statistical_tests.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Review of Statistical Tests"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Kruskal-Wallis\n",
    "\n",
    "El test de Kruskal-Wallis, también conocido como test H, es la alternativa no paramétrica al test ANOVA de una vía para datos no pareados. Se trata de una extensión del test de Mann-Whitney para más de dos grupos. Es por lo tanto de un test que emplea rangos para contrastar la hipótesis de que k muestras han sido obtenidas de una misma población.\n",
    "\n",
    "A diferencia del ANOVA en el que se comparan medias, el test de Kruskal-Wallis contrasta si las diferentes muestras están equidistribuidas y que por lo tanto pertenecen a una misma distribución (población). Bajo ciertas simplificaciones puede considerarse que el test de Kruskal-Wallis compara las medianas.\n",
    "\n",
    "- H0: todas las muestras provienen de la misma población (distribución).\n",
    "- HA: Al menos una muestra proviene de una población con una distribución distinta.\n",
    "\n",
    "El test de Kruskal-Wallis es el test adecuado cuando los datos tienen un orden natural, es decir, cuando para darles sentido tienen que estar ordenados o bien cuando no se satisfacen las condiciones para poder aplicar un ANOVA.\n",
    "\n",
    "\n",
    "Supóngase que se dispone de k grupos cada uno con n observaciones. Si se ordenan todas las observaciones de menor a mayor y se le asigna a cada una de ellas su rango, cuando se obtenga la suma de rangos para cada uno de los grupos (Ri) es de esperar que, si se cumple la hipótesis nula, todos los grupos tengan un valor similar. Partiendo de esta idea se calcula el estadístico H como:\n",
    "\n",
    "\n",
    "$$ H = 12/(N/(N+1)) * (\\sum_{i = 1}^{k} R_{i}^2 - 3(N+1)) $$\n",
    "\n",
    "**Condiciones**\n",
    "\n",
    "- No es necesario que las muestras que se comparan provengan de una distribución normal.\n",
    "\n",
    "- Homocedasticidad: dado que la hipótesis nula asume que todos los grupos pertenecen a una misma población y que por lo tanto tienen las mismas medianas, es requisito necesario que todos los grupos tengan la misma varianza. Se puede comprobar con representaciones gráficas o con los test de Levenne o Barttlet.\n",
    "\n",
    "- Misma distribución para todos los grupos: la distribución de los grupos no tiene que ser normal pero ha de ser igual en todos (por ejemplo que todos muestren asimetría hacia la derecha).\n",
    "\n",
    "\n",
    "Si estos requerimientos se cumplen, el estadístico H del test de Kruskal-Wallis se compara con:\n",
    "\n",
    "Si el tamaño de grupos k es igual a 3 y el número de observaciones en cada uno no es mayor que 5, se recurre a tablas tabuladas con valores teóricos de H.\n",
    "\n",
    "En el resto de casos se asume que el estadístico H sigue una distribución χ2 con k-1 grados de libertad (siendo k el número de grupos a comparar)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>condicion</th><th scope=col>n_huevos</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>condicion1</td><td>1</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>condicion1</td><td>2</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>condicion1</td><td>3</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>condicion1</td><td>4</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>condicion1</td><td>5</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>condicion1</td><td>6</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 2\n",
       "\\begin{tabular}{r|ll}\n",
       "  & condicion & n\\_huevos\\\\\n",
       "  & <fct> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & condicion1 & 1\\\\\n",
       "\t2 & condicion1 & 2\\\\\n",
       "\t3 & condicion1 & 3\\\\\n",
       "\t4 & condicion1 & 4\\\\\n",
       "\t5 & condicion1 & 5\\\\\n",
       "\t6 & condicion1 & 6\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 2\n",
       "\n",
       "| <!--/--> | condicion &lt;fct&gt; | n_huevos &lt;dbl&gt; |\n",
       "|---|---|---|\n",
       "| 1 | condicion1 | 1 |\n",
       "| 2 | condicion1 | 2 |\n",
       "| 3 | condicion1 | 3 |\n",
       "| 4 | condicion1 | 4 |\n",
       "| 5 | condicion1 | 5 |\n",
       "| 6 | condicion1 | 6 |\n",
       "\n"
      ],
      "text/plain": [
       "  condicion  n_huevos\n",
       "1 condicion1 1       \n",
       "2 condicion1 2       \n",
       "3 condicion1 3       \n",
       "4 condicion1 4       \n",
       "5 condicion1 5       \n",
       "6 condicion1 6       "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "datos <- data.frame(\n",
    "    condicion = c(rep(\"condicion1\", 18), rep(\"condicion2\", 18), rep(\"condicion3\", 18)),\n",
    "    n_huevos = c(\n",
    "        1, 2, 3, 4, 5, 6, 7, 8, 9, 16, 27, 28, 29, 30, 51, 52, 53, 342, 40,\n",
    "        41, 42, 43, 44, 45, 46, 47, 48, 67, 88, 89, 90, 91, 92, 93, 94, 293,\n",
    "        19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 25, 36, 37, 58, 59, 60, 71, 72\n",
    "    )\n",
    ")\n",
    "head(datos)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 3 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>condicion</th><th scope=col>n_huevos</th></tr>\n",
       "\t<tr><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>condicion1</td><td>12.5</td></tr>\n",
       "\t<tr><td>condicion2</td><td>57.5</td></tr>\n",
       "\t<tr><td>condicion3</td><td>26.5</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 3 × 2\n",
       "\\begin{tabular}{ll}\n",
       " condicion & n\\_huevos\\\\\n",
       " <fct> & <dbl>\\\\\n",
       "\\hline\n",
       "\t condicion1 & 12.5\\\\\n",
       "\t condicion2 & 57.5\\\\\n",
       "\t condicion3 & 26.5\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 3 × 2\n",
       "\n",
       "| condicion &lt;fct&gt; | n_huevos &lt;dbl&gt; |\n",
       "|---|---|\n",
       "| condicion1 | 12.5 |\n",
       "| condicion2 | 57.5 |\n",
       "| condicion3 | 26.5 |\n",
       "\n"
      ],
      "text/plain": [
       "  condicion  n_huevos\n",
       "1 condicion1 12.5    \n",
       "2 condicion2 57.5    \n",
       "3 condicion3 26.5    "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aggregate(n_huevos ~ condicion, data = datos, FUN = median)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 3 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>condicion</th><th scope=col>n_huevos</th></tr>\n",
       "\t<tr><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>condicion1</td><td>78.10637</td></tr>\n",
       "\t<tr><td>condicion2</td><td>58.41750</td></tr>\n",
       "\t<tr><td>condicion3</td><td>18.59097</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 3 × 2\n",
       "\\begin{tabular}{ll}\n",
       " condicion & n\\_huevos\\\\\n",
       " <fct> & <dbl>\\\\\n",
       "\\hline\n",
       "\t condicion1 & 78.10637\\\\\n",
       "\t condicion2 & 58.41750\\\\\n",
       "\t condicion3 & 18.59097\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 3 × 2\n",
       "\n",
       "| condicion &lt;fct&gt; | n_huevos &lt;dbl&gt; |\n",
       "|---|---|\n",
       "| condicion1 | 78.10637 |\n",
       "| condicion2 | 58.41750 |\n",
       "| condicion3 | 18.59097 |\n",
       "\n"
      ],
      "text/plain": [
       "  condicion  n_huevos\n",
       "1 condicion1 78.10637\n",
       "2 condicion2 58.41750\n",
       "3 condicion3 18.59097"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aggregate(n_huevos ~ condicion, data = datos, FUN = sd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "\n",
    "ggplot(data = datos, mapping = aes(x = condicion, y = n_huevos, colour = condicion)) +\n",
    "    geom_boxplot() +\n",
    "    theme_bw() +\n",
    "    theme(legend.position = \"none\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ggplot(data = datos, mapping = aes(x = n_huevos, colour = condicion)) +\n",
    "    geom_histogram() +\n",
    "    theme_bw() +\n",
    "    facet_grid(. ~ condicion) +\n",
