{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Contraste Bilateral:  Cálculo del Error de tipo II\n",
    "\n",
    "## Parámetro $p$ en variables de $Bernoulli$\n",
    "\n",
    "#### Autor:\n",
    "Sergio García Prado - [garciparedes.me](https://garciparedes.me)\n",
    "\n",
    "#### Fecha:\n",
    "Abril de 2018\n",
    "\n",
    "#### Agradecimientos:\n",
    "Me gustaría agradecer a la profesora [Pilar Rodríguez del Tío](http://www.eio.uva.es/~pilar/) la revisión y correcciones sobre este trabajo."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Descripción:\n",
    "\n",
    "Las variables aleatorias de $Bernoulli$ surgen cuando se pretende estudiar fenómenos de carácter binario como por ejemplo, la ocurrencia o no de un determinado suceso. Estas variables se caracterizan por el ratio de ocurrencia del suceso de estudio, el cual se denota por $p \\in [0, 1]$. \n",
    "\n",
    "\n",
    "Sin embargo, este parámetro es desconocido en la mayoría de casos, por lo que es habitual que surja la pregunta sobre qué valor es el que toma. Para hacer inferencia sobre $p$ existen distintas técnicas, entre las que se encuentran los contrastes de hipótesis. En los contrastes se utilizan por dos parámetros de error conocidos como $\\alpha$ y $\\beta$ que representan la probabilidad de rechazar la hipótesis cuando era cierta y de aceptarla cuando era falsa.\n",
    "\n",
    "Estos errores están relacionados entre si, y cuando uno disminuye el otro aumenta, por lo que es necesario estudiar su comportamiento en detalle para llegar a extraer conclusiones razonables de nuestros datos.\n",
    "\n",
    "En este trabajo nos hemos centrado en estudiar la variación del error de tipo II (probabilidad de aceptar la hipótesis $p = c$ cuando en realidad era falsa) en el contraste bilateral para el parámetro p sobre una muestra aleatoria simple de variables de Bernoulli."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Procedimiento:\n",
    "\n",
    "Sea: \n",
    "\n",
    "$$X_1,..., X_i,..., X_n \\ m.a.s \\mid X_i \\sim B(p) $$\n",
    "\n",
    "Sabemos que:\n",
    "\n",
    "$$\\widehat{p} = \\bar{X} = \\frac{\\sum_{i = 1}^nX_i}{n}$$\n",
    "\n",
    "Para realizar el contraste:\n",
    "\n",
    "$$H_0: p = c\\\\H_1:p \\neq c$$\n",
    "\n",
    "Sabemos que:\n",
    "\n",
    "\\begin{align}\n",
    "\\widehat{p} \\simeq N(p, \\frac{p(1-p)}{n}) &\\quad \\text{(bajo cualquier hipótesis)}\\\\\n",
    "\\widehat{p} \\simeq N(c, \\frac{c(1-c)}{n}) &\\quad \\text{(bajo $H_0$)}\n",
    "\\end{align}\n",
    "\n",
    "Si tipificamos para en ambos casos:\n",
    "\n",
    "\\begin{align}\n",
    "\\frac{\\widehat{p} - p}{\\sqrt{\\frac{p(1-p)}{n}}} \\simeq N(0, 1) &\\quad \\text{(bajo cualquier hipótesis)}\\\\\n",
    "\\frac{\\widehat{p} - c}{\\sqrt{\\frac{c(1-c)}{n}}} \\simeq N(0, 1) &\\quad \\text{(bajo $H_0$)}\n",
    "\\end{align}\n",
    "\n",
    "Ahora, queremos construir la región crítica o de rechazo tal que: \n",
    "\n",
    "$$P_{H_0}(C) = \\alpha$$\n",
    "\n",
    "Por lo tanto:\n",
    "\n",
    "\\begin{align}\n",
    "C \n",
    "&= \\left\\{ \\left| \\ N(0,1) \\ \\right| \\geq Z_{1 - \\frac{\\alpha}{2}}\\right\\} \\\\\n",
    "&= \\left\\{ \\left| \\ \\frac{\\widehat{p} - c}{\\sqrt{\\frac{c(1-c)}{n}}} \\ \\right| \\geq Z_{1 - \\frac{\\alpha}{2}} \\right\\} \\\\\n",
    "&= \\left\\{ \\left| \\ \\widehat{p} - c \\ \\right| \\geq Z_{1 - \\frac{\\alpha}{2}} \\sqrt{\\frac{c(1-c)}{n}}\\right\\} \\\\\n",
    "&= \\left\\{ \\widehat{p} \\leq c - Z_{1 - \\frac{\\alpha}{2}}  \\sqrt{\\frac{c(1-c)}{n}}\\right\\} \\cup \\left\\{c + Z_{1 - \\frac{\\alpha}{2}} \\sqrt{\\frac{c(1-c)}{n}} \\leq \\widehat{p}\\right\\}  \\\\\n",
    "\\end{align}\n",
    "\n",
    "(Donde $Z_{1 - \\frac{\\alpha}{2}}$ se refiere al cuantil $1-\\alpha/2$ de la distribución Normal estándar)\n",
    "\n",
    "Sin embargo, buscamos calcular el error de tipo II: \n",
    "\n",
    "$$\\beta\\left(p\\right) = P_p(\\bar{C})$$\n",
    "\n",
    "Luego, obtenemos el complementario de la región crítica:\n",
    "\n",
    "\\begin{align}\n",
    "\\bar{C} \n",
    "&= \\left\\{ \\left| \\ N(0,1) \\ \\right| < Z_{1 - \\frac{\\alpha}{2}}\\right\\} \\\\\n",
    "&= \\left\\{ \\left| \\ \\frac{\\widehat{p} - c}{\\sqrt{\\frac{c(1-c)}{n}}} \\ \\right| < Z_{1 - \\frac{\\alpha}{2}} \\right\\} \\\\\n",
