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[lab-goodfit-indeptests] Henrik Söder #167

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232 changes: 226 additions & 6 deletions your_code/main.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -12,13 +12,66 @@
"Based on these results, we create a Poisson distribution with the sample mean parameter = 2.435. Is there any reason to believe that at a .05 level the number of scores is a Poisson variable?"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import scipy.stats as st\n",
"from scipy.stats import bernoulli, binom, geom, poisson, uniform, expon, norm,chisquare\n"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [],
"source": [
"#H0: follows poisson\n",
"#H1: does not follow poisson\n",
"\n",
"points = np.array([35, 99, 104, 110, 62, 25, 10, 3])\n",
"\n",
"mu = 2.435\n",
"poisson_dist = poisson(mu)\n",
"\n",
"poisson_pmf = np.array([poisson_dist.pmf(i) for i in range(7)])\n",
"\n",
"with_tail = np.append(poisson_pmf, 1-poisson_pmf.sum())\n",
"f_exp = with_tail*sum(points)\n",
"\n",
"\n",
"output = st.chisquare(f_obs = f_obs, f_exp = f_exp)"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The p_value is: 0.4836889068537269\n"
]
}
],
"source": [
"print(\"The p_value is:\", output[1])"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# your answer here"
"# we can not reject the hypothesis ==> it might be a poisson distribution"
]
},
{
Expand Down Expand Up @@ -60,11 +113,52 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 34,
"metadata": {},
"outputs": [],
"source": [
"# your answer here"
"#H0: follows Binominal\n",
"#H1: Does not follow Binominal\n",
"\n",
"f_obs = np.array([138,53,9])\n",
"\n",
"n = 10\n",
"p = 0.05\n",
"\n",
"binom_dist = binom(n,p)\n",
"pmfs = np.array([binom_dist.pmf(i) for i in range(2)])\n",
"\n",
"with_tail = np.append(pmfs, 1 - pmfs.sum())\n",
"f_exp = with_tail*sum(f_obs)\n",
"\n",
"output = st.chisquare(f_obs = f_obs, f_exp = f_exp)"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"P_value 0.015715783395950946\n"
]
}
],
"source": [
"print(\"P_value\", output[1])"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [],
"source": [
"#can reject the hypothesis\n",
"# it does not follow a binomial distribution with 0.05"
]
},
{
Expand All @@ -77,19 +171,145 @@
"![](table4.png)"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Yes</th>\n",
" <th>No</th>\n",
" <th>Total</th>\n",
" </tr>\n",
" <tr>\n",
" <th>Physical Activity</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>low</th>\n",
" <td>32</td>\n",
" <td>12</td>\n",
" <td>44</td>\n",
" </tr>\n",
" <tr>\n",
" <th>medium</th>\n",
" <td>14</td>\n",
" <td>22</td>\n",
" <td>36</td>\n",
" </tr>\n",
" <tr>\n",
" <th>high</th>\n",
" <td>6</td>\n",
" <td>9</td>\n",
" <td>15</td>\n",
" </tr>\n",
" <tr>\n",
" <th>total</th>\n",
" <td>51</td>\n",
" <td>43</td>\n",
" <td>95</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Yes No Total\n",
"Physical Activity \n",
"low 32 12 44\n",
"medium 14 22 36\n",
"high 6 9 15\n",
"total 51 43 95"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df =pd.DataFrame({\"Yes\":[32,14,6,51], \"No\":[12,22,9,43], \"Total\":[44,36,15,95], \"Physical Activity\":[\"low\", \"medium\", \"high\", \"total\"]})\n",
"df = df.set_index(\"Physical Activity\")\n",
"df"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"scrolled": true
},
"outputs": [],
"source": [
"#H0: Pattern Association\n",
"#H1: Not a Pattern Association\n",
"\n",
"from scipy import stats\n",
"\n",
"f_obs = [\n",
" [32, 12],\n",
" [14, 22],\n",
" [6, 9]\n",
"]\n",
"\n",
"output = stats.chi2_contingency(f_obs)"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.004719280137040844\n"
]
}
],
"source": [
"print(output[1])"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"#your answer here"
"# we can reject the hypothesis \n",
"# there is a no pattern "
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
Expand All @@ -103,7 +323,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.3"
"version": "3.11.4"
}
},
"nbformat": 4,
Expand Down