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App.R
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App.R
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library(shiny)
library(ggplot2)
library(EnvStats)
library(bslib)
library(waiter)
# ESTÉTICA ------------
theme_AGR <- bs_theme(
version = 5,
bg = "#FFFFFF",
fg = "#212529",
primary = "#9CAF88",
secondary = "#667b68",
success = "#38FF12",
info = "#00F5FB",
warning = "#FFF100",
danger = "#FF00E3",
base_font = font_collection(font_google("Roboto", local = FALSE), "Roboto", "sans-serif"),
heading_font = "Roboto",
code_font = "Chalkduster",
)
# Define UI for application that draws a histogram
ui <- shiny::tagList(
withMathJax(),
includeCSS(path = "www/css/styles.css"),
tags$head(
tags$link(
rel = "shortcut icon",
href = "https://cdn-icons-png.flaticon.com/512/11083/11083341.png"
)
),
tags$div(
tags$div(
class = "app_title",
titlePanel(
title = "Inferencia estadística",
windowTitle = "Inferencia"
),
tags$h5(
tags$a(
href = "https://gestion2.urjc.es/pdi/ver/alejandro.garcia",
target = "_blank",
"Alejandro García Romero (creador de la versión actual)"
)
)
),
# INPUTS -----------------
## SELECTOR DE CONTRASTES---------
fluidPage(
autoWaiter(),
theme = theme_AGR,
sidebarLayout(
sidebarPanel(
selectInput(
inputId = "inference",
label = "Inferencia para:",
choices = c("Una media", "Dos medias (independientes)",
"Dos medias (relacionadas)",
"Una proporción",
"Dos proporciones",
"Una varianza",
"Dos varianzas"),
multiple = FALSE,
selected = "Una media"
),
conditionalPanel(
condition = "input.inference == 'Una media' |
input.inference == 'Dos medias (independientes)'|
input.inference == 'Dos medias (relacionadas)' |
input.inference == 'Una varianza'|
input.inference == 'Dos varianzas'
",
selectInput(
inputId = "inference2",
label = "Introducir datos usando:",
choices = c("Valores poblaciones y muestrales", "Un conjunto de datos de forma manual"),
multiple = FALSE,
selected = "Valores poblaciones y muestrales"
),
hr()
),
### Opciones sobre contrastes ---------
#### Una muestra y valores específicos sobre la muestra y la población ---------
conditionalPanel(
condition = "input.inference == 'Una media' & input.inference2 == 'Valores poblaciones y muestrales'",
numericInput("smean_onemean", "\\(\\bar{X} = \\)",
value = 1, step = 0.1
),
numericInput("sd_onemean", "\\(S_x = \\)",
value = 1, min = 0, step = 0.1
),
numericInput("n_onemean", "\\(n = \\)",
value = 10, min = 0, step = 1
),
checkboxInput("popsd_onemean2", "La varianza de la población es conocida", FALSE),
conditionalPanel(
condition = "input.popsd_onemean2 == 1",
numericInput("sigma2_onemean", "\\(\\sigma^2 = \\)",
value = 1, min = 0, step = 1
)
)
),
#### Una muestra y datos de forma manual ---------
conditionalPanel(
condition = "input.inference == 'Una media' & input.inference2 == 'Un conjunto de datos de forma manual'",
textInput("muestra_onemean", "Muestra", value = "0.9, -0.8, 1.3, -0.3, 1.7",
placeholder = "Introduzca valores separados por una coma con decimales como puntos, por ejemplo 4.2, 4.4, 5, 5.03, etc."),
hr(),
checkboxInput("popsd_onemean", "La varianza de la población es conocida", FALSE),
conditionalPanel(
condition = "input.popsd_onemean == 1",
numericInput("sigma2_onemean", "\\(\\sigma^2 = \\)",
value = 1, min = 0, step = 1
)
)
),
#### Dos medias independientes y valores ---------
conditionalPanel(
condition = "input.inference == 'Dos medias (independientes)' & input.inference2 == 'Valores poblaciones y muestrales'",
tags$b("Muestra 1"),
tags$br(),