    "&= \\left\\{ \\left| \\ \\widehat{p}  - c\\ \\right| < Z_{1 - \\frac{\\alpha}{2}} \\sqrt{\\frac{c(1-c)}{n}}\\right\\} \\\\\n",
    "&= \\left\\{ c - Z_{1-\\frac{\\alpha}{2}} \\sqrt{\\frac{c(1-c)}{n}} < \\widehat{p} < c + Z_{1 - \\frac{\\alpha}{2}} \\sqrt{\\frac{c(1-c)}{n}}\\right\\} \\\\\n",
    "\\end{align}\n",
    "\n",
    "Para después desarrollar el cálculo de dicha probabilidad:\n",
    "\n",
    "\\begin{align}\n",
    "\\beta(p) \n",
    "&= P_p(\\bar{C}) \\\\\n",
    "&= P_p\\left(\\left| \\frac{\\widehat{p} - c}{\\sqrt{\\frac{c(1-c)}{n}}} \\right| < Z_{1 - \\frac{\\alpha}{2}}\\right) \\\\\n",
    "&= P_p\\left(c - Z_{\\frac{\\alpha}{2}} \\sqrt{\\frac{c(1-c)}{n}} < \\widehat{p} < c + Z_{ 1- \\frac{\\alpha}{2}} \\sqrt{\\frac{c(1-c)}{n}}\\right) \\\\\n",
    "&= \\Phi\\left(\\frac{\\left(c + Z_{1 - \\frac{\\alpha}{2}} \\sqrt{\\frac{c(1-c)}{n}}\\right)-p}{\\sqrt{\\frac{p(1-p)}{n}}}\\right) - \\Phi\\left(\\frac{\\left(c - Z_{1 - \\frac{\\alpha}{2}} \\sqrt{\\frac{c(1-c)}{n}}\\right)-p}{\\sqrt{\\frac{p(1-p)}{n}}}\\right)\n",
    "\\end{align}\n",
    "\n",
    "(Donde $\\Phi(x)$ se refiere a la función de distribución de la Normal estándar)\n",
    "\n",
    "A continuación se muestra la implementación de los cálculos superiores en __R__:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementación:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Cálculo del varlor crítico de nivel $\\alpha$ para variables de Bernoulli:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "CriticalValue <- function(n, p, alpha) {\n",
    "  qnorm(alpha) * sqrt((p * (1 - p)) / n)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Cálculo de la probabilidad $P(\\bar{C})$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "PNegateC <- function(p, n, c, alpha) {\n",
    "  pnorm(\n",
    "    (\n",
    "      c + CriticalValue(n, c, 1 - alpha / 2)  - p\n",
    "    ) / sqrt((p * (1 - p)) / n)\n",
    "  ) - \n",
    "  pnorm(\n",
    "    (\n",
    "      c - CriticalValue(n, c,  1 - alpha / 2)  - p\n",
    "    ) / sqrt((p * (1 - p)) / n)\n",
    "  )\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Representación gráfica de $\\beta(p)$ tomando distintos valores $c$ y $n$ (manteniendo $\\alpha$ fijo) para comprobar su variación "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "n.vec <- 10 ^ (1:3)\n",
    "c.vec <- c(0.25, 0.5, 0.75)\n",
    "p <- seq(0, 1, length = 200)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Resultados:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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DtJabNIHhh5etqDHZ/bOIO0Xy39cn1G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cV2vaHCBdJ13S9In6lD8BUlyttVrFWV/ysGrTRoDUNGHyhwAEQgicrcQexeniOSSf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\n61YCpL623DDLTf9lmO3ah1p5mt3mqYK6b5j0E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sq2ydo6uUf0yl5HTZTVecbSfk3Vr4/5hlzLIWlDWZS9lkPzDUkfy/UZwhn/Mm3hWNpv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\nAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title “c = 0.75 \n",
       "n = 1000”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "par(mfrow = c(length(n.vec), length(c.vec)))\n",
    "for (n in n.vec) {\n",
    "  for (c in c.vec) {\n",
    "    plot(p, 1 - PNegateC(p, n, c, 0.05), type = \"l\", \n",
    "         main = paste(\"c =\", c, \"\\nn =\", n),\n",
    "         ylab = \"A(p) = 1 - B(p)\")\n",
    "  }\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tal y como se puede apreciar, la función del error tan solo es simétrica en el caso $c = \\frac{1}{2}$, lo cual es más marcado para valores de $n$ pequeños. Además, conforme aumenta $n$ la función $\\beta(p)$ se vuelve mucho más apuntada entorno a $c$, por lo que el error de tipo II se mantiene muy bajo excepto para valores $p \\simeq c$. Esto tiene sentido ya que el error cometido por rechazar que el verdadero valor de $p$ es $c$ será bajo cuando realmente no sea $c$, mientras que será elevado cuando si que lo sea. En dicho caso, este error está condicionado por el error de no rechazo, es decir, de tipo I (en este ejemplo $\\alpha = 0.05$)."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.5.0"
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 "nbformat": 4,
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}