    "    theme(legend.position = \"none\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La representación gráfica de los datos muestra que las muestras no se distribuyen de forma normal, lo que supone una limitación para emplear un test ANOVA. Las tres muestras presentan el mismo tipo de distribución, asimetría hacia la derecha, a falta de comprobar la homogeneidad de varianza el test de Kruskal-Wallis es la opción más adecuada (otra alternativa serían las técnicas de resampling).\n",
    "\n",
    "\n",
    "**Condiciones**\n",
    "\n",
    "Homocedasticidad: la varianza debe de ser constante entre todos los grupos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: carData\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A anova: 2 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>Df</th><th scope=col>F value</th><th scope=col>Pr(&gt;F)</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>group</th><td> 2</td><td>0.7929454</td><td>0.458009</td></tr>\n",
       "\t<tr><th scope=row> </th><td>51</td><td>       NA</td><td>      NA</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A anova: 2 × 3\n",
       "\\begin{tabular}{r|lll}\n",
       "  & Df & F value & Pr(>F)\\\\\n",
       "  & <int> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\tgroup &  2 & 0.7929454 & 0.458009\\\\\n",
       "\t  & 51 &        NA &       NA\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A anova: 2 × 3\n",
       "\n",
       "| <!--/--> | Df &lt;int&gt; | F value &lt;dbl&gt; | Pr(&gt;F) &lt;dbl&gt; |\n",
       "|---|---|---|---|\n",
       "| group |  2 | 0.7929454 | 0.458009 |\n",
       "| <!----> | 51 |        NA |       NA |\n",
       "\n"
      ],
      "text/plain": [
       "      Df F value   Pr(>F)  \n",
       "group  2 0.7929454 0.458009\n",
       "      51        NA       NA"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(car)\n",
    "leveneTest(n_huevos ~ condicion, data = datos, center = \"median\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Ahora empleamos el test de Kruskal-Wallis**\n",
    "\n",
    "El test encuentra significancia en la diferencia de al menos dos grupos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tKruskal-Wallis rank sum test\n",
       "\n",
       "data:  n_huevos by condicion\n",
       "Kruskal-Wallis chi-squared = 19.964, df = 2, p-value = 4.623e-05\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kruskal.test(n_huevos ~ condicion, data = datos)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Comparaciones post-hoc para saber que dos grupos difieren**\n",
    "\n",
    "Existen diferentes métodos de corrección del nivel de significancia, entre ellos destacan el de Bonferroni que es muy estricto y el de holm, este último parece ser más recomendado.\n",
    "\n",
    "*Las comparaciones por pares encuentran diferencias significativas entre todas las condiciones.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in wilcox.test.default(xi, xj, paired = paired, ...):\n",
      "“cannot compute exact p-value with ties”\n",
      "Warning message in wilcox.test.default(xi, xj, paired = paired, ...):\n",
      "“cannot compute exact p-value with ties”\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "\tPairwise comparisons using Wilcoxon rank sum test \n",
       "\n",
       "data:  datos$n_huevos and datos$condicion \n",
       "\n",
       "           condicion1 condicion2\n",
       "condicion2 0.00029    -         \n",
       "condicion3 0.04795    0.00058   \n",
       "\n",
       "P value adjustment method: holm "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pairwise.wilcox.test(x = datos$n_huevos, g = datos$condicion, p.adjust.method = \"holm\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Cálculo de tamaño del efecto**\n",
    "\n",
    "Finalmente, para aquellas comparaciones que se consideren significativas se tiene que reportar el tamaño del efecto (no existe forma de calcular el tamaño del efecto para el test de Kruskal-Wallis en conjunto). En este caso se han realizado comparaciones con Mann-Whitney-wilcox (ver en capítulo dedicado a este test para saber cómo se calcula)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "ename": "ERROR",
     "evalue": "Error in loadNamespace(name): there is no package called ‘devtools’\n",
     "output_type": "error",
     "traceback": [
      "Error in loadNamespace(name): there is no package called ‘devtools’\nTraceback:\n",
      "1. devtools::session_info",
      "2. getExportedValue(pkg, name)",
      "3. asNamespace(ns)",
      "4. getNamespace(ns)",
      "5. loadNamespace(name)",
      "6. withRestarts(stop(cond), retry_loadNamespace = function() NULL)",
      "7. withOneRestart(expr, restarts[[1L]])",
      "8. doWithOneRestart(return(expr), restart)"
     ]
    }
   ],
   "source": [
    "sesion_info <- devtools::session_info()\n",
    "dplyr::select(\n",
    "    tibble::as_tibble(sesion_info$packages),\n",
    "    c(package, loadedversion, source)\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test de Friedman\n",
    "\n",
    "El test de Friedman es la alternativa no paramétrica a la prueba ANOVA de una vía cuando los datos son dependientes (pareados). Se trata de una extensión de la prueba de los rangos con signo de Wilcoxon para más de dos grupos (basada en suma de rangos). Asumiendo ciertas simplificaciones, puede considerarse como una comparación entre las medianas de varios grupos.\n",
    "\n",
    "El test de Friedman es el test adecuado cuando los datos tienen un orden natural, (cuando para darles sentido tienen que estar ordenados) y además son pareados. Por ejemplo, si se quiere estudiar la diferencia en el rendimiento de un grupo de corredores dependiendo de la estación del año, se hace correr al mismo grupo de personas una vez en cada estación. Como resultado, se puede disponer de dos tipos de datos: los tiempos de cada participante (análisis con ANOVA pareado) o las posiciones en las que han terminado la carrera cada participante en cada una de las carreras (análisis con Friedman test).\n",
    "\n",
    "EL concepto es similar a la suma de rangos de Wilcoxon para dos grupos pero esta vez asignando los rangos dentro de cada fila (ya que hay más de dos medidas para cada individuo) y después haciendo la suma de rangos para cada columna.\n",
    "\n",
    "El test de Friedman genera un estadístico conocido como Fr o Q que se distribuye:\n",
    "\n",
    "- Si el número total de individuos (N) es mayor de 10, la distribución de Fr se aproxima a una distribución χ2 con k−1 grados de libertad (siendo k el número de grupos a comparar).\n",
    "\n",
    "- Si el número de individuos es menor de 10, se recurre a tablas con los valores de significancia para un test de Friedman."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparaciones Post-Hoc\n",
    "\n",
    "Al igual que ocurre con un ANOVA, si el test de Friedman es significativo implica que, al menos dos grupos de entre los comparados, son significativamente diferentes, pero no indica cuales. Para saberlo es necesario compararlos todos entre ellos. Esto implica realizar una corrección del nivel de significancia para evitar incrementar el error de tipo I. Los dos métodos de comparación post-hoc más empleados para un test de Friedman son:\n",
    "\n",
    "- Test de rangos con signo de Wilcoxon entre cada par de grupos con corrección de significancia:\n",
    "   pairwise.wilcox.test( paried = TRUE ).\n",
    "\n",
    "- Tukey’s range test: en R existe la función friedmanmc() del paquete pgirmess."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tamaño del efecto\n",
    "\n",
