpS9xW7",
"outputId": "5834083e-a686-402a-911e-04abf7957f38",
"colab": {
"base_uri": "https://localhost:8080/"
}
},
"execution_count": 3,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"0.2266"
]
},
"metadata": {},
"execution_count": 3
}
]
}
]
}
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