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+                    GNU GENERAL PUBLIC LICENSE
+                       Version 3, 29 June 2007
+
+ Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
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+                            Preamble
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+  IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
+WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
+THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
+GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
+USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
+DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
+PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
+EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
+SUCH DAMAGES.
+
+  17. Interpretation of Sections 15 and 16.
+
+  If the disclaimer of warranty and limitation of liability provided
+above cannot be given local legal effect according to their terms,
+reviewing courts shall apply local law that most closely approximates
+an absolute waiver of all civil liability in connection with the
+Program, unless a warranty or assumption of liability accompanies a
+copy of the Program in return for a fee.
+
+                     END OF TERMS AND CONDITIONS
+
+            How to Apply These Terms to Your New Programs
+
+  If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+  To do so, attach the following notices to the program.  It is safest
+to attach them to the start of each source file to most effectively
+state the exclusion of warranty; and each file should have at least
+the "copyright" line and a pointer to where the full notice is found.
+
+    {one line to give the program's name and a brief idea of what it does.}
+    Copyright (C) {year}  {name of author}
+
+    This program is free software: you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+Also add information on how to contact you by electronic and paper mail.
+
+  If the program does terminal interaction, make it output a short
+notice like this when it starts in an interactive mode:
+
+    {project}  Copyright (C) {year}  {fullname}
+    This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+    This is free software, and you are welcome to redistribute it
+    under certain conditions; type `show c' for details.
+
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License.  Of course, your program's commands
+might be different; for a GUI interface, you would use an "about box".
+
+  You should also get your employer (if you work as a programmer) or school,
+if any, to sign a "copyright disclaimer" for the program, if necessary.
+For more information on this, and how to apply and follow the GNU GPL, see
+<http://www.gnu.org/licenses/>.
+
+  The GNU General Public License does not permit incorporating your program
+into proprietary programs.  If your program is a subroutine library, you
+may consider it more useful to permit linking proprietary applications with
+the library.  If this is what you want to do, use the GNU Lesser General
+Public License instead of this License.  But first, please read
+<http://www.gnu.org/philosophy/why-not-lgpl.html>.

auxiliar.R

@@ -0,0 +1,86 @@
+# En este archivo estan los datos que usa la app por defecto
+
+datos <- structure(list(Weight = c(50.5503, 61.25258, 56.24894, 65.65679, 
+                                   62.83388, 73.24405, 58.51261, 60.9063, 56.73146, 67.22003, 60.3634, 
+                                   75.02256, 62.80754, 60.5175, 78.42197, 73.45075, 64.05179, 65.38776, 
+                                   76.63673, 55.08314, 80.88494, 88.58204, 71.54954, 48.32583, 40.44927, 
+                                   74.15086, 84.90795, 58.40049, 60.76984, 70.56893, 75.76796, 71.19564, 
+                                   51.64917, 62.73287, 56.2491, 73.9991, 79.95774, 55.57182, 76.37397, 
+                                   66.56973, 65.86066, 71.20084, 54.67018, 70.4005, 69.4797, 66.60614, 
+                                   75.68068, 56.37009, 72.16496, 67.85384, 71.6978, 70.04701, 70.3357, 
+                                   54.63944, 53.3318, 42.86249, 40.68829, 55.59472, 53.09797, 75.49655, 
+                                   43.54653, 51.60253, 45.47439, 71.48804, 71.06496, 65.36183, 57.63302, 
+                                   71.52314, 60.2691, 76.1195, 43.15393, 74.32763, 73.74856, 64.92062, 
+                                   76.22805, 64.14468, 46.66684, 57.44771, 49.5207, 49.02281, 75.89785, 
+                                   66.45265, 64.021, 74.89705, 106.29634, 62.43153, 85.64085, 75.20969, 
+                                   78.75479, 71.47283, 72.24819, 72.96063, 81.44395, 59.13345, 56.81112, 
+                                   63.75622, 49.76463, 75.51193, 66.75562, 44.02623, 76.37441, 63.37802, 
+                                   69.7395, 70.36453, 68.46488, 76.44103, 69.25948, 61.82844, 76.20195, 
+                                   71.00959, 64.29619, 77.64101, 73.84479, 61.46269, 67.22959, 78.4518, 
+                                   71.52198, 71.12362, 70.71162, 66.09589, 69.55674, 67.42492, 61.32901, 
+                                   84.71004, 59.35111, 71.81532, 78.88253, 80.55406, 72.09338, 60.84449, 
+                                   69.26214, 70.95307, 73.94863, 70.8474, 70.04736, 77.00465, 64.2028, 
+                                   70.5274, 72.2358, 70.30635, 73.85537, 63.46842, 71.55005, 76.91536, 
+                                   67.95931, 67.46876, 72.85655, 68.19556, 75.64152, 61.33369, 66.13137, 
+                                   75.53459, 74.72881, 77.7697, 72.62453, 61.77881, 72.81865, 83.61184, 
+                                   65.61744, 71.70281, 70.3708, 64.10026, 65.19349, 69.15764, 70.83526, 
+                                   70.02046, 71.0855, 71.94166, 73.76781, 66.20942, 72.23653, 75.84131, 
+                                   67.7486, 69.04712, 62.66672, 68.00322, 71.35661, 67.92959, 63.38161, 
+                                   68.01821, 75.97187, 61.44667, 70.94835, 74.35324, 64.30971, 75.68054, 