    "No hay una manera general de calcular el tamaño del efecto de una prueba de Friedman. Lo que se suele hacer es calcular el tamaño del efecto sobre las parejas que hayan resultado significativamente distintas en el análisis post-hoc. Si las comparaciones post-hoc se hacen mediante la prueba de rangos con signo de Wilcoxon, se tendrá que calcular el efecto asociado a dicho test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 6 × 3</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>valoracion</th><th scope=col>hora</th><th scope=col>sujeto</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;fct&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>9</td><td>mañana</td><td>1</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>5</td><td>tarde </td><td>1</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>2</td><td>noche </td><td>1</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>6</td><td>mañana</td><td>2</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>3</td><td>tarde </td><td>2</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>1</td><td>noche </td><td>2</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 3\n",
       "\\begin{tabular}{r|lll}\n",
       "  & valoracion & hora & sujeto\\\\\n",
       "  & <dbl> & <fct> & <fct>\\\\\n",
       "\\hline\n",
       "\t1 & 9 & mañana & 1\\\\\n",
       "\t2 & 5 & tarde  & 1\\\\\n",
       "\t3 & 2 & noche  & 1\\\\\n",
       "\t4 & 6 & mañana & 2\\\\\n",
       "\t5 & 3 & tarde  & 2\\\\\n",
       "\t6 & 1 & noche  & 2\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 3\n",
       "\n",
       "| <!--/--> | valoracion &lt;dbl&gt; | hora &lt;fct&gt; | sujeto &lt;fct&gt; |\n",
       "|---|---|---|---|\n",
       "| 1 | 9 | mañana | 1 |\n",
       "| 2 | 5 | tarde  | 1 |\n",
       "| 3 | 2 | noche  | 1 |\n",
       "| 4 | 6 | mañana | 2 |\n",
       "| 5 | 3 | tarde  | 2 |\n",
       "| 6 | 1 | noche  | 2 |\n",
       "\n"
      ],
      "text/plain": [
       "  valoracion hora   sujeto\n",
       "1 9          mañana 1     \n",
       "2 5          tarde  1     \n",
       "3 2          noche  1     \n",
       "4 6          mañana 2     \n",
       "5 3          tarde  2     \n",
       "6 1          noche  2     "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "valoracion <- c(9, 5, 2, 6, 3, 1, 5, 5, 5, 11, 5, 1, 8, 4, 3, 10, 4, 1, 7, 3, 4)\n",
    "hora <- factor(rep(c(\"mañana\", \"tarde\", \"noche\"), 7))\n",
    "sujeto <- factor(rep(1:7, each = 3))\n",
    "datos <- data.frame(valoracion, hora, sujeto)\n",
    "head(datos)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "datos$hora: mañana\n",
       "[1] 8\n",
       "------------------------------------------------------------ \n",
       "datos$hora: noche\n",
       "[1] 2\n",
       "------------------------------------------------------------ \n",
       "datos$hora: tarde\n",
       "[1] 4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "by(data = datos$valoracion, INDICES = datos$hora, FUN = median)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "ggplot(data = datos, mapping = aes(x = hora, y = valoracion, colour = hora)) +\n",
    "    geom_boxplot() +\n",
    "    theme_bw() +\n",
    "    theme(legend.position = \"none\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tFriedman rank sum test\n",
       "\n",
       "data:  valoracion, hora and sujeto\n",
       "Friedman chi-squared = 10.333, df = 2, p-value = 0.005704\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "friedman.test(valoracion, hora, sujeto)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El test encuentra diferencias significativas entre al menos dos grupos. Para saber cuáles son, se realizan comparaciones dos a dos empleando el test de Wilcoxon rangos con signo.\n",
    "\n",
    "**Comparaciones múltiples**\n",
    "\n",
    "A pesar de que el test de Friedman resulta significativo, las comparaciones por pares mediante wilcox test con corrección de holm no encuentran ninguna diferencia significativa."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in wilcox.test.default(xi, xj, paired = paired, ...):\n",
      "“cannot compute exact p-value with ties”\n",
      "Warning message in wilcox.test.default(xi, xj, paired = paired, ...):\n",
      "“cannot compute exact p-value with zeroes”\n",
      "Warning message in wilcox.test.default(xi, xj, paired = paired, ...):\n",
      "“cannot compute exact p-value with ties”\n",
      "Warning message in wilcox.test.default(xi, xj, paired = paired, ...):\n",
      "“cannot compute exact p-value with zeroes”\n",
      "Warning message in wilcox.test.default(xi, xj, paired = paired, ...):\n",
      "“cannot compute exact p-value with ties”\n",
      "Warning message in wilcox.test.default(xi, xj, paired = paired, ...):\n",
      "“cannot compute exact p-value with zeroes”\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "\tPairwise comparisons using Wilcoxon signed rank test \n",
       "\n",
       "data:  datos$valoracion and datos$hora \n",
       "\n",
       "      mañana noche\n",
       "noche 0.1    -    \n",
       "tarde 0.1    0.1  \n",
       "\n",
       "P value adjustment method: holm "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pairwise.wilcox.test(datos$valoracion, datos$hora, paired = TRUE, p.adjust.method = \"holm\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test de Wilcoxon Mann Whitney como alternativa al t-test\n",
    "\n",
    "En este capítulo se hace una comparativa entre el test estadístico no paramétrico Mann–Whitney–Wilcoxon y el t-test.\n",
    "\n",
    "El t-test es un test estadístico paramétrico que permite contrastar la hipótesis nula de que las medias de dos poblaciones son iguales, frente a la hipótesis alternativa de que no lo son.\n",
    "\n",
    "A pesar de la sencillez y utilidad del t-test, para que sus resultados sean válidos es necesario que se cumplan una serie de condiciones, entre las que se encuentran:\n",
    "\n",
    "- Independencia: Las observaciones tienen que ser independientes las unas de las otras. Para ello, el muestreo debe ser aleatorio y el tamaño de la muestra inferior al 10% de la población. (Existe una adaptación de t-test para datos pareados)\n",
    "\n",
    "- Normalidad: Las poblaciones que se comparan tienen que seguir una distribución normal. Si bien la condición de normalidad recae sobre las poblaciones, no se suele disponer de información sobre ellas, por lo que se emplean las muestras (dado que son reflejo de la población) para determinarlo. En caso de cierta asimetría, los t-test son considerablemente robustos si el tamaño de las muestras es mayor o igual a 30.\n",
    "\n",
    "- Igualdad de varianza (homocedasticidad): la varianza de las poblaciones comparadas debe de ser igual. Tal como ocurre con la condición de normalidad, si no se dispone de información de las poblaciones, esta condición se ha de asumir a partir de las muestras. En caso de no cumplirse esta condición se puede emplear un Welch Two Sample t-test, que incorpora una corrección a través de los grados de libertad que compensa la diferencia de varianzas, con el inconveniente de que pierde poder estadístico."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluación del t-test con distribuciones no normales para distintos tamaños muestrales\n",
    "\n",
    "Una de las principales razones que por las que los investigadores descartan la utilización del t-test es por la falta de normalidad en la distribución de las muestras. Si bien es cierto que el t-test requiere como condición que las poblaciones de origen sigan una distribución normal, a medida que se incrementa el tamaño de las muestras se vuelve menos sensible al no cumplimiento de esta condición. En el siguiente ejemplo se simulan dos poblaciones con la misma media, una de las cuales tiene mucha asimetría, y se evalúa el resultado de un t-test para diferentes tamaños muestrales."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Plot with title “Distribuciones lognormal y normal con misma media”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x <- seq(0, 10, length = 1000)\n",
    "y <- dlnorm(x = x, meanlog = 0.5, sdlog = 1)\n",
    "plot(x, y,\n",
    "    type = \"l\", lty = 1, xlab = \"x\", col = \"blue\", ylab = \"Densidad\",\n",
