{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Lab 2-2: Type II Error and Power\n", "---\n", "\n", "**What is the Type II error and Power for your test on the mean from Lab 2-1?**\n", "\n", "In this case, we will assume that true mean has increased by 30% (true mean is 1.3 times the early mean), and that the pooled standard deviation has increased by 10% (true pooled standard deviation is 1.1 times $\\sigma'$, where $\\sigma'$ is our test estimate of pooled estimator for the two observed data sets)." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# import libraries we'll need\n", "import pandas as pd\n", "import numpy as np\n", "import scipy.stats as stats\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/opt/conda/lib/python3.10/site-packages/openpyxl/worksheet/_read_only.py:81: UserWarning: Unknown extension is not supported and will be removed\n", " for idx, row in parser.parse():\n" ] }, { "data": { "text/html": [ "
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date of peakwater yearpeak value (cfs)gage_ht (feet)
01928-10-0919291880010.55
11930-02-0519301580010.44
21931-01-2819313510014.08
\n", "
" ], "text/plain": [ " date of peak water year peak value (cfs) gage_ht (feet)\n", "0 1928-10-09 1929 18800 10.55\n", "1 1930-02-05 1930 15800 10.44\n", "2 1931-01-28 1931 35100 14.08" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Read the excel file\n", "skykomish_data_file = '../data/Skykomish_peak_flow_12134500_WY1929_2023.xlsx'\n", "skykomish_data = pd.read_excel(skykomish_data_file)\n", "# Preview our data\n", "skykomish_data.head(3)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# Divide the data into the early period (before 1977) and late period (after and including 1977).\n", "skykomish_before = skykomish_data[ skykomish_data['water year'] < 1977 ] \n", "skykomish_after = skykomish_data[ skykomish_data['water year'] >= 1977 ] " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "### Calculate Type II error and Power\n", "Recall from the class lectures that the Type II error, $\\beta$, is the probability that we would incorrectly conclude that a change in the probability distribution had NOT taken place, if in fact a change of a certain assumed magnitude had occurred (failure to reject a false null hypothesis). \n", "\n", "Type II error is a function of both $\\alpha$ (expressed in the equation below with $z_{\\alpha}$), and the posited true nature of the probability distribution we are hoping to detect (we get to decide how different the true probability distribution is from the null hypothesis, and then see how likely we would be to make a mistake). \n", "\n", "\n", "${ \\beta = P\\big((\\overline{X}-\\overline{Y}) < \\Delta_0 + z_{\\alpha}\\sigma'\\big)}$\n", "\n", "where $\\sigma'$ is the pooled standard deviation from $\\overline{X}$ (the later period) and $\\overline{Y}$ (the earlier period):\n", "\n", "$\\sigma' = \\displaystyle\\sqrt{ \\displaystyle\\frac{s^2_X}{n_X} + \\displaystyle\\frac{s^2_Y}{n_Y} }$\n", "\n", "\n", "Power, $(1-\\beta)$, is the probability that we would correctly conclude that a change in the probability distribution had taken place, given a certain assumed magnitude change had occurred." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we assume a true normal distribution with mean $(\\overline{X}-\\overline{Y}) = \\Delta^* = 0.3\\cdot\\overline{Y}$ \n", "\n", "and a true standard deviation $\\sigma^* = 1.1\\cdot\\sigma'$\n", "\n", "then we need to solve for the intersection of $ \\Delta^* + z_{eff}\\sigma^* = \\Delta_0 + z_{\\alpha}\\sigma'$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Type II error: 0.162\n", "Power: 0.838\n" ] } ], "source": [ "# Get the length of our two datasets\n", "nX = len(skykomish_after)\n", "nY = len(skykomish_before)\n", "\n", "# Set our alpha and confidence\n", "alpha = 0.05\n", "conf = 1 - alpha\n", "\n", "# Calculate z_alpha from a normal distribution\n", "z_alpha = stats.norm.ppf(conf)\n", "\n", "# Get our means\n", "meanX = skykomish_after['peak value (cfs)'].mean()\n", "meanY = skykomish_before['peak value (cfs)'].mean()\n", "\n", "# Get our standard deviations\n", "sdX = skykomish_after['peak value (cfs)'].std(ddof=1)\n", "sdY = skykomish_before['peak value (cfs)'].std(ddof=1)\n", "\n", "# Calculate the pooled standard deivation\n", "sigma_prime = np.sqrt(sdX**2/nX + sdY**2/nY)\n", "\n", "# For our null hypothesis PDF\n", "delta_0 = 0\n", "\n", "# Set our expected change in the mean (30% of early period mean)\n", "delta_star = .3 * meanY\n", "\n", "# Set our expected change in the standard deviation (1.1 times the pooled standard deviation)\n", "sigma_star = 1.1 * sigma_prime\n", "\n", "# Rearranging the equation above to solve for the \"z effective\" value, the z value on our postulated \"true\" PDF\n", "z_eff = ((delta_0 + z_alpha*sigma_prime) - delta_star) / sigma_star\n", "\n", "# Look up the cdf value of the postulated true distribution at this point to get our beta vlaue\n", "beta = stats.norm.cdf(z_eff)\n", "print(\"Type II error: {}\".format(np.round(beta,4)))\n", "\n", "# Thus, our confidence that we are not commiting Type II error is\n", "power = 1 - beta\n", "print(\"Power: {}\".format(np.round(power,4)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compute the two-sample z-test value:\n", "\n", "$ztest = \\displaystyle\\frac{(\\bar{X}-\\bar{Y})-\\Delta_0}{\\sigma'}$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "z-test = 2.63\n", "p = 0.0043\n" ] } ], "source": [ "z_test = ((meanX - meanY) - delta_0) / sigma_prime\n", "print(\"z-test = {}\".format(np.round(z_test,2)))\n", "\n", "p = 1 - stats.norm.cdf(z_test)\n", "print(\"p = {}\".format(np.round(p,4)))" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Make a plot\n", "plt.figure(figsize=(10,6))\n", "\n", "# Create values for z\n", "z = np.linspace(-4, 4, num=160) * sigma_prime\n", " \n", "# Plot the Null PDF\n", "plt.plot(z, stats.norm.pdf(z, delta_0, sigma_prime), label='Null PDF: ($\\overline{x}$ - $\\overline{y}$) = $\\Delta_0$ = 0')\n", "\n", "## Plot the postulated True PDF\n", "plt.plot(z, stats.norm.pdf(z, delta_star, sigma_star), color='red', label=r'\"True\" PDF: ($\\overline{x}$ - $\\overline{y}$) = $\\Delta^*$')\n", "\n", "# Plot where z_alpha is\n", "plt.axvline(z_alpha*sigma_prime, color='black', linestyle='--', label=r'Z$_\\alpha$')\n", "# Add labels here with z_alpha and z_eff values\n", "plt.text(z_alpha*sigma_prime+300, 4e-5, r'Z$_{eff}$ = ' + str(round(z_eff,2)),fontsize=12, color='r')\n", "plt.text(z_alpha*sigma_prime+300, 4.5e-5, r'Z$_{\\alpha}$ = ' + str(round(z_alpha,2)),fontsize=12, color='k')\n", "\n", "# Plot where z_test is\n", "#plt.axvline(z_test*sigma_prime, color='k', linestyle=':', label=r'z-test')\n", "# Add labels here with z_test\n", "#plt.text(z_test*sigma_prime+300, 1e-5, r'z-test = ' + str(round(z_test,2)),fontsize=12, color='k')\n", "\n", "# Shade in the Type I Error area\n", "shade = np.linspace(z_alpha*sigma_prime, np.max(z), 10)\n", "plt.fill_between(shade, stats.norm.pdf(shade, delta_0, sigma_prime) , color='red', alpha=0.5, label='Type I Error')\n", "# Add label here with alpha value\n", "plt.text(z_alpha*sigma_prime+200, 0.1e-5, r'$\\alpha$ = ' + str(round(alpha,2)),fontsize=12, color='w')\n", "\n", "# Shade in the Type II Error area\n", "shade = np.linspace(np.min(z),z_alpha*sigma_prime, 30)\n", "plt.fill_between(shade, stats.norm.pdf(shade, delta_star, sigma_star) , color='m', alpha=0.5, label='Type II Error')\n", "# Add label here with Beta value\n", "plt.text(z_alpha*sigma_prime-6000, 1e-5, r'$\\beta$ = ' + str(round(beta,2)),fontsize=12, color='w')\n", "\n", "# Add title, legend, and labels\n", "plt.title('Visualization of Type I & II Error',fontsize=20)\n", "plt.xlabel('($\\overline{x}$ - $\\overline{y}$) [cfs]', fontsize=15)\n", "plt.ylabel('Probability',fontsize=15)\n", "plt.ylim(0, 9e-5)\n", "plt.ticklabel_format(axis='both', style='sci', scilimits=(0,0))\n", "plt.legend(loc='upper left',fontsize=12);" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.13" } }, "nbformat": 4, "nbformat_minor": 4 }