+                                   66.42512, 76.27227, 61.55411, 66.45667, 78.82515, 66.11034, 68.67467, 
+                                   75.94628, 74.39378, 72.7763, 67.22345, 72.16216, 77.03907, 63.57204, 
+                                   74.58805, 78.82659, 74.29897, 69.4074, 77.2088, 72.57719, 72.86812, 
+                                   72.11492, 79.84081, 74.09459, 74.45922, 79.49065, 72.83807, 69.96743, 
+                                   63.05169, 68.71237, 72.00973, 71.96866, 73.13164, 68.70975, 74.04752, 
+                                   62.79878, 75.78519, 71.50944, 78.1028, 71.48194, 68.81004, 75.34631, 
+                                   70.80994, 61.97276, 64.22399, 72.6092, 71.30278, 73.54538, 72.33739, 
+                                   63.02031, 72.74572, 70.31417, 65.31908, 66.99437, 63.19804, 66.66398, 
+                                   78.33904, 74.0347, 66.44705, 83.54124, 79.72041, 69.41476, 63.05741, 
+                                   70.75567), Group = c("Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", 
+                                                        "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", 
+                                                        "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", 
+                                                        "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", 
+                                                        "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", 
+                                                        "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", 
+                                                        "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", 
+                                                        "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", 
+                                                        "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", 
+                                                        "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", 
+                                                        "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", 
+                                                        "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", 
+                                                        "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", 
+                                                        "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", 
+                                                        "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", 
+                                                        "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", 
+                                                        "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", "Grupo 1", 
+                                                        "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", 
+                                                        "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", 
+                                                        "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", 
+                                                        "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", 
+                                                        "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", 
+                                                        "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", 
+                                                        "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", 
+                                                        "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", 
+                                                        "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", 
+                                                        "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", 
+                                                        "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", 
+                                                        "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", 
+                                                        "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", 
+                                                        "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", 
+                                                        "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", 
+                                                        "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", 
+                                                        "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", 
+                                                        "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", 
+                                                        "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", 
+                                                        "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", 
+                                                        "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", 
+                                                        "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", 
+                                                        "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", 
+                                                        "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", 
+                                                        "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2", "Grupo 2"
+                                   )), row.names = c(NA, -250L), spec = structure(list(cols = list(
+                                     Weight = structure(list(), class = c("collector_double", 
+                                                                          "collector")), Group = structure(list(), class = c("collector_character", 