    "    main = \"Distribuciones lognormal y normal con misma media\",\n",
    "    xlim = c(-2, 10)\n",
    ")\n",
    "x_2 <- seq(-2, 10, length = 1000)\n",
    "y_2 <- dnorm(x = x_2, mean = 2.718282, sd = 1)\n",
    "lines(x_2, y_2, col = \"red\")\n",
    "legend(\"topright\",\n",
    "    legend = c(\"media lognormal = 2.72\", \"media normal = 2.72\"),\n",
    "    col = c(\"blue\", \"red\"), lty = 1, cex = 0.7\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para los tamaños muestrales 5, 10, 20, 30, 50, 100, 200, 300, 500 se extraen 1000 observaciones y se identifica el porcentaje test que se considerarían significativos para un nivel de significancia α=0.05. El nivel basal esperado es del 5%."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".dl-inline {width: auto; margin:0; padding: 0}\n",
       ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
       ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
       ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
       "</style><dl class=dl-inline><dt>5</dt><dd>14.9</dd><dt>10</dt><dd>12.5</dd><dt>20</dt><dd>13.2</dd><dt>30</dt><dd>7.8</dd><dt>50</dt><dd>8</dd><dt>100</dt><dd>7.8</dd><dt>200</dt><dd>6.3</dd><dt>300</dt><dd>6.3</dd><dt>500</dt><dd>6.4</dd></dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[5] 14.9\n",
       "\\item[10] 12.5\n",
       "\\item[20] 13.2\n",
       "\\item[30] 7.8\n",
       "\\item[50] 8\n",
       "\\item[100] 7.8\n",
       "\\item[200] 6.3\n",
       "\\item[300] 6.3\n",
       "\\item[500] 6.4\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "5\n",
       ":   14.910\n",
       ":   12.520\n",
       ":   13.230\n",
       ":   7.850\n",
       ":   8100\n",
       ":   7.8200\n",
       ":   6.3300\n",
       ":   6.3500\n",
       ":   6.4\n",
       "\n"
      ],
      "text/plain": [
       "   5   10   20   30   50  100  200  300  500 \n",
       "14.9 12.5 13.2  7.8  8.0  7.8  6.3  6.3  6.4 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "test_significativos <- vector(mode = \"numeric\")\n",
    "tamanyo_muestral <- c(5, 10, 20, 30, 50, 100, 200, 300, 500)\n",
    "for(i in tamanyo_muestral){\n",
    "  p_values <- rep(NA, 1000)\n",
    "  for(j in 1:1000) {\n",
    "    muestra_a <- rlnorm(n = i, meanlog =  0.5, sdlog = 1)\n",
    "    muestra_b <- rnorm(n = i, mean = 2.718282, sd = 1)\n",
    "    p_values[j] <- t.test(muestra_a, muestra_b, var.equal = FALSE)$p.value\n",
    "  }\n",
    "test_significativos <- c(test_significativos, mean(p_values < 0.05)*100)\n",
    "}\n",
    "names(test_significativos) <- c(5, 10, 20, 30, 50, 100, 200, 300, 500)\n",
    "test_significativos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(\n",
    "    x = tamanyo_muestral, y = test_significativos, type = \"b\", ylim = c(0, 20),\n",
    "    ylab = \"% de test significativos\", xlab = \"tamaño muestral\"\n",
    ")\n",
    "abline(h = 5, col = \"firebrick\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La simulación muestra que, debido a la pronunciada desviación respecto de la normalidad que presenta una de las poblaciones, para tamaños muestrales por debajo de 100 observaciones el % de test que resultan significativos está bastante por encima del nivel basal, lo que da lugar a demasiados falsos positivos. A partir de 100 observaciones, el % de test significativos se aproxima al nivel basal teórico (5%), por lo que la capacidad del t-test pasa a ser buena."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Mann Whitney Wilcoxon\n",
    "\n",
    "El test de Mann–Whitney–Wilcoxon (WMW), también conocido como Wilcoxon rank-sum test o u-test, es un test no paramétrico que contrasta si dos muestras proceden de poblaciones equidistribuidas.\n",
    "\n",
    "La idea en la que se fundamenta este test es la siguiente: si las dos muestras comparadas proceden de la misma población, al juntar todas las observaciones y ordenarlas de menor a mayor, cabría esperar que las observaciones de una y otra muestra estuviesen intercaladas aleatoriamente. Por lo contrario, si una de las muestras pertenece a una población con valores mayores o menores que la otra población, al ordenar las observaciones, estas tenderán a agruparse de modo que las de una muestra queden por encima de las de la otra."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "set.seed(567)\n",
    "datos <- data.frame(muestra = rep(c(\"A\", \"B\"), each = 10),\n",
    "valor = rnorm(n = 20, mean = 10, sd = 5),\n",
    "cordenada_y = rep(0, 20))\n",
    "\n",
    "ggplot(data = datos, aes(x = valor, y = cordenada_y)) +\n",
    "geom_point(aes(colour = muestra), size = 3) +\n",
    "ylab(\"\") + xlab(\"rango\") +\n",
    "theme_bw() +\n",
    "theme(axis.text.y = element_blank()) + \n",
    "ggtitle(\"Muestras procedentes de la misma población\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "set.seed(567)\n",
    "datos <- data.frame(\n",
    "    muestra = rep(c(\"A\", \"B\"), each = 10),\n",
    "    valor = c(rnorm(n = 10, mean = 10, sd = 5), rnorm(n = 10, mean = 20, sd = 5)),\n",
    "    cordenada_y = rep(0, 20)\n",
    ")\n",
    "\n",
    "ggplot(data = datos, aes(x = valor, y = cordenada_y)) +\n",
    "    geom_point(aes(colour = muestra), size = 3) +\n",
    "    ylab(\"\") +\n",
    "    xlab(\"rango\") +\n",
    "    theme_bw() +\n",
    "    theme(axis.text.y = element_blank()) +\n",
    "    ggtitle(\"Muestras procedentes de distintas poblaciones\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Acorde a esta idea, el test de Mann–Whitney–Wilcoxon contrasta que la probabilidad de que una observación de la población X supere a una observación de la población Y es igual a la probabilidad de que una observación de la población Y supere a una de la población X. Es decir, que los valores de una población no tienden a ser mayores que los de otra.\n",
    "\n",
    "\n",
    "$$ H_{0} : P(X > Y) = P(Y > X) $$\n",
    "$$ H_{0} : P(X > Y) = 0.5 $$\n",
    "$$ H_{1} : P(X > Y) != P(Y > X) $$\n",
    "$$ H_{1} : P(X > Y) != 0.5 $$\n",
    "\n",
    "Es común encontrar mencionado que el test de Mann–Whitney–Wilcoxon compara medianas, sin embargo, esto solo es cierto cuando las poblaciones comparadas difieren únicamente es su localización, pero el resto de características (dispersión, asimetría…) son iguales.\n",
    "\n",
    "Al igual que ocurre con muchos test no paramétricos, el test de Mann–Whitney–Wilcoxon es menos potente que el t-test (tienen menos probabilidad de rechazar la H0 cuando realmente es falsa) ya que ignora valores extremos. En el caso de los t-test, al trabajar con medias, si los tienen en cuenta. Esto hace a su vez que el test de Mann–Whitney–Wilcoxon sea una prueba más robusta que los t-test. En concreto, la perdida de potencia es del 5%."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Condiciones necesarias del test de Mann–Whitney–Wilcoxon\n",
    "\n",
    "- Los datos tienen que ser independientes.\n",
    "- Los datos tienen que ser ordinales o bien se tienen que poder ordenar de menor a mayor.\n",
    "- No es necesario asumir que las muestras se distribuyen de forma normal o que proceden de poblaciones normales. Pero, para que el test compare medianas, ambas han de tener el mismo tipo de distribución (varianza, asimetría…).\n",
    "- Igualdad de varianza entre grupos (homocedasticidad)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Supóngase que se dispone de dos muestras, de las que no se conoce el tipo de distribución de las poblaciones de origen y cuyo tamaño es demasiado pequeño para determinar si siguen una distribución normal. ¿Existe una diferencia significativa entre poblaciones? Se emplea un ejemplo con muestras pequeñas para poder ilustrar fácilmente los pasos, no significa que con muestras tan pequeñas el test de Mann–Whitney–Wilcoxon sea preciso."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tFligner-Killeen test of homogeneity of variances\n",
       "\n",
       "data:  list(muestraX, muestraY)\n",
