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Moved examples 1BT and 2BT to new ch3 problems nb
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@ivanistheone
ivanistheone committed Jul 27, 2023
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219 changes: 3 additions & 216 deletions notebooks/34_analytical_approx.ipynb
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"### Bootstrap estimate of the standard error\n",
"\n",
"Another way to obtain the standard error of the mean\n",
"(the standard deviation sampling distribution of the mean)\n",
"is to use the bootstrap approach.\n",
"(the standard deviation of the sampling distribution of the mean)\n",
"is to use the bootstrap estimate.\n",
"\n",
"\n",
"TODO: import formulas"
]
},
{
"cell_type": "markdown",
"id": "b85af6aa-078a-4a02-9f0c-a71871d0985a",
"metadata": {},
"source": [
"#### Example 1BT: test for the mean of Batch 04"
]
},
{
"cell_type": "code",
"execution_count": 132,
"id": "65005726-e0a2-421c-aada-27842968d6eb",
"metadata": {},
"outputs": [],
"source": [
"kombucha = pd.read_csv(\"../datasets/kombucha.csv\")\n",
"ksample04 = kombucha[kombucha[\"batch\"]==4][\"volume\"]\n",
"n04 = len(ksample04)"
]
},
{
"cell_type": "code",
"execution_count": 133,
"id": "ed62b815-5faf-458e-9849-85cb09a76892",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.2252842390160474"
]
},
"execution_count": 133,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# bootstrap estimate for standard error of the mean\n",
"from stats_helpers import gen_boot_dist\n",
"kbars_boot04 = gen_boot_dist(ksample04, estfunc=mean)\n",
"sehat_boot04 = std(kbars_boot04)\n",
"sehat_boot04"
]
},
{
"cell_type": "code",
"execution_count": 134,
"id": "3769ca83-069b-407f-8712-4f3b44fc8fbe",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3.128661805915673"
]
},
"execution_count": 134,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# compute the t statistic using bootstrap se\n",
"obst04bt = (obsmean04 - muK0) / sehat_boot04\n",
"obst04bt"
]
},
{
"cell_type": "code",
"execution_count": 135,
"id": "5316bae0-aae8-4b97-8602-68fe70e7a248",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.012147863549560177"
]
},
"execution_count": 135,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from scipy.stats import t as tdist\n",
"rvT04 = tdist(n04 - 1)\n",
"pvalue04bt = tailprobs(rvT, obst04bt, alt=\"two-sided\")\n",
"pvalue04bt"
]
},
{
"cell_type": "markdown",
"id": "78df6c04-514c-4515-9ef8-5700de0861e9",
"metadata": {},
"source": [
"The $p$-value is very small,\n",
"so our decision is to reject $H_0$."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "275cff66-0f71-46ed-ac3f-4448936397f0",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "660fa68f-0140-4d7d-91f9-47466f4c881c",
"metadata": {},
"source": [
"#### Example 2BT: test for the mean of Batch 01"
]
},
{
"cell_type": "code",
"execution_count": 136,
"id": "90aa8990-0fa7-4e80-9206-d62c34a3990e",
"metadata": {},
"outputs": [],
"source": [
"kombucha = pd.read_csv(\"../datasets/kombucha.csv\")\n",
"ksample01 = kombucha[kombucha[\"batch\"]==1][\"volume\"]\n",
"n01 = len(ksample01)"
]
},
{
"cell_type": "code",
"execution_count": 137,
"id": "178af06b-310a-43f1-94c1-daa0b9c5ed1f",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.5501517384893604"
]
},
"execution_count": 137,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# bootstrap estimate for standard error of the mean\n",
"from stats_helpers import gen_boot_dist\n",
"kbars_boot01 = gen_boot_dist(ksample01, estfunc=mean)\n",
"sehat_boot01 = std(kbars_boot01)\n",
"sehat_boot01"
]
},
{
"cell_type": "code",
"execution_count": 138,
"id": "c02d1766-5a31-4963-9603-62d545742e1e",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-0.5781692061148894"
]
},
"execution_count": 138,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# compute the t statistic using bootstrap se\n",
"obst01bt = (obsmean01 - muK0) / sehat_boot01\n",
"obst01bt"
]
},
{
"cell_type": "code",
"execution_count": 139,
"id": "0a858812-cd15-4b32-adfb-a3d7f4f1ed6e",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.5664736858023267"
]
},
"execution_count": 139,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from scipy.stats import t as tdist\n",
"\n",
"rvT01 = tdist(n01-1)\n",
"#######################################################\n",
"pvalue01bt = tailprobs(rvT01, obst01bt, alt=\"two-sided\")\n",
"pvalue01bt"
]
},
{
"cell_type": "markdown",
"id": "50db8103-3aee-430e-bf2a-c1ca6ef1262d",
"metadata": {},
"source": [
"The $p$-value is very large,\n",
"so we have no reason to reject $H_0$."
"See problems...\n"
]
},
{
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18 changes: 3 additions & 15 deletions notebooks/35_two_sample_tests.ipynb
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Expand Up @@ -2414,27 +2414,15 @@
},
{
"cell_type": "code",
"execution_count": 54,
"execution_count": 55,
"id": "1e0fc5ae-ae1a-4fdc-98af-5f25d8563e88",
"metadata": {},
"outputs": [
{
"ename": "TypeError",
"evalue": "ttest_dmeans() got an unexpected keyword argument 'equal_var'",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)",
"Cell \u001b[0;32mIn[54], line 4\u001b[0m\n\u001b[1;32m 2\u001b[0m scoresD \u001b[38;5;241m=\u001b[39m students[students[\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mcurriculum\u001b[39m\u001b[38;5;124m\"\u001b[39m]\u001b[38;5;241m==\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mdebate\u001b[39m\u001b[38;5;124m\"\u001b[39m][\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mscore\u001b[39m\u001b[38;5;124m\"\u001b[39m]\n\u001b[1;32m 3\u001b[0m scoresL \u001b[38;5;241m=\u001b[39m students[students[\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mcurriculum\u001b[39m\u001b[38;5;124m\"\u001b[39m]\u001b[38;5;241m==\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mlecture\u001b[39m\u001b[38;5;124m\"\u001b[39m][\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mscore\u001b[39m\u001b[38;5;124m\"\u001b[39m]\n\u001b[0;32m----> 4\u001b[0m \u001b[43mttest_dmeans\u001b[49m\u001b[43m(\u001b[49m\u001b[43mscoresD\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mscoresL\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mequal_var\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43;01mTrue\u001b[39;49;00m\u001b[43m)\u001b[49m\n",
"\u001b[0;31mTypeError\u001b[0m: ttest_dmeans() got an unexpected keyword argument 'equal_var'"
]
}
],
"outputs": [],
"source": [
"students = pd.read_csv(\"../datasets/students.csv\")\n",
"scoresD = students[students[\"curriculum\"]==\"debate\"][\"score\"]\n",
"scoresL = students[students[\"curriculum\"]==\"lecture\"][\"score\"]\n",
"ttest_dmeans(scoresD, scoresL, equal_var=True)"
"# ttest_dmeans(scoresD, scoresL, equal_var=True)"
]
},
{
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