+                                                                                                                             "collector"))), default = structure(list(), class = c("collector_guess", 
+                                                                                                                                                                                   "collector")), delim = "\t"), class = "col_spec"), class = c("spec_tbl_df", 
+                                                                                                                                                                                                                                                                                          "tbl_df", "tbl", "data.frame"))

daticos.txt

@@ -0,0 +1,11 @@
+peso	barrio
+63.75622	1
+49.76463	1
+75.51193	1
+66.75562	1
+44.02623	1
+76.37441	2
+63.37802	2
+69.73950	2
+70.36453	2
+68.46488	2

funciones.R

@@ -0,0 +1,217 @@
+
+
+
+#Funcion que crea un data frame con todos los elementos de 
+#la prueba de hip�tesis de la igualdad de dos varianzas poblacionales
+ph_igual_varianzas <- function(var_cuant, var_cual, nivel_de_significancia,tipo_de_prueba){
+        grados_de_libertad_num <- tapply(var_cuant, var_cual, length)[1]-1
+        grados_de_libertad_den <- tapply(var_cuant, var_cual, length)[2]-1
+        nivel_de_significancia <- 1 - nivel_de_significancia
+        
+        if(tipo_de_prueba == "two.sided"){
+                
+                #Lado izquierdo y lado de recho donde inician las zonas de rechazo de la hipotesis nula
+                lado_der <- qf(1-(nivel_de_significancia/2), grados_de_libertad_num, grados_de_libertad_den)
+                lado_izq <- qf(nivel_de_significancia/2, grados_de_libertad_num, grados_de_libertad_den)
+                
+                #Varianza muestral grupo 1
+                var1 <- tapply(var_cuant, var_cual, var)[1]
+                
+                #Varianza muestral grupo 2
+                var2 <- tapply(var_cuant, var_cual, var)[2]
+                
+                #Estadistico de prueba
+                ep <- var1/var2
+                
+                #Valor P
+                ValorP <- if(pf(ep,grados_de_libertad_num,grados_de_libertad_den) <= pf(ep,grados_de_libertad_num,grados_de_libertad_den,lower.tail = FALSE)){
+                        pf(ep,grados_de_libertad_num,grados_de_libertad_den)*2 #Valor P
+                }else{
+                        pf(ep,grados_de_libertad_num,grados_de_libertad_den,lower.tail = FALSE)*2 #Valor P
+                }
+                
+                #Data frame que se imprime en el aplicativo
+                bd <- data.frame(Resultados=c("Varianza muestral del numerador",
+                                              "Varianza muestral del denominador",
+                                              "Estadistico de prueba (EP)",
+                                              "Nivel de significancia",
+                                              "Grados de libertad del numerador",
+                                              "Grados de libertad del denominador",
+                                              "Valor P",
+                                              "Regiones criticas de rechazo de hipotesis nula",
+                                              "Conclusion con el valor P",
+                                              "Conclusion con la region de rechazo")
+                                 ,
+                                 Valores=c(as.character(var1),
+                                           as.character(var2),
+                                           as.character(round(ep,8)),
+                                           as.character(nivel_de_significancia),
+                                           as.character(grados_de_libertad_num),
+                                           as.character(grados_de_libertad_den),
+                                           as.character(ValorP),
+                                           paste("EP <= ",as.character(round(lado_izq,4)),
+                                                 "o",
+                                                 "EP >= ", as.character(round(lado_der,4)),
+                                                 sep = "  "),
+                                           if(ValorP <= nivel_de_significancia){
+                                                   paste("El estadistico de prueba es igual a", round(ep,8),
+                                                         "con un valor p igual a", ValorP,
+                                                         "Como el valor p es inferior o igual a", nivel_de_significancia,
+                                                         "(nivel de significancia), entonces se rechaza la hipotesis nula en favor de la hipotesis
+                                                         alternativa.")
+                                           }else{
+                                                   paste("El estadistico de prueba es igual a", round(ep,8),
+                                                         "con un valor p igual a", ValorP,
+                                                         "Como el valor es mayor a",nivel_de_significancia,
+                                                         "(nivel de significancia), entonces se concluye que los datos no son suficientes para
+                                                         rechazar la hipotesis nula.")
+                                           },
+                                           if(ep <= lado_izq |
+                                              ep >= lado_der){
+                                                   paste("El estadistico de prueba es igual a", round(ep,8),
+                                                         ". Como el estadistico de prueba se encuentra
+                              dentro de la region critica de rechazo entonces se rechaza
+                              la hipotesis nula en favor de la hipotesis alternativa.")