       "Fligner-Killeen:med chi-squared = 0.07201, df = 1, p-value = 0.7884\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "muestraX <- c(1.1, 3.4, 4.3, 2.1, 7.0, 2.5)\n",
    "muestraY <- c(7.0, 8.0, 3.0, 5.0, 6.2, 4.4)\n",
    "\n",
    "fligner.test(x = list(muestraX, muestraY))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "No hay evidencias en contra de la igualdad de varianzas.\n",
    "\n",
    "Una vez comprobadas las condiciones necesarias para que el test de Mann–Whitney–Wilcoxon sea válido se procede a calcular su estadístico, p-value asociado y tamaño de efecto.\n",
    "\n",
    "**Ordenación de las observaciones**\n",
    "\n",
    "Se juntan todas las observaciones, se ordenan y se les asigna un número de posición, siendo la posición 1 para el valor más pequeño. En caso de haber valores repetidos, fenómeno conocido como ligadura o ties, se les asigna como valor de posición la media de las posiciones que ocupan. En este caso, el valor “7.0” está repetido dos veces, por lo que en lugar de asignarles “10” y “11”, se les asigna “10.5” a cada uno."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 12 × 2 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>observaciones</th><th scope=col>rango_observaciones</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>1.1</td><td> 1.0</td></tr>\n",
       "\t<tr><td>2.1</td><td> 2.0</td></tr>\n",
       "\t<tr><td>2.5</td><td> 3.0</td></tr>\n",
       "\t<tr><td>3.0</td><td> 4.0</td></tr>\n",
       "\t<tr><td>3.4</td><td> 5.0</td></tr>\n",
       "\t<tr><td>4.3</td><td> 6.0</td></tr>\n",
       "\t<tr><td>4.4</td><td> 7.0</td></tr>\n",
       "\t<tr><td>5.0</td><td> 8.0</td></tr>\n",
       "\t<tr><td>6.2</td><td> 9.0</td></tr>\n",
       "\t<tr><td>7.0</td><td>10.5</td></tr>\n",
       "\t<tr><td>7.0</td><td>10.5</td></tr>\n",
       "\t<tr><td>8.0</td><td>12.0</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 12 × 2 of type dbl\n",
       "\\begin{tabular}{ll}\n",
       " observaciones & rango\\_observaciones\\\\\n",
       "\\hline\n",
       "\t 1.1 &  1.0\\\\\n",
       "\t 2.1 &  2.0\\\\\n",
       "\t 2.5 &  3.0\\\\\n",
       "\t 3.0 &  4.0\\\\\n",
       "\t 3.4 &  5.0\\\\\n",
       "\t 4.3 &  6.0\\\\\n",
       "\t 4.4 &  7.0\\\\\n",
       "\t 5.0 &  8.0\\\\\n",
       "\t 6.2 &  9.0\\\\\n",
       "\t 7.0 & 10.5\\\\\n",
       "\t 7.0 & 10.5\\\\\n",
       "\t 8.0 & 12.0\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 12 × 2 of type dbl\n",
       "\n",
       "| observaciones | rango_observaciones |\n",
       "|---|---|\n",
       "| 1.1 |  1.0 |\n",
       "| 2.1 |  2.0 |\n",
       "| 2.5 |  3.0 |\n",
       "| 3.0 |  4.0 |\n",
       "| 3.4 |  5.0 |\n",
       "| 4.3 |  6.0 |\n",
       "| 4.4 |  7.0 |\n",
       "| 5.0 |  8.0 |\n",
       "| 6.2 |  9.0 |\n",
       "| 7.0 | 10.5 |\n",
       "| 7.0 | 10.5 |\n",
       "| 8.0 | 12.0 |\n",
       "\n"
      ],
      "text/plain": [
       "      observaciones rango_observaciones\n",
       " [1,] 1.1            1.0               \n",
       " [2,] 2.1            2.0               \n",
       " [3,] 2.5            3.0               \n",
       " [4,] 3.0            4.0               \n",
       " [5,] 3.4            5.0               \n",
       " [6,] 4.3            6.0               \n",
       " [7,] 4.4            7.0               \n",
       " [8,] 5.0            8.0               \n",
       " [9,] 6.2            9.0               \n",
       "[10,] 7.0           10.5               \n",
       "[11,] 7.0           10.5               \n",
       "[12,] 8.0           12.0               "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# unión de las muestras y ordenación\n",
    "\n",
    "observaciones <- sort(c(muestraX, muestraY))\n",
    "\n",
    "# La función rank() de R calcula las posiciones automáticamente,\n",
    "# solucionando las ligaduras en caso de que las haya.\n",
    "\n",
    "rango_observaciones <- rank(observaciones)\n",
    "observaciones <- cbind(observaciones, rango_observaciones)\n",
    "observaciones"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Calculo del estadistico U**\n",
    "\n",
    "$$ U = \\min(U_{1}, U_{2}) $$ \n",
    "\n",
    "siendo U1 y U2 los valores estadísticos de U Mann-Whitney:\n",
    "\n",
    "$$ U_{1} = n_{1}n_{2} + n1(n1+1)/2 - R_{1}$$\n",
    "\n",
    "$$ U_{1} = n_{1}n_{2} + n2(n2+1)/2 - R_{2}$$\n",
    "\n",
    "- n1 = tamaño de la muestra del grupo 1\n",
    "- n2 = tamaño de la muestra del grupo 2\n",
    "- R1 = sumatoria de los rangos del grupo 1\n",
    "- R2 = sumatoria de los rangos del grupo 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "6.5"
      ],
      "text/latex": [
       "6.5"
      ],
      "text/markdown": [
       "6.5"
      ],
      "text/plain": [
       "[1] 6.5"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R1 <- sum(1, 5, 6, 2, 10.5, 3)\n",
    "R2 <- sum(10.5, 12, 4, 8, 9, 7)\n",
    "n1 <- length(muestraX)\n",
    "n2 <- length(muestraY)\n",
    "U1 <- (n1 * n2) + (n1 * (n1 + 1) / 2) - R1\n",
    "U2 <- (n1 * n2) + (n2 * (n2 + 1) / 2) - R2\n",
    "U <- min(c(U1, U2))\n",
    "U"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Calculo de p-value**\n",
    "\n",
    "Una vez ha obtenido el valor del estadístico U se puede calcular cual es la probabilidad de que adquiera un valor igual o más extremo que el observado. Si el tamaño de las muestras es inferior a 10, se compara el valor obtenido de U con los valores de una tabla U de Mann-Whitney. Si el U es menor que el valor correspondiente en la tabla, la diferencia es significativa. En este caso, el valor de la tabla para α=0.05, n1=6 y n2=6 es de 5. Dado que U obtenido es >5 no se considera significativa la diferencia. Si n1>10 y n2>10 se puede asumir que U se distribuye de forma aproximadamente normal, rechazando H0 si Z calculado es mayor que el valor de Z para el α elegido (este es método utilizado por defecto en R).\n",
    "\n",
    "$$ Z = U - (n_{1}n_{2}/2)/ \\sqrt(n_{1}n_{2}(n_{1}+n_{2}+1)/12) $$ \n",
    "se distribuye como Normal Estandar"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Cálculo del tamaño del efeto (side effect)**\n",
    "\n",
    "Como en todo test estadístico, no solo hay que indicar el p-value sino también el tamaño del efecto observado, ya que esto permitirá saber si, además de significativa, la diferencia es práctica. El tamaño del efecto para un test de Mann–Whitney–Wilcoxon se calcula a partir del Z-factor (es necesario haber asumido que U se distribuye ~ Normal).\n",
    "\n",
    "$$ r = abs(Z/\\sqrt(N)) $$\n",
    "\n",
    "Donde N es la suma de n_{1} y n_{2}. Una de las clasificaciones del tamaño más utilizada es:\n",
    "\n",
    "- 0.1 = pequeño\n",
    "- 0.3 = mediano\n",
    "- => 0.5 = grande "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in wilcox.test.default(x = muestraX, y = muestraY, alternative = \"two.sided\", :\n",
      "“cannot compute exact p-value with ties”\n",
      "Warning message in wilcox.test.default(x = muestraX, y = muestraY, alternative = \"two.sided\", :\n",
      "“cannot compute exact confidence intervals with ties”\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "\tWilcoxon rank sum test with continuity correction\n",
       "\n",
       "data:  muestraX and muestraY\n",
       "W = 6.5, p-value = 0.07765\n",
       "alternative hypothesis: true location shift is not equal to 0\n",
       "95 percent confidence interval:\n",
       " -4.9000274  0.4000139\n",
       "sample estimates:\n",
       "difference in location \n",
       "             -2.390035 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "wilcox.test(x = muestraX, y = muestraY, alternative = \"two.sided\", mu = 0,\n",
    "            paired = FALSE, conf.int = 0.95)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: survival\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "\tExact Wilcoxon-Mann-Whitney Test\n",
       "\n",
