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[lab-goodfit-indeptests] Ekraj Pokhrel #145

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173 changes: 160 additions & 13 deletions your_code/main.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -14,11 +14,54 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# your answer here"
"import numpy as np\n",
"import pandas as pd\n",
"import scipy.stats as st\n",
"from scipy.stats import poisson\n",
"from scipy.stats import binom"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"p_value is: 0.483688906853727\n",
"We can not reject the null hypothesis: there is reason to believe that at a .05 level the number of scores is a Poisson variable\n"
]
}
],
"source": [
"# your answer here\n",
"# our observation O:\n",
"O = [35,99,104,110,62,25,10,3]\n",
"alpha = 0.05\n",
"mu = 2.435\n",
"poisson_dist = poisson(mu)\n",
"\n",
"# poisson distribution for 1 to 6th value of probability\n",
"poisson_pmfs = np.array([poisson_dist.pmf(i) for i in range(0,7)]) \n",
"# probabilityo of scoring more than 7 will be 1 - cumulative probability of getting less than 7 i.e. sum of all value poisson_pmfs\n",
"poisson_pmfs_tail = 1-sum(poisson_pmfs) \n",
"# Now our final pmfs will be with the tail value\n",
"with_tail = np.append(poisson_pmfs, poisson_pmfs_tail)\n",
"# Calcualte the expected score according to our calculated pmfs where population will be the sum of our observed score\n",
"E = with_tail * sum(O)\n",
"\n",
"stats, p_value = st.chisquare(f_obs = O, f_exp = E)\n",
"print(f\"p_value is: {p_value}\")\n",
"if p_value < alpha:\n",
" print(\"We can reject the null hypothesis : there is no reason to believe that at a .05 level the number of scores is a Poisson variable\")\n",
"else: \n",
" print(\"We can not reject the null hypothesis: there is reason to believe that at a .05 level the number of scores is a Poisson variable\")\n"
]
},
{
Expand All @@ -41,11 +84,50 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 34,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"p_value is: 3.008342324775625e-07\n",
"We can reject the null hypothesis : there is no reason to believe that at a .05 level the number of defective items follow Poisson distribution\n"
]
}
],
"source": [
"# your code here"
"# your code here\n",
"defective_quantity = np.array([0, 1, 2, 3, 4])\n",
"O = np.array([32,15, 0, 9, 4])\n",
"# mu = ∑(x * f(x)) / n\n",
"mu = ((0*32)+(1*15)+(3*15)+(4*4))/60\n",
"alpha = 0.05\n",
"poisson_dist = poisson(mu)\n",
"\n",
"# poisson distribution for each observed defective items\n",
"pmf_0 = poisson_dist.pmf(0)\n",
"pmf_1 = poisson_dist.pmf(1)\n",
"pmf_2 = poisson_dist.pmf(2)\n",
"pmf_3 = poisson_dist.pmf(3)\n",
"pmf_4 = poisson_dist.pmf(4)\n",
"\n",
"\n",
"# calculate pmf for each occurance\n",
"pmfs = np.array([pmf_0, pmf_1, pmf_2, pmf_3, pmf_4])\n",
"# Calcualte the expected frequency according to our calculated pmfs where population will be the sum of our observed frequency\n",
"E = pmfs * sum(O)\n",
"# normalize the expected frequency with the observed frequency\n",
"E_norm = E / np.sum(E) * np.sum(O)\n",
"\n",
"stats, p_value = st.chisquare(f_obs = O, f_exp = E_norm, ddof = 1)\n",
"\n",
"print(f\"p_value is: {p_value}\")\n",
"if p_value < alpha:\n",
" print(\"We can reject the null hypothesis : there is no reason to believe that at a .05 level the number of defective items follow Poisson distribution\")\n",
"else: \n",
" print(\"We can not reject the null hypothesis: there is reason to believe that at a .05 level the number of defective items follow Poisson distribution\")\n",
"\n"
]
},
{
Expand All @@ -60,11 +142,46 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 40,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"8.306179519542757\n",
"P_value: 0.015715783395951262\n",
"We can reject the null hypothesis\n"
]
}
],
"source": [
"# your answer here"
"# your answer here\n",
"n = 10\n",
"p = 0.05\n",
"O = np.array([138, 53, 9])\n",
"Population = O.sum()\n",
"\n",
"binom_dist = binom(n,p)\n",
"binom_pmfs = np.array([binom_dist.pmf(i) for i in range(2)])\n",
"pmf_tail = 1 - binom_pmfs.sum()\n",
"with_tail = np.append(binom_pmfs, pmf_tail)\n",
"\n",
"E = with_tail * Population\n",
"\n",
"stats, p_value = st.chisquare(O, E)\n",
"\n",
"print(stats)\n",
"print(f\"P_value: {p_value}\")\n",
"\n",
"if p_value < alpha:\n",
" print(\"We can reject the null hypothesis\")\n",
"else:\n",
" print(\"We can not reject the null hypothesis\")\n",
"\n",
"\n",
"\n",
"\n"
]
},
{
Expand All @@ -79,17 +196,47 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 47,
"metadata": {},
"outputs": [],
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.004719280137040844\n",
"We can reject the null hypothesis: There is association between physical activity and sugary drinks consumption\n"
]
}
],
"source": [
"#your answer here"
"#your answer here\n",
"\n",
"# H0: there is no association between physical activity and the consumption of sugary drinks\n",
"# H1: there is an association between physical activity and the consumption of sugary drinks\n",
"\n",
"alpha = 0.05\n",
"category = np.array([[32, 12],\n",
" [14, 22],\n",
" [6, 9]])\n",
"stats, p_value, df, E = st.chi2_contingency(category)\n",
"print(p_value)\n",
"if p_value < alpha:\n",
" print(\"We can reject the null hypothesis: There is association between physical activity and sugary drinks consumption\")\n",
"else:\n",
" print(\"We can not reject the null hypothesis. We can not say that there is association between phsical activity and sugary drinks consumption\")"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
Expand All @@ -103,7 +250,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.3"
"version": "3.9.13"
}
},
"nbformat": 4,
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