+                                           }else{
+                                                   paste("El estadistico de prueba es igual a", round(ep,8),
+                                                         ". Como el estadistico de prueba se encuentra fuera
+                              de la region critica de rechazo entonces se concluye que
+                              los datos no son suficientes para rechazar la hipotesis nula.")
+                                           }
+                                 ))
+                bd
+                
+        }else{
+                if(tipo_de_prueba == "less"){
+                        
+                        #Lado izquierdo  donde inicia la zona de rechazo de la hipotesis nula
+                        lado_izq <- qf(nivel_de_significancia, grados_de_libertad_num, grados_de_libertad_den)
+                        
+                        #Varianza muestral grupo 1
+                        var1 <- tapply(var_cuant, var_cual, var)[1]
+                        
+                        #Varianza muestral grupo 2
+                        var2 <- tapply(var_cuant, var_cual, var)[2]
+                        
+                        #Estadistico de prueba
+                        ep <- var1/var2
+                        
+                        #Valor P
+                        ValorP <- pf(ep, grados_de_libertad_num, grados_de_libertad_den)
+                        
+                        #Data frame que se imprime en el aplicativo
+                        bd <- data.frame(Resultados=c("Varianza muestral del numerador",
+                                                      "Varianza muestral del denominador",
+                                                      "Estadistico de prueba (EP)",
+                                                      "Nivel de significancia",
+                                                      "Grados libertad numerador",
+                                                      "Grados libertad denominador",
+                                                      "Valor P",
+                                                      "Region critica de rechazo de hipotesis nula",
+                                                      "Conclusion con el valor P",
+                                                      "Conclusion con la region de rechazo")
+                                         ,
+                                         Valores=c(as.character(var1),
+                                                   as.character(var2),
+                                                   as.character(round(ep,8)),
+                                                   as.character(nivel_de_significancia),
+                                                   as.character(grados_de_libertad_num),
+                                                   as.character(grados_de_libertad_den),
+                                                   as.character(ValorP),
+                                                   paste("EP <= ",as.character(round(lado_izq,4))),
+                                                   if(ValorP <= nivel_de_significancia){
+                                                           paste("El estadistico de prueba es igual a", round(ep,8),
+                                                                 "con un valor p igual a", ValorP,
+                                                                 "Como el valor p es inferior o igual a", nivel_de_significancia,
+                                                                 "(nivel de significancia), entonces se rechaza la hipotesis nula en favor de la hipotesis
+                                                                 alternativa.")
+                                                   }else{
+                                                           paste("El estadistico de prueba es igual a", round(ep,8),
+                                                                 "con un valor p igual a", ValorP,
+                                                                 "Como el valor es mayor a", nivel_de_significancia,
+                                                                 "(nivel de significancia), entonces se concluye que los datos no son suficientes para
+                                                                 rechazar la hipotesis nula.")
+                                                   },
+                                                   if(ep <= lado_izq){
+                                                           paste("El estadistico de prueba es igual a", round(ep,8),
+                                                                 ". Como el estadistico de prueba se encuentra
+                                                                 dentro de la region critica de rechazo entonces se rechaza
+                                                                 la hipotesis nula en favor de la hipotesis alternativa.")
+                                                   }else{
+                                                           paste("El estadistico de prueba es igual a", round(ep,8),
+                                                                 ". Como el estadistico de prueba se encuentra fuera
+                                                                 de la region critica de rechazo entonces se concluye que
+                                                                 los datos no son suficientes para rechazar la hipotesis nula.")