       "data:  valores by grupo (A, B)\n",
       "Z = -1.8447, p-value = 0.06926\n",
       "alternative hypothesis: true mu is not equal to 0\n",
       "95 percent confidence interval:\n",
       " -4.9  0.4\n",
       "sample estimates:\n",
       "difference in location \n",
       "                  -2.4 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(coin)\n",
    "# La función wilcox.test() del paquete coin requiere pasarle los argumentos en\n",
    "# forma de función (~), por lo que los datos tienen que estar almacenados en\n",
    "# forma de data frame.\n",
    "datos <- data.frame(\n",
    "    grupo   = as.factor(rep(c(\"A\", \"B\"), c(6, 6))),\n",
    "    valores = c(muestraX, muestraY)\n",
    ")\n",
    "\n",
    "wilcox_test(valores ~ grupo, data = datos, distribution = \"exact\", conf.int = 0.95)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.53260562332743"
      ],
      "text/latex": [
       "0.53260562332743"
      ],
      "text/markdown": [
       "0.53260562332743"
      ],
      "text/plain": [
       "[1] 0.5326056"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# La función devuelve el valor de Z, por lo que se puede calcular fácilmente el\n",
    "# tamaño del efecto\n",
    "tamanyo_efecto <- 1.845 / sqrt(n1 + n2)\n",
    "tamanyo_efecto"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Resultado**\n",
    "\n",
    "La diferencia entre las probabilidades de que observaciones de una población superen a las de la otra no difiere de forma significativa (p-value = 0.06926). El tamaño del efecto observado es grande (0.53) pero no significativo."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparación entre t-test y test de Mann–Whitney–Wilcoxon\n",
    "\n",
    "Una de las aplicaciones más frecuentes del test de Mann–Whitney–Wilcoxon es su uso como alternativa al t-test cuando las muestras no proceden de poblaciones con distribución normal (asimetría o colas) o porque tienen un tamaño demasiado reducido para poder afirmarlo. Es importante tener en cuenta que, aunque ambos test permiten realizar inferencia sobre la diferencia entre poblaciones, las hipótesis contrastadas no son las mismas. Mientras que el t-test siempre compara las medias de los grupos, el test de Mann–Whitney–Wilcoxon es menos específico. Si las distribuciones de las poblaciones subyacentes se diferencian únicamente en localización, entonces el test de Mann–Whitney–Wilcoxon compara medianas, para el resto de escenarios (poblaciones con distinta distribución, dispersión, asimetría…) contrasta si P(X>Y)=P(Y>X). En este segundo caso la interpretación de los p-values no es tan directa. Es debido a esta naturaleza flexible por lo que hay que ser cauteloso con el test de Mann–Whitney–Wilcoxon. Por ejemplo, si las dos muestras comparadas proceden de poblaciones con asimetrías en direcciones opuestas, a pesar de que tanto la media como la mediana sean exactamente las mismas en ambos grupos, el p-value obtenido puede ser muy bajo.\n",
    "\n",
    "En la práctica, el escenario en el que la única diferencia entre poblaciones es la localización es poco realista. Si las distribuciones tienen colas (asimetría) y las medias o medianas son distintas, es muy probable que las varianzas también lo sean. De hecho, la distribución normal es la única distribución estándar en la que la media y la varianza son independientes. Por lo tanto, si el test de Mann–Whitney–Wilcoxon se está aplicando por falta de normalidad y las medias-medianas no son iguales, lo más seguro es que no se cumpla con total rigurosidad la igualdad de varianzas. Es necesario evaluar estas características para poder determinar si el test de Mann–Whitney–Wilcoxon es suficientemente robusto para el estudio en cuestión.\n",
    "\n",
    "Cuando la hipótesis que se quiere contrastar tiene que ser exclusivamente la igualdad de medianas se puede recurrir a la regresión de cuantiles, en concreto al cuantil 0.5."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test de Mann–Whitney–Wilcoxon aplicado a muestras con asimetría opuesta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Plot with title “”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "grupo_a <- c(5, 5, 5, 5, 5, 5, 7, 8, 9, 10)\n",
    "grupo_b <- c(1, 2, 3, 4, 5, 5, 5, 5, 5, 5)\n",
    "par(mfrow = c(1, 2))\n",
    "hist(grupo_a, col = \"cyan4\", main = \"\")\n",
    "hist(grupo_b, col = \"firebrick\", main = \"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En vista de que el tamaño muestral es pequeño y de que ambos grupos muestran una clara asimetría, el t-test queda descartado. Una posible alternativa es emplear el test de Mann–Whitney–Wilcoxon con la intención de comparar las medianas.\n",
    "\n",
    "El p-value obtenido indica claras evidencias en contra de la hipótesis nula de que las medianas de ambos grupos son iguales. Sin embargo, si se calculan las medianas de las muestras, el resultado es el mismo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in wilcox.test.default(grupo_a, grupo_b, paired = FALSE):\n",
      "“cannot compute exact p-value with ties”\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "\tWilcoxon rank sum test with continuity correction\n",
       "\n",
       "data:  grupo_a and grupo_b\n",
       "W = 82, p-value = 0.007196\n",
       "alternative hypothesis: true location shift is not equal to 0\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "wilcox.test(grupo_a, grupo_b, paired = FALSE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Potencial problema del test de Mann–Whitney–Wilcoxon con tamaños muestrales grandes\n",
    "\n",
    "Suele recomendarse emplear el test de Mann–Whitney–Wilcoxon en lugar del t-test cuando los tamaños muestrales son pequeños y no se tiene evidencias de que las poblaciones de origen siguen una distribución normal. Si bien esta práctica está bastante fundamentada, no hay que confundirla con la de utilizar el test de Mann–Whitney–Wilcoxon como alternativa al t-test siempre que no se cumpla la normalidad y sin tener en cuenta el tamaño muestral. A medida que el número de observaciones aumenta, también lo hace la robustez del t-test frente a desviaciones de la normalidad. Por otro lado, el test de Mann–Whitney–Wilcoxon incrementa su sensibilidad a diferencias más allá de las medianas. Por ejemplo, aumenta el poder estadístico de detectar diferencias significativas en la probabilidad de que observaciones de un grupo superen a las del otro debido únicamente a diferencias en la dispersión de las poblaciones de origen y no porque sus medianas sean distintas. Si el objetivo del estudio es identificar cualquier diferencia distribucional, esto no supone un problema, pero si lo que se quiere comparar son las medianas, se obtendrán p-values que no se corresponden con la pregunta que el investigador quiere responder.\n",
    "\n",
    "Considérese dos muestras que proceden de dos poblaciones distintas, una con distribución normal y otra con distribución log-normal (asimetría derecha). Ambas poblaciones tienen la misma mediana pero claramente siguen distribuciones distintas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Plot with title “Distribuciones lognormal y normal con misma mediana”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x <- seq(0, 5, length = 1000)\n",
    "y <- dlnorm(x = x, meanlog = 0.5, sdlog = 1.7)\n",
    "plot(x, y,\n",
    "    type = \"l\", lty = 1, xlab = \"x\", col = \"blue\", ylab = \"Densidad\",\n",
    "    main = \"Distribuciones lognormal y normal con misma mediana\", xlim = c(-5, 5)\n",
    ")\n",
    "x_2 <- seq(-5, 5, length = 1000)\n",
    "y_2 <- dnorm(x = x_2, mean = 1.648721, sd = 1)\n",
    "lines(x_2, y_2, col = \"red\")\n",
    "legend(\"topright\",\n",
    "    legend = c(\"mediana lognormal = 0.5\", \"mediana normal = 0.5\"),\n",
    "    col = c(\"blue\", \"red\"), lty = 1, cex = 0.7\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "Plot with title “”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Supóngase ahora que el investigador, que desconoce la distribución real de las poblaciones, \n",
