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Hypothesentest_IU/Tutorium 2.ipynb

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{
"cells": [
{
"cell_type": "code",
"execution_count": null,
"id": "9b437a81-b193-48ae-91bf-48edcfb12e18",
"metadata": {},
"outputs": [],
"source": [
"#pip install numpy matplotlib scipy"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "a4ea5fe4-eaa9-4cc4-8677-385a68577332",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import scipy.stats as stats"
]
},
{
"cell_type": "markdown",
"id": "df08071e-cd3c-49dd-8623-baf38082eab0",
"metadata": {},
"source": [
"Generate a normal distribution with sample of an experiment"
]
},
{
"cell_type": "markdown",
"id": "ed78c89c-0bee-4b52-be93-31a2698112ad",
"metadata": {},
"source": [
"Sample of people and measure their heights. Re run the code...also the average is changing."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "280f78b3-4338-49ec-8929-732d429762db",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Generate 1000 random numbers from a normal distribution\n",
"mu, sigma = 180, 10 # mean and standard deviation\n",
"data = np.random.normal(mu, sigma, 1000)\n",
"mean_sample = data.mean().item()\n",
"# Create a histogram of the data\n",
"plt.hist(data, bins=30, density=True, alpha=0.6, color='g')\n",
"title = \"Histogram with random numbers from: mu = %.2f, std = %.2f\" % (mu, sigma)\n",
"plt.axvline(x=mean_sample , color='m', linestyle='--', label='mu sample = %.2f' % (mean_sample))\n",
"plt.legend()\n",
"plt.title(title)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "82712fee-3e30-4e03-8be5-636d4193fb50",
"metadata": {},
"source": [
"As we can see, it seems to be appropriate, to approx this with the normal distribution"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "0df9c2e5-ae6d-48c0-93a4-12a6e70240c2",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Show the approximation with the normal distribution\n",
"plt.hist(data, bins=30, density=True, alpha=0.6, color='g')\n",
"xmin, xmax = plt.xlim()\n",
"x = np.linspace(xmin, xmax, 100)\n",
"p = stats.norm.pdf(x, mu, sigma)\n",
"plt.plot(x, p, 'k', linewidth=2)\n",
"title = \"Fit results: mu = %.2f, std = %.2f\" % (mu, sigma)\n",
"plt.title(title)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "967b597a-6602-49dc-882f-8a6ae69ccba8",
"metadata": {},
"source": [
"Generate the distribution for mu_sample"
]
},
{
"cell_type": "markdown",
"id": "5533817e-90ec-4671-b1ec-196916c079e2",
"metadata": {},
"source": [
"Now we don't are interested in the height of the person, now we are looking the average. So we multiple generate samples of people and then we are calculating the average. Also teh average should be normal distrubited. Re run the code at above."
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "43be8991-a5b0-4f0f-be9c-0f86b77d96a7",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Show the approximation with the normal distribution\n",
"mu, sigma = 180, 0.5 # mean and standard deviation\n",
"data = np.random.normal(mu, sigma, 1000)\n",
"plt.hist(data, bins=30, density=True, alpha=0.6, color='g')\n",
"xmin, xmax = plt.xlim()\n",
"x = np.linspace(xmin, xmax, 100)\n",
"p = stats.norm.pdf(x, mu, sigma)\n",
"plt.plot(x, p, 'k', linewidth=2)\n",
"title = \"Fit results: mu = %.2f, std = %.2f\" % (mu, sigma)\n",
"plt.title(title)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "f3c0c504-e041-4d85-8da0-3ef766f8e87a",
"metadata": {},
"source": [
"Generate the distribution of mu_sample and theoretical distribtion"
]
},
{
"cell_type": "markdown",
"id": "db5f4ad9-c37a-40b2-b815-6b1c34769f69",
"metadata": {},
"source": [
" <h1>Now one-way t-test</h1>\n",
" <p>We are assuming that the average height in the population is 178 cm, for example, in a sample from 1990. We want to prove that nowadays people are getting taller.</p>\n",