+                                                   }
+                                         ))
+                        bd
+                        
+                }else{
+                        if(tipo_de_prueba == "greater"){
+                                
+                                #Lado derecho donde inician las zonas de rechazo de la hipotesis nula
+                                lado_der <- qf(1-nivel_de_significancia, grados_de_libertad_num, grados_de_libertad_den)
+                                
+                                #Varianza muestral del numerador
+                                var1 <- tapply(var_cuant, var_cual, var)[1]
+                                
+                                #Varianza muestral del denominador
+                                var2 <- tapply(var_cuant, var_cual, var)[2]
+                                
+                                #Estadistico de prueba
+                                ep <- var1/var2
+                                
+                                #Valor P
+                                ValorP <- pf(ep,grados_de_libertad_num,grados_de_libertad_den,lower.tail = FALSE)
+                                
+                                #Data frame que se imprime en el aplicativo
+                                bd <- data.frame(Resultados=c("Varianza muestral del numerador",
+                                                              "Varianza muestral del denominador",
+                                                              "Estadistico de prueba (EP)",
+                                                              "Nivel de significancia",
+                                                              "Grados de libertad del numerador",
+                                                              "Grados de libertad del denominador",
+                                                              "Valor P",
+                                                              "Region critica de rechazo de hipotesis nula",
+                                                              "Conclusion con el valor P",
+                                                              "Conclusion con la region de rechazo")
+                                                 ,
+                                                 Valores=c(as.character(var1),
+                                                           as.character(var2),
+                                                           as.character(round(ep,8)),
+                                                           as.character(nivel_de_significancia),
+                                                           as.character(grados_de_libertad_num),
+                                                           as.character(grados_de_libertad_den),
+                                                           as.character(ValorP),
+                                                           paste("EP >= ", as.character(round(lado_der,4)),
+                                                                 sep = "  "),
+                                                           if(ValorP <= nivel_de_significancia){
+                                                                   paste("El estadistico de prueba es igual a", round(ep,8),
+                                                                         "con un valor p igual a", ValorP,
+                                                                         "Como el valor p es inferior o igual a", nivel_de_significancia,
+                                                                         "(nivel de significancia), entonces se rechaza la hipotesis nula en favor de la hipotesis
+                                                                         alternativa.")
+                                                           }else{
+                                                                   paste("El estadistico de prueba es igual a", round(ep,8),
+                                                                         "con un valor p igual a", ValorP,
+                                                                         "Como el valor es mayor a",nivel_de_significancia,
+                                                                         "(nivel de significancia), entonces se concluye que los datos no son suficientes para
+                                                                         rechazar la hipotesis nula.")
+                                                           },
+                                                           if(ep >= lado_der){
+                                                                   paste("El estadistico de prueba es igual a", round(ep,8),
+                                                                         ". Como el estadistico de prueba se encuentra
+                                                                         dentro de la region critica de rechazo entonces se rechaza
+                                                                         la hipotesis nula en favor de la hipotesis alternativa.")
+                                                           }else{
+                                                                   paste("El estadistico de prueba es igual a", round(ep,8),
+                                                                         ". Como el estadistico de prueba se encuentra fuera
+                                                                         de la region critica de rechazo entonces se concluye que
+                                                                         los datos no son suficientes para rechazar la hipotesis nula.")
+                                                           }
+                                                 ))
+                                bd
+                }
+        }
+        }
+}

include.md

@@ -0,0 +1,28 @@
+# Prueba de hipótesis para el cociente de varianzas
+
+Suponga que se tienen dos muestras aleatorias que provienen de poblaciones normales así:
+
+- $n_1$ observaciones $X_{11}, X_{12}, \ldots, X_{1,n1}$ de una población I con  varianza $\sigma^2_1$, 
+- $n_2$ observaciones $X_{21}, X_{22}, \ldots, X_{2,n2}$ de una población II con varianza $\sigma^2_2$,
+- ambas muestras son independientes entre sí.
+
+En este problema se desea estudiar la hipótesis nula $H_0: \sigma_1^2 / \sigma_2^2 = 1$ de igualdad de varianzas y se sospecha que el cociente de varianzas podría estar en alguna de las siguientes situaciones:
+
+- $H_a: \sigma_1^2 / \sigma_2^2 < 1$
+- $H_a: \sigma_1^2 / \sigma_2^2 \neq 1$
+- $H_a: \sigma_1^2 / \sigma_2^2 > 1$
+
+El estadístico para realizar la prueba es:
+$$
+F_0=\frac{S_1^2}{S_1^2},
+$$
+donde $S_1^2$ y $S_2^2$ son las varianzas de las muestras I y II respectivamente. El estadístico $F_0$, bajo la suposición de que $H_0$ es verdadera, tiene distribución $f$ con $n_1-1$ grados de libertad en el numerador y $n_2-1$ grados de libertad en el denominador.