    "# obtiene dos muestras de 20 observaciones cada una.\n",
    "\n",
    "set.seed(888)\n",
    "muestra_a <- rlnorm(n = 20, meanlog = 0.5, sdlog = 1.7)\n",
    "muestra_b <- rnorm(n = 20, mean = 1.648721, sd = 1)\n",
    "par(mfrow = c(1, 2))\n",
    "hist(muestra_a, breaks = 10, main = \"\", col = \"blue\")\n",
    "hist(muestra_b, breaks = 10, main = \"\", col = \"firebrick\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En base a la falta de normalidad de la muestra a, el investigador considera que el t-test no es adecuado para comparar la localización de las poblaciones y decide que quiere comparar medianas con el test de Mann–Whitney–Wilcoxon."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tWilcoxon rank sum test\n",
       "\n",
       "data:  muestra_a and muestra_b\n",
       "W = 196, p-value = 0.9254\n",
       "alternative hypothesis: true location shift is not equal to 0\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "wilcox.test(muestra_a, muestra_b, paired = FALSE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El resultado le indica que no hay evidencias para considerar que la localización de las poblaciones es distinta y concluye que las medianas de ambas poblaciones son iguales.\n",
    "\n",
    "Véase lo que ocurre si el tamaño muestral se incrementa de 20 a 1000 observaciones."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tWilcoxon rank sum test with continuity correction\n",
       "\n",
       "data:  muestra_a and muestra_b\n",
       "W = 551900, p-value = 5.842e-05\n",
       "alternative hypothesis: true location shift is not equal to 0\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "set.seed(888)\n",
    "muestra_a <- rlnorm(n = 1000, meanlog = 0.5, sdlog = 1.7)\n",
    "muestra_b <- rnorm(n = 1000, mean = 1.648721, sd = 1)\n",
    "wilcox.test(muestra_a, muestra_b, paired = FALSE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En este caso, la conclusión obtenida es totalmente opuesta, hay muchas evidencias en contra de la hipótesis nula de que ambas poblaciones tienen la misma localización por lo que el investigador podría concluir erróneamente que las medianas de ambas poblaciones son distintas.\n",
    "\n",
    "Este ejemplo pone de manifiesto la importancia que tiene el tamaño muestral en la potencia del test de Mann–Whitney–Wilcoxon y la necesidad de entender que, si las distribuciones no son iguales a excepción de su localización, el test es muy sensible detectando diferencias en las distribuciones a pesar de que sus medianas sean las mismas. En este caso, el investigador solo podría concluir que hay evidencias de que la distribución de las dos poblaciones se diferencia en algún aspecto, pero no podría concretar cuál."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prueba de los rangos con signo de Wilcoxon\n",
    "\n",
    "El test no paramétrico prueba de los rangos con signo de Wilcoxon, también conocido como Wilcoxon signed-rank test, permite comparar poblaciones cuando sus distribuciones (normalmente interpretadas a partir de las muestras) no satisfacen las condiciones necesarias para otros test paramétricos. Es una alternativa al t-test de muestras dependientes cuando las muestras no siguen una distribución normal (muestran asimetría o colas) o cuando tienen un tamaño demasiado reducido para poder determinar si realmente proceden de poblaciones normales.\n",
    "\n",
    "A la hora de elegir entre t-test o Wilcoxon signed-rank test, es importante tener en cuenta que, el problema de las muestras pequeñas, no se soluciona con ninguno de los dos. Si el tamaño de las muestras es pequeño, también lo es la calidad de la inferencia que se puede hacer con ellas. Ahora bien, existen dos situaciones en las que, a priori, se puede recomendar utilizar un Wilcoxon signed-rank test antes que un t-test:\n",
    "\n",
    "- Si el tamaño de las muestras es suficientemente grande para determinar (por métodos gráficos o contrastes de hipótesis) que la distribución de las poblaciones a comparar no es de tipo normal, en tal caso, los t-test no son adecuados, por lo que mejor emplear un Wilcoxon signed-rank test (bootstrapping, regresión cuantílica, o test de permutación también podrían ser otras alternativa).\n",
    "- Si el tamaño de las muestras no permite determinar con seguridad si las poblaciones de las que proceden se distribuyen de forma normal, y no se dispone de información que pueda orientar sobre la naturaleza de las poblaciones de origen (estudios anteriores, que sea un tipo de variable que se sabe que se distribuye casi siempre de forma normal…), entonces es más apropiado el Wilcoxon signed-rank test ya que no requiere asumir la normalidad de las poblaciones."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### El test Wilcoxon signed-rank test presenta las siguientes características:\n",
    "\n",
    "- Es frecuente encontrar descrito que, el Wilcoxon signed-rank test, compara la mediana de las diferencias, sin embargo, esto solo es correcto bajo determinadas condiciones. A modo general, el Wilcoxon signed-rank test compara si las diferencias entre pares de datos siguen una distribución simétrica entorno a un valor. Si dos muestras proceden de la misma población, es de esperar que las diferencias entre cada par de observaciones se distribuyan de forma simétrica entorno al cero.\n",
    "\n",
    "- Trabaja sobre rangos de orden, es decir, utilizan las posiciones que ocupan los datos una vez ordenados. Por lo tanto, solo es aplicable a variables cuyos valores se pueden ordenar.\n",
    "\n",
    "- Tienen menos poder estadístico (menor probabilidad de rechazar la hipótesis nula cuando realmente es falsa) ya que ignoran valores extremos. En el caso de los t-test, al trabajar con medias, sí los tienen en cuenta. Esto a su vez, hace que el Wilcoxon signed-rank test sean una prueba más robusta que el t-test."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Condiciones para la prueba de los rangos con signo de Wilcoxon\n",
    "\n",
    "- Los datos tienen que ser dependientes.\n",
    "\n",
    "- Los datos tienen que ser ordinales, se tienen que poder ordenar de menor a mayor o viceversa.\n",
    "\n",
    "- No es necesario asumir que las muestras se distribuyen de forma normal o que proceden de poblaciones normales. Pero sea cual sea el tipo de distribución de las diferencias, tiene que ser simétrica.\n",
    "\n",
    "- A pesar de considerarse el equivalente no paramétrico del t-test, el Wilcoxon signed-rank test trabaja con medianas, no con medias.\n",
    "\n",
    "- Preferible al t-test cuando hay valores atípicos, no hay normalidad de los datos o el tamaño de las muestras es pequeño."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in wilcox.test.default(x = antes, y = despues, alternative = \"two.sided\", :\n",
      "“cannot compute exact p-value with ties”\n",
      "Warning message in wilcox.test.default(x = antes, y = despues, alternative = \"two.sided\", :\n",
      "“cannot compute exact p-value with zeroes”\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "\tWilcoxon signed rank test with continuity correction\n",
       "\n",
       "data:  antes and despues\n",
       "V = 3, p-value = 0.2763\n",
       "alternative hypothesis: true location shift is not equal to 0\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "antes <- c(2, 5, 4, 6, 1, 3)\n",
    "despues <- c(5, 6, 2, 7, 1, 6)\n",
    "\n",
    "wilcox.test(x = antes, y = despues, alternative = \"two.sided\", mu = 0, paired = TRUE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En la salida devuelta por wilcox.test(), el estadístico se denomina V en lugar de W.\n",
    "\n",