" <p><strong>H<sub>0</sub></strong> = 178 cm and <strong>H<sub>A</sub></strong> > 178 cm</p>\n",
" <p>So we have a one-sided test.</p>"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "f7118230-fc88-4a71-b813-2daa0c63c97c",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Generate 1000 random numbers from the first normal distribution\n",
"mu1, sigma1 = 180, 0.5 # mean and standard deviation for the first normal distribution\n",
"data = np.random.normal(mu1, sigma1, 1000)\n",
"\n",
"# Create a histogram of the data\n",
"plt.hist(data, bins=30, density=True, alpha=0.6, color='g')\n",
"\n",
"# Add a graph of the first normal distribution used to generate the data\n",
"xmin, xmax = 175, 182\n",
"x = np.linspace(xmin, xmax, 100)\n",
"p1 = stats.norm.pdf(x, mu1, sigma1)\n",
"plt.plot(x, p1, 'k', linewidth=2)\n",
"\n",
"# Add a graph of the second normal distribution with mu = 1 and sigma = 0.4\n",
"mu2, sigma2 = 178, 0.5\n",
"p2 = stats.norm.pdf(x, mu2, sigma2)\n",
"plt.plot(x, p2, 'r', linewidth=2)\n",
"\n",
"# Add vertical lines at x = 1 and x = 3 with labels\n",
"plt.axvline(x=178, color='b', linestyle='--', label='mu theoretical distribution')\n",
"plt.axvline(x=180, color='m', linestyle='--', label='mu in sample')\n",
"\n",
"title = \"Fit results: mu1 = %.2f, std1 = %.2f; mu2 = %.2f, std2 = %.2f\" % (mu1, sigma1, mu2, sigma2)\n",
"plt.title(title)\n",
"plt.xlim(xmin, xmax)\n",
"plt.legend()\n",
"\n",
"# Show the plot\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "8b4766b1-6fb5-487b-b552-790f43f83707",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Generate 1000 random numbers from the first normal distribution\n",
"mu1, sigma1 = 180, 0.5 # mean and standard deviation for the first normal distribution\n",
"data = np.random.normal(mu1, sigma1, 1000)\n",
"\n",
"# Create a histogram of the data\n",
"plt.hist(data, bins=30, density=True, alpha=0.6, color='g')\n",
"\n",
"# Add a graph of the first normal distribution used to generate the data\n",
"xmin, xmax = 175, 182\n",
"x = np.linspace(xmin, xmax, 100)\n",
"p1 = stats.norm.pdf(x, mu1, sigma1)\n",
"plt.plot(x, p1, 'k', linewidth=2)\n",
"\n",
"# Add a graph of the second normal distribution with mu = 1 and sigma = 0.4\n",
"mu2, sigma2 = 178, 0.5\n",
"p2 = stats.norm.pdf(x, mu2, sigma2)\n",
"plt.plot(x, p2, 'r', linewidth=2)\n",
"\n",
"# Add vertical lines at x = 1 and x = 3 with labels\n",
"plt.axvline(x=178, color='b', linestyle='--', label='mu theoretical distribution')\n",
"plt.axvline(x=180, color='m', linestyle='--', label='mu in sample')\n",
"\n",
"# Calculate the 95% quantile for the second normal distribution\n",
"quantile_95 = stats.norm.ppf(0.95, mu2, sigma2)\n",
"\n",
"# Plot the hatched area under the red curve for the 95% quantile and above\n",
"x_fill = np.linspace(quantile_95, xmax, 100)\n",
"p_fill = stats.norm.pdf(x_fill, mu2, sigma2)\n",
"plt.fill_between(x_fill, p_fill, color='blue', alpha=0.5, hatch='/')\n",
"\n",
"title = \"Fit results: mu1 = %.2f, std1 = %.2f; mu2 = %.2f, std2 = %.2f\" % (mu1, sigma1, mu2, sigma2)\n",
"plt.title(title)\n",
"plt.xlim(xmin, xmax)\n",
"plt.legend()\n",
"\n",
"# Show the plot\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "665a50fe-8404-4db3-b412-aec36d81016e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"T-statistic: 89.44271909999159, P-value: 0.0\n",
"The means of the two theoretical distributions are statistically different (reject H0).\n"
]
}
],
"source": [
"# Define the parameters for the two normal distributions\n",
"mu1, sigma1 = 180, 0.5 # mean and standard deviation for the first normal distribution\n",
"mu2, sigma2 = 178, 0.5 # mean and standard deviation for the second normal distribution\n",
"\n",
"# Perform a t-test to compare the means of the two theoretical distributions\n",