+
+Si el valor calculado para el estadístico dado en la ecuación anterior se denota por $f_0$, entonces el valor-$P$ de la prueba se calcula de acuerdo a la hipótesis alterna $H_a$ así:
+
+- Si $H_a: \sigma_1^2 / \sigma_2^2 < \sigma^2_0$ entonces valor-$P$=$P(f_{n_1-1,n_2-1} < f_0)$.
+- Si $H_a: \sigma_1^2 / \sigma_2^2 \neq \sigma^2_0$, valor-$P$=$2 \times \min \left\{ P(f_{n_1-1,n_2-1} < f_0), P(f_{n_1-1,n_2-1} > f_0) \right\}$.
+- Si $H_a: \sigma_1^2 / \sigma_2^2 > \sigma^2_0$ entonces valor-$P$=$P(f_{n_1-1,n_2-1} > f_0)$.
+
+
+En esta prueba, al no rechazar la hipótesis nula $H_0$, se concluye que $\sigma_1^2 / \sigma_2^2 = 1$ lo que implica en términos prácticos que $\sigma_1^2 = \sigma_2^2$, es decir que las varianzas poblacionales se pueden considerar iguales.

server.R

@@ -0,0 +1,172 @@
+library(shiny)
+
+source("auxiliar.R")
+
+shinyServer(function(input,output,session){
+  
+  observe({
+    inFile <- input$file1
+    if(is.null(inFile)) 
+      dt <- datos
+    else dt <- read.csv(inFile$datapath, header=input$header, sep=input$sep)
+    
+    updateSelectInput(session, "variable1",
+                      choices = names(dt),
+                      selected = "Weight")
+    
+    updateSelectInput(session, "variable2",
+                      choices = names(dt),
+                      selected = "Group")
+    
+  })
+  
+  output$summary <- renderTable({
+    inFile <- input$file1
+    if(is.null(inFile)) 
+      dt <- datos
+    else dt <- read.csv(inFile$datapath, header=input$header, sep=input$sep)
+    dt <- na.omit(dt)  # Para eliminar obs con NA
+    dt
+  })
+  
+  output$appPlot <- renderPlot({
+    inFile <- input$file1
+    if(is.null(inFile)) 
+      dt <- datos
+    else dt <- read.csv(inFile$datapath, header=input$header, sep=input$sep)
+    # Para eliminar obs con NA
+    dt <- na.omit(dt)  
+    # Para obtener x y grupo
+    x <- dt[, input$variable1]
+    group <- dt[, input$variable2]
+    group <- as.factor(group)
+    
+    if (nlevels(group) != 2) {
+      plot(1, type = "n", xlab = "", ylab = "", axes = FALSE) 
+      mensaje <- "La variable cualitativa \n que eligió debe tener sólo \n 2 niveles."
+      text(x=1, y=1, mensaje, cex=2, col = "blue", pos=3)
+    }
+    else {
+      par(mfrow=c(1, 2), bg="gray98")
+      
+      # Para dibujar las densidades
+      xx <- split(x, group)
+      den <- lapply(xx, density)
+      plot(den[[1]], lwd=4, col="deepskyblue3",
+           main="Densidad", las=1,
+           xlab=as.character(input$variable1),
+           ylab="Densidad",
+           xlim=range(range(den[[1]]$x), range(den[[2]]$x)),
+           ylim=c(0, max(c(den[[1]]$y, den[[2]]$y))))
+      lines(den[[2]], lwd=4, col="firebrick3")
+      
+      # Leyenda para distinguir las densidades
+      legend("topright", bty="n",
+             lwd=4,
+             col=c("deepskyblue3", "firebrick3"),
+             legend=unique(group))
+      