    "Cuando hay ligaduras o ties, wilcox.test() no es capaz de calcular el p-value exacto, por lo que devuelve un p-value aproximado asumiendo que W se distribuye de forma aproximadamente normal. En estos casos, o cuando los tamaños muestrales son mayores de 25, es recomendable emplear la función wilcoxsigned_test() del paquete coin, que devuelve el valor exacto de p-value en lugar de una aproximación."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "\tExact Wilcoxon-Pratt Signed-Rank Test\n",
       "\n",
       "data:  y by x (pos, neg) \n",
       "\t stratified by block\n",
       "Z = -1.272, p-value = 0.25\n",
       "alternative hypothesis: true mu is not equal to 0\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "require(coin)\n",
    "# La función wilcoxsigned_test() del paquete coin requiere pasarle los argumentos\n",
    "# en forma de función (~), por lo que los datos tienen que estar almacenados en\n",
    "# forma de data frame.\n",
    "\n",
    "datos <- data.frame(antes = antes, despues = despues)\n",
    "wilcoxsign_test(antes ~ despues, data = datos, distribution = \"exact\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test de Bartlett (python)\n",
    "\n",
    "Perform Bartlett’s test for equal variances.\n",
    "\n",
    "Bartlett’s test tests the null hypothesis that all input samples are from populations with equal variances. For samples from significantly non-normal populations, Levene’s test levene is more robust."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1254782518834628e-05"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import bartlett\n",
    "import numpy as np\n",
    "\n",
    "a = [8.88, 9.12, 9.04, 8.98, 9.00, 9.08, 9.01, 8.85, 9.06, 8.99]\n",
    "b = [8.88, 8.95, 9.29, 9.44, 9.15, 9.58, 8.36, 9.18, 8.67, 9.05]\n",
    "c = [8.95, 9.12, 8.95, 8.85, 9.03, 8.84, 9.07, 8.98, 8.86, 8.98]\n",
    "stat, p = bartlett(a, b, c)\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.007054444444444413, 0.13073888888888888, 0.008890000000000002]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#The results corresponds to the big size difference of the variance of b:\n",
    "\n",
    "[np.var(x, ddof=1) for x in [a, b, c]] "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test de Levene\n",
    "\n",
    "Perform Levene test for equal variances.\n",
    "\n",
    "The Levene test tests the null hypothesis that all input samples are from populations with equal variances. Levene’s test is an alternative to Bartlett’s test bartlett in the case where there are significant deviations from normality.\n",
    "\n",
    "Three variations of Levene’s test are possible. The possibilities and their recommended usages are:\n",
    "\n",
    "- ‘median’ : Recommended for skewed (non-normal) distributions>\n",
    "\n",
    "- ‘mean’ : Recommended for symmetric, moderate-tailed distributions.\n",
    "\n",
    "- ‘trimmed’ : Recommended for heavy-tailed distributions.\n",
    "\n",
    "The test version using the mean was proposed in the original article of Levene ([2]) while the median and trimmed mean have been studied by Brown and Forsythe ([3]), sometimes also referred to as Brown-Forsythe test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.002431505967249681"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import levene\n",
    "\n",
    "a = [8.88, 9.12, 9.04, 8.98, 9.00, 9.08, 9.01, 8.85, 9.06, 8.99]\n",
    "b = [8.88, 8.95, 9.29, 9.44, 9.15, 9.58, 8.36, 9.18, 8.67, 9.05]\n",
    "c = [8.95, 9.12, 8.95, 8.85, 9.03, 8.84, 9.07, 8.98, 8.86, 8.98]\n",
    "stat, p = levene(a, b, c)\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.007054444444444413, 0.13073888888888888, 0.008890000000000002]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[np.var(x, ddof=1) for x in [a, b, c]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data drift detection large datasets\n",
    "\n",
    "TL;DR: We compared five different statistical tests for drift detection on large datasets. Our goal was to build intuition on how the tests react to data changes of varying magnitude. We also share the code so you can run the experiments on your data.\n",
    "\n",
    "When ML models are in production, one often needs to keep tabs on the data drift. The goal is to detect changes in the input data distributions to make sure the model still operates in a familiar environment. Applying statistical tests to compare the new data with the old is one way to do it.\n",
    "\n",
    "However, the test outcomes may differ for \"small\" and \"large\" datasets.\n",
    "\n",
    "**Too much data, too much drift**\n",
    "\n",
    "Each statistical test has particular properties and in-built assumptions.\n",
    "\n",
    "*Let's take a two-sample Kolmogorov-Smirnov (KS) test.* It is often a default choice for detecting a distributional change in numerical features. While it does the job in many cases, the test can be \"too sensitive\" for larger datasets. It would fire alarms for many real-world use cases all the time, just because you have a lot of data and small changes add up. You need to account for such test behavior when picking your drift metric."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Picking the drift metric\n",
    "\n",
    "OK, so measuring data drift for large datasets is hard. The good news is choosing the proper statistical test for the occasion is half the battle.\n",
    "\n",
    "But there are dozens of tests out there! How do you choose the best one?\n",
    "\n",
    "We've run some experiments and compared five popular statistical tests to answer this. In particular, we wanted to explore how the test results differ based on the data volume and magnitude of change.\n",
    "\n",
    "We hope it will help shape your intuition on how different tests behave on large datasets and how to choose the right one for your scenario.\n",
    "\n",
    "The list of statistical tests that will be use are:\n",
    "- Kolmogorov-Smirnov test\n",
    "- Population Stability index (PSI)\n",
    "- Wasserstein distance test (earth-mover-distance)\n",
    "- Kullback-leibler divergence\n",
    "- Jensen-Shannon distance\n",
    "\n",
    "First, we chose three features with different characteristics:\n",
    "\n",
    "- Feature 1— a continuous feature with non-normal distribution. For convenience, let's call it the \"Multimodal feature.\"\n",
    "- Feature 2— a variable with a heavy right tail. We'll call it the \"Right-tailed feature.\"\n",
    "- Feature 3— hereafter referred to as \"Feature with outliers.\"\n",
    "\n",
    "We picked these variables from three different publicly available datasets. The goal was to have features with various distribution shapes. For each variable, we had from 500,000 to 1 million observations.\n",
    "\n",
    "Then, we implemented a function to imitate data drift. We wanted to introduce an artificial change that would resemble real-world drift. To do that, we decided to shift the whole distribution for each feature by a fixed value. Here is the formula we used to create drift:\n",
    "\n",
    "$$ (alpha + mean(feature))*perc $$\n",
    "\n",
    "By using the mean value of each feature, we ensured that:\n",
    "\n",
    "1. The shift was relative to the feature value range\n",
    "2. It was possible to compare how tests behave for different features with a specific \"drift size.\"\n",
    "\n",
    "\n",
    "Once we came up with this artificial drift function, we applied this change to all or some points in the \"current\" dataset. We used two sets of parameters to imitate various degrees of drift:\n",
    "\n",
    "- drift_size: the percent by which we increase the initial values,\n",
    "- drift_ratio: the share of data points to which we apply the defined increase to imitate drift in a segment of data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.8.11 ('bru_ds')",
   "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": "3.8.11"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "ba7033ad42021d8fde750941f7374709dc7fad13ee27a9cd8f3ab36e378bdd7b"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}