"# Since we don't have samples, we use the means and standard deviations directly\n",
"# Calculate the t-statistic and p-value manually\n",
"n1 = n2 = 1000 # sample sizes (assuming large sample sizes for theoretical distributions)\n",
"se = ((sigma1**2 / n1) + (sigma2**2 / n2))**0.5 # standard error\n",
"t_statistic = (mu1 - mu2) / se # t-statistic\n",
"df = n1 + n2 - 2 # degrees of freedom\n",
"p_value = stats.t.sf(abs(t_statistic), df) * 2 # two-tailed p-value\n",
"\n",
"# Print the t-test result\n",
"print(f\"T-statistic: {t_statistic}, P-value: {p_value}\")\n",
"\n",
"# Interpret the result\n",
"alpha = 0.05\n",
"if p_value < alpha:\n",
" print(\"The means of the two theoretical distributions are statistically different (reject H0).\")\n",
"else:\n",
" print(\"The means of the two theoretical distributions are not statistically different (fail to reject H0).\")"
]
},
{
"cell_type": "markdown",
"id": "63072dac-c7e6-4237-b5cc-b9832a2c7707",
"metadata": {},
"source": [
"Now with narrowed mu and alpha error"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "aa9ea3d5-3559-4fd7-a2c7-f041486c090e",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Generate 1000 random numbers from the first normal distribution\n",
"mu1, sigma1 = 180, 0.5 # mean and standard deviation for the first normal distribution\n",
"data = np.random.normal(mu1, sigma1, 1000)\n",
"\n",
"# Create a histogram of the data\n",
"plt.hist(data, bins=30, density=True, alpha=0.6, color='g')\n",
"\n",
"# Add a graph of the first normal distribution used to generate the data\n",
"xmin, xmax = 175, 182\n",
"x = np.linspace(xmin, xmax, 100)\n",
"p1 = stats.norm.pdf(x, mu1, sigma1)\n",
"plt.plot(x, p1, 'k', linewidth=2)\n",
"\n",
"# Add a graph of the second normal distribution with mu = 1 and sigma = 0.4\n",
"mu2, sigma2 = 179, 0.5\n",
"p2 = stats.norm.pdf(x, mu2, sigma2)\n",
"plt.plot(x, p2, 'r', linewidth=2)\n",
"\n",
"# Add vertical lines at x = 1 and x = 3 with labels\n",
"plt.axvline(x=mu2, color='b', linestyle='--', label='mu theoretical distribution')\n",
"plt.axvline(x=mu1, color='m', linestyle='--', label='mu in sample')\n",
"\n",
"# Calculate the 95% quantile for the second normal distribution\n",
"quantile_95 = stats.norm.ppf(0.95, mu2, sigma2)\n",
"\n",
"# Plot the hatched area under the red curve for the 95% quantile and above\n",
"x_fill = np.linspace(quantile_95, xmax, 100)\n",
"p_fill = stats.norm.pdf(x_fill, mu2, sigma2)\n",
"plt.fill_between(x_fill, p_fill, color='blue', alpha=0.5, hatch='/')\n",
"\n",
"title = \"Fit results: mu1 = %.2f, std1 = %.2f; mu2 = %.2f, std2 = %.2f\" % (mu1, sigma1, mu2, sigma2)\n",
"plt.title(title)\n",
"plt.xlim(xmin, xmax)\n",
"plt.legend()\n",
"\n",
"# Show the plot\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "0db5895c-28ab-4617-ad67-7ad8311d0341",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"T-statistic: 44.721359549995796, P-value: 2.8557430532137358e-303\n",
"The means of the two theoretical distributions are statistically different (reject H0).\n"
]
}
],
"source": [
"# Define the parameters for the two normal distributions\n",
"mu1, sigma1 = 180, 0.5 # mean and standard deviation for the first normal distribution\n",
"mu2, sigma2 = 179, 0.5 # mean and standard deviation for the second normal distribution\n",
"\n",
"# Perform a t-test to compare the means of the two theoretical distributions\n",
"# Since we don't have samples, we use the means and standard deviations directly\n",
"# Calculate the t-statistic and p-value manually\n",
"n1 = n2 = 1000 # sample sizes (assuming large sample sizes for theoretical distributions)\n",
"se = ((sigma1**2 / n1) + (sigma2**2 / n2))**0.5 # standard error\n",
"t_statistic = (mu1 - mu2) / se # t-statistic\n",
"df = n1 + n2 - 2 # degrees of freedom\n",