+      # Para dibujar los qqplot
+      qq1 <- qqnorm(xx[[1]], plot.it=FALSE)
+      qq2 <- qqnorm(xx[[2]], plot.it=FALSE)
+      
+      plot(qq1, las=1, main="QQplot",
+           pch=19, col="deepskyblue3",
+           xlim=range(c(qq1$x, qq2$x)),
+           ylim=range(c(qq1$y, qq2$y)),
+           xlab="Cuantiles teóricos N(0, 1)",
+           ylab=as.character(input$variable1))
+      points(qq2, pch=19, col="firebrick3")
+      
+      # Para construir los qqplot
+      qqline(xx[[1]], col="deepskyblue3")
+      qqline(xx[[2]], col="firebrick3")
+      
+      # Para incluir el valor P de Shapiro
+      shapi <- lapply(xx, shapiro.test)
+      leyenda <- c(paste("Valor P=", round(shapi[[1]]$p.value, 2)),
+                   paste("Valor P=", round(shapi[[2]]$p.value, 2)))
+      legend("topleft", bty="n",
+             text.col=c("deepskyblue3", "firebrick3"),
+             legend=leyenda)
+    }
+    
+  })
+  
+  output$statistic <- renderTable({
+    inFile <- input$file1
+    if(is.null(inFile)) 
+      dt <- datos
+    else dt <- read.csv(inFile$datapath, header=input$header, sep=input$sep)
+    # Para eliminar obs con NA
+    dt <- na.omit(dt)  
+    # Para obtener x y grupo
+    x <- dt[, input$variable1]
+    group <- dt[, input$variable2]
+    group <- as.factor(group)
+    
+    xx <- split(x, group)  # Lista con variable interes
+    resumen <- function(x) c(mean(x), var(x), length(x))
+    res <- sapply(xx, resumen)
+    rownames(res) <- c("Media", "Varianza", "Número de observaciones")
+    t(res)
+  }, rownames = TRUE, align="c", bordered = TRUE)
+  
+  output$resul1 <- renderText({
+    inFile <- input$file1
+    if(is.null(inFile)) 
+      dt <- datos
+    else dt <- read.csv(inFile$datapath, header=input$header, sep=input$sep)
+    # Para eliminar obs con NA
+    dt <- na.omit(dt)  
+    # Para obtener x y grupo
+    x <- dt[, input$variable1]
+    group <- dt[, input$variable2]
+    group <- as.factor(group)
+    
+    if (nlevels(group) != 2) {
+      paste0("La variable cualitativa \n que eligió debe tener sólo \n 2 niveles.")
+    }
+    else {
+      xx <- split(x, group)
+      ph <- var.test(x=xx[[1]], y=xx[[2]],
+                     alternative=input$h0, 
+                     ratio=1, 
+                     conf.level=input$alfa)
+      paste0('El estadístico de prueba es f0=', round(ph$statistic, 4),
+             ' con un valor-P de ', round(ph$p.value, 2), '.')
+    }
+  })
+  
+  output$resul2 <- renderText({
+    inFile <- input$file1
+    if(is.null(inFile)) 
+      dt <- datos
+    else dt <- read.csv(inFile$datapath, header=input$header, sep=input$sep)
+    
+    dt <- na.omit(dt)  # Para eliminar obs con NA
+    
+    x <- dt[, input$variable1]
+    group <- dt[, input$variable2]
+    group <- as.factor(group)
+    
+    if (nlevels(group) != 2) {
+      paste0("La variable cualitativa \n que eligió debe tener sólo \n 2 niveles.")
