example- Ratio.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exploring ratio.py module"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate random samples\n",
    "np.random.seed(1984)\n",
    "T1 = np.random.normal(loc=14.0, scale=3.0, size=6)\n",
    "T2 = np.random.normal(loc=7.0, scale=2.0, size=6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from dcstats.ratio import Ratio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Ratio = 1.87 +/- 0.17 (approximate SDM)\n",
      "\tapproximate 95% confidence limits:\n",
      "\tlower= 1.5; upper= 2.24\n",
      "\tFieller 95% confidence limits:\n",
      "\tlower= 1.44; upper= 2.49\n",
      "\n",
      "Bootsrapping statistics (repeats = 50000):\n",
      "Ratio= 1.87 +/- 0.21 (bootstrapped SDM); bias= -0.014\n",
      "\t95% confidence limits (bootstrapped):\n",
      "\tlower= 1.53; upper= 2.35\n"
     ]
    }
   ],
   "source": [
    "rt = Ratio(T1, T2)\n",
    "rt.run_bootstrap(50000)\n",
    "print(rt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = rt.plot_bootstrap()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "#### Compare to GraphPad calculator results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "meanA = 13.8156018784828 ; meanB = 7.373761350516429\n",
      "sdA = 2.5318571014924607 ;sdB = 1.7214705715414245\n"
     ]
    }
   ],
   "source": [
    "print('meanA =', rt.meanA, '; meanB =', rt.meanB)\n",
    "print('sdA =', rt.sdA, ';sdB =', rt.sdB)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Following are results from GraphPad calculator:   \n",
    "https://www.graphpad.com/quickcalcs/errorProp2/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " CI of a quotient\n",
    "\n",
    "Mean of Variable A divided by Mean of Variable B = 1.873616628169721 \n",
    "\n",
    "95% CI: \t1.436957351945638 \tto \t2.487248647961153 \n",
    "\n",
    "These results assume that both variables follow a Gaussian distribution\n",
    "and that the measurements of Variable A are not paired or matched to\n",
    "measurements of Variable B.\n",
    "\n",
    "Results computed by the method of EC Fieller, Suppl to\n",
    "J.R.Statist.Soc, 7,1-64"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Wikipedia:   https://en.wikipedia.org/wiki/Fieller%27s_theorem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Old fieller.py module (supperseeded by ratio.py)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "FIELLER: calculates confidence limits for a ratio according Fieller's theorem. Output includes the approximate SD of the ratio r = a / b, given the SD of a (the numerator) and of b (the denominator) and the correlation coefficient between a & b (zero if they are independent). \n",
    "Fieller requires the t-statistic which is calculated from alpha and the degrees of freedom. Alpha is taken as for two-tailed t-distribution ution (e.g. 0.05 leaves 95% area: limits calculated at 2.5% and 97.5%)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "from dcstats.fieller import Fieller"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "a, b = 14, 7 # Nominator and denominator\n",
    "sa, sb = 3, 2 # SD of nominator and denominator\n",
    "r = 0 # Correlation coefficient (a,b)\n",
    "alpha = 0.05 # alpha\n",
    "n = 12 # Total number of observations na + nb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " Fieller calculation result: \n",
      " Ratio (a/b) = 2.000000\n",
      " t(df=10, alpha=0.05) = 2.228138\n",
      "\n",
      " Confidence limits: lower 0.889734, upper 5.836045\n",
      " Approximate SD of ratio = 0.714286\n",
      " Approximate CV of ratio (%) = 35.714286\n",
      " Approximate limits: lower 0.408473, upper 3.591527\n"
     ]
    }
   ],
   "source": [
    "flr = Fieller(a, b, sa, sb, r, alpha, n)\n",
    "print(flr)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.6"
  }
 },
 "nbformat": 4,
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