"p_value = stats.t.sf(abs(t_statistic), df) * 2 # two-tailed p-value\n",
"\n",
"# Print the t-test result\n",
"print(f\"T-statistic: {t_statistic}, P-value: {p_value}\")\n",
"\n",
"# Interpret the result\n",
"alpha = 0.05\n",
"if p_value < alpha:\n",
" print(\"The means of the two theoretical distributions are statistically different (reject H0).\")\n",
"else:\n",
" print(\"The means of the two theoretical distributions are not statistically different (fail to reject H0).\")"
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "ab987426-9a37-4c22-b561-d2870b856071",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Generate 1000 random numbers from the first normal distribution\n",
"mu1, sigma1 = 180, 0.5 # mean and standard deviation for the first normal distribution\n",
"data = np.random.normal(mu1, sigma1, 1000)\n",
"\n",
"# Create a histogram of the data\n",
"plt.hist(data, bins=30, density=True, alpha=0.6, color='g')\n",
"\n",
"# Add a graph of the first normal distribution used to generate the data\n",
"xmin, xmax = 175, 182\n",
"x = np.linspace(xmin, xmax, 100)\n",
"p1 = stats.norm.pdf(x, mu1, sigma1)\n",
"plt.plot(x, p1, 'k', linewidth=2)\n",
"\n",
"# Add a graph of the second normal distribution with mu = 1 and sigma = 0.4\n",
"mu2, sigma2 = 179.8, 0.5\n",
"p2 = stats.norm.pdf(x, mu2, sigma2)\n",
"plt.plot(x, p2, 'r', linewidth=2)\n",
"\n",
"# Add vertical lines at x = 1 and x = 3 with labels\n",
"plt.axvline(x=mu2, color='b', linestyle='--', label='mu theoretical distribution')\n",
"plt.axvline(x=mu1, color='m', linestyle='--', label='mu in sample')\n",
"\n",
"# Calculate the 95% quantile for the second normal distribution\n",
"quantile_95 = stats.norm.ppf(0.95, mu2, sigma2)\n",
"\n",
"# Plot the hatched area under the red curve for the 95% quantile and above\n",
"x_fill = np.linspace(quantile_95, xmax, 100)\n",
"p_fill = stats.norm.pdf(x_fill, mu2, sigma2)\n",
"plt.fill_between(x_fill, p_fill, color='blue', alpha=0.5, hatch='/')\n",
"\n",
"title = \"Fit results: mu1 = %.2f, std1 = %.2f; mu2 = %.2f, std2 = %.2f\" % (mu1, sigma1, mu2, sigma2)\n",
"plt.title(title)\n",
"plt.xlim(xmin, xmax)\n",
"plt.legend()\n",
"\n",
"# Show the plot\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "9c019dea-d687-4dc1-b48f-fe629e54172e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"T-statistic: 8.944271909998651, P-value: 8.328998310440721e-19\n",
"The means of the two theoretical distributions are not statistically different (fail to reject H0).\n"
]
}
],
"source": [
"# Define the parameters for the two normal distributions\n",
"mu1, sigma1 = 180, 0.5 # mean and standard deviation for the first normal distribution\n",
"mu2, sigma2 = 179.8, 0.5 # mean and standard deviation for the second normal distribution\n",
"\n",
"# Perform a t-test to compare the means of the two theoretical distributions\n",
"# Since we don't have samples, we use the means and standard deviations directly\n",
"# Calculate the t-statistic and p-value manually\n",
"n1 = n2 = 1000 # sample sizes (assuming large sample sizes for theoretical distributions)\n",
"se = ((sigma1**2 / n1) + (sigma2**2 / n2))**0.5 # standard error\n",
"t_statistic = (mu1 - mu2) / se # t-statistic\n",
"df = n1 + n2 - 2 # degrees of freedom\n",
"p_value = stats.t.sf(abs(t_statistic), df) * 2 # two-tailed p-value\n",
"\n",
"# Print the t-test result\n",
"print(f\"T-statistic: {t_statistic}, P-value: {p_value}\")\n",
"\n",
"# Interpret the result\n",
"alpha = 5e-20\n",
"if p_value < alpha:\n",
" print(\"The means of the two theoretical distributions are statistically different (reject H0).\")\n",
"else:\n",
" print(\"The means of the two theoretical distributions are not statistically different (fail to reject H0).\")"
]
}
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