+    }
+    else {
+      xx <- split(x, group)
+      ph <- var.test(x=xx[[1]], y=xx[[2]],
+                     alternative=input$h0, 
+                     ratio=1, 
+                     conf.level=input$alfa)
+      intervalo <- paste("(", round(ph$conf.int[1], digits=4),
+                         ", ",
+                         round(ph$conf.int[2], digits=4),
+                         ").", sep='')
+      paste0('El intervalo de confianza del ', 100*input$alfa,
+             '% para el cociente de varianzas poblacionales es ',
+             intervalo)
+    }
+  })
+  
+})

ui.R

@@ -0,0 +1,117 @@
+library(shiny)
+library(markdown)
+
+shinyUI(pageWithSidebar(
+  headerPanel(title=HTML("Prueba de hipótesis para el cociente de 
+                         varianzas &sigma;<sup>2</sup><sub>1</sub> / 
+                         &sigma;<sup>2</sup><sub>2</sub>"),
+              windowTitle="PH coc varianzas"),
+  
+  sidebarPanel(
+    h5("Esta aplicación sirve para realizar prueba de hipotesis 
+        para el cociente de varianzas de variables cuantitativas
+        con distribución normal."),
+    
+    h6("La aplicación usa una base de datos de ejemplo pero el usuario
+       puede cargar su propia base de datos."),
+    
+    fileInput(inputId="file1",
+              label="Use el botón siguiente para cargar su base de datos.",
+              accept = c(
+                "text/csv",
+                "text/comma-separated-values",
+                "text/tab-separated-values",
+                "text/plain",
+                ".csv",
+                ".tsv"
+              )),
+    
+    checkboxInput(inputId="header",
+                  label="¿Tiene encabezado la base de datos?", 
+                  value=TRUE),
+    
+    selectInput(inputId="sep",
+                label = "¿Cuál es la separación de los datos?", 
+                choices = list(Tab="\t", Comma=",",
+                               Semicolon=";", "Space"=" "),
+                selected = ";"),
+    
+    selectInput(inputId="variable1",
+                label=p("Elija la variable",
+                        span("cuantitativa", style = "color:red"),
+                        "para realizar la prueba de hipótesis."),
+                choices=""),
+    
+    selectInput(inputId="variable2",
+                label=p("Elija la variable",
+                        span("cualitativa", style = "color:blue"),
+                        "de agrupacion, DEBE tener 2 niveles y ser un factor."),
+                choices=""),
+    
+    selectInput(inputId="h0", 
+                label=HTML("La hipótesis nula de la prueba es Ho:
+                            &sigma;<sup>2</sup><sub>1</sub> / 
+                            &sigma;<sup>2</sup><sub>2</sub> = 1, 
+                            elija el tipo de hipotesis alterna
+                           < , &ne; o >"), 
+                choices=list("Menor" = "less", 
+                             "Diferente" = "two.sided",
+                             "Mayor" = "greater"),
+                selected = "two.sided"),
+    
+    sliderInput(inputId="alfa", 
+                label=HTML("Opcional: elija un nivel de confianza para 
+                           construir el intervalo de confianza para 
+                           el cociente
+                           &sigma;<sup>2</sup><sub>1</sub> / 
+                         &sigma;<sup>2</sup><sub>2</sub>"),
+                min=0.90, max=0.99,
+                value=0.95, step=0.01),
+    
+    img(src="https://raw.githubusercontent.com/fhernanb/fhernanb.github.io/refs/heads/main/my_docs/logo_unal_shiny.png", 
+        height = 60, width = 120),
+    img(src="https://raw.githubusercontent.com/fhernanb/fhernanb.github.io/refs/heads/main/my_docs/logo_udea_shiny.png", 
+        height = 25, width = 70),
+    img(src="https://raw.githubusercontent.com/fhernanb/fhernanb.github.io/refs/heads/main/my_docs/logo_cua_shiny.png", 
+        height = 40, width = 110),
+    br(),
+    br(),
+    tags$a(href="https://srunal.github.io", "https://srunal.github.io")
+    
+  ),
+  
+  mainPanel(
+    tabsetPanel(type = "pills",
+                tabPanel(title="Resultados",
+                         h5("A continuación el histograma, densidad, QQplot
+                          y valor-P para la prueba de normalidad
+                          Shapiro-Wilk de cada una de las
+                          dos muestras."),
+                         plotOutput("appPlot",
+                                    width="500px",
+                                    height="300px"),
+                         
+                         h4("- Tabla de resumen con estadísticos muestrales:"),
+                         tableOutput("statistic"),
+                         
+                         h4("- Resultados de la prueba de hipótesis:"),
+                         textOutput("resul1"),
+                         
+                         h4(HTML("- Intervalo de confianza para
+                                el cociente
+                               &sigma;<sup>2</sup><sub>1</sub> / 
+                         &sigma;<sup>2</sup><sub>2</sub>:")),
+                         textOutput("resul2")
+                         ),
+                
+                tabPanel("Datos", 
+                         "A continuación los datos que está usando 
+                       la aplicación.",
+                         uiOutput("summary")),
+                
+                tabPanel("Teoría", includeHTML("include.html"))
+                
+    )
+  )
+  
+))

unequal_var_data99.txt

@@ -0,0 +1,251 @@
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