numericInput("mean1_2indemean", "\\(\\bar{X}_{1} = \\)",
value = 0.02, step = 0.1
),
numericInput("sd1_2indemean", "\\(\\ S_{1} = \\)",
value = 0.63, step = 0.1
),
numericInput("n1_2indemean", "\\(\\ n_{1} = \\)",
value = 5, step = 1
),
tags$b("Muestra 2"),
numericInput("mean2_2indemean", "\\(\\bar{X}_{2} = \\)",
value = 0.06, step = 0.1
),
numericInput("sd2_2indemean", "\\(\\ S_{2} = \\)",
value = 0.634, step = 0.1
),
numericInput("n2_2indemean", "\\(\\ n_{2} = \\)",
value = 5, step = 1
),
conditionalPanel(
condition = "input.popsd_twomeans2 == 0",
radioButtons(
inputId = "var.equal2",
label = "Asumiendo",
choices = c(
"\\( \\sigma^2_1 = \\sigma^2_2 \\)" = TRUE,
"\\( \\sigma^2_1 \\neq \\sigma^2_2 \\)" = FALSE
)
)
),
checkboxInput("popsd_twomeans2", "Las varianzas poblacionales son conocidas", FALSE),
conditionalPanel(
condition = "input.popsd_twomeans2 == 1",
numericInput("sigma21_twomeans", "\\(\\sigma^2_1 = \\)",
value = 1, min = 0, step = 1
),
numericInput("sigma22_twomeans", "\\(\\sigma^2_2 = \\)",
value = 1, min = 0, step = 1
)
)),
#### Dos medias independientes y datos manuales ---------
conditionalPanel(
condition = "input.inference == 'Dos medias (independientes)' & input.inference2 == 'Un conjunto de datos de forma manual'",
textInput("muestra1_twomeans", "Muestra 1", value = "0.9, -0.8, 0.1, -0.3, 0.2", placeholder = "Introduzca valores separados por una coma con decimales como puntos, p.ej. 4.2, 4.4, 5, 5.03, etc."),
textInput("muestra2_twomeans", "Muestra 2", value = "0.8, -0.9, -0.1, 0.4, 0.1", placeholder = "Introduzca valores separados por una coma con decimales como puntos, p.ej. 4.2, 4.4, 5, 5.03, etc."),
hr(),
conditionalPanel(
condition = "input.popsd_twomeans == 0",
radioButtons(
inputId = "var.equal",
label = "Asumiendo",
choices = c(
"\\( \\sigma^2_1 = \\sigma^2_2 \\)" = TRUE,
"\\( \\sigma^2_1 \\neq \\sigma^2_2 \\)" = FALSE
)
)
),
checkboxInput("popsd_twomeans", "La varianza de las poblaciones es conocida", FALSE),
conditionalPanel(
condition = "input.popsd_twomeans == 1",
numericInput("sigma21_twomeans", "\\(\\sigma^2_1 = \\)",
value = 1, min = 0, step = 1
),
numericInput("sigma22_twomeans", "\\(\\sigma^2_2 = \\)",
value = 1, min = 0, step = 1
)
)
),
#### Dos medias relacionadas y valores ---------
conditionalPanel(
condition = "input.inference == 'Dos medias (relacionadas)' & input.inference2 == 'Valores poblaciones y muestrales'",
hr(),
numericInput("dif_twomeanspaired", "\\( \\bar{Y_1} - \\bar{Y}_{2} = \\bar{D} = \\)",
value = 0.04, min = 0, step = 0.1),
numericInput("sd_difs_twomeanspaired", "\\({S_{D}} = \\)",
value = 0.371, min = 0, step = 0.1),
numericInput("n_twomeanspaired", "\\(n = \\)",
value = 5, min = 0, step = 1),
checkboxInput("popsd_twomeanspaired2", "\\( \\sigma^2_D \\) es conocida", FALSE),
conditionalPanel(
condition = "input.popsd_twomeanspaired2 == 1",
numericInput("sigma2_twomeanspaired2", "\\(\\sigma^2_D = \\)",
value = 1, min = 0, step = 1
)
)
),
#### Dos medias relacionadas y datos manuales ---------
conditionalPanel(
condition = "input.inference == 'Dos medias (relacionadas)' & input.inference2 == 'Un conjunto de datos de forma manual'",
textInput("muestra1_twomeanspaired", "Muestra 1", value = "0.9, -0.8, 0.1, -0.3, 0.2", placeholder = "Introduzca valores separados por una coma con decimales como puntos (p. ej.,4.2, 4.4, 5, 5.03, etc.)"),
textInput("muestra2_twomeanspaired", "Muestra 2", value = "0.8, -0.9, -0.1, 0.4, 0.1", placeholder = "Introduzca valores separados por una coma con decimales como puntos (p. ej.,4.2, 4.4, 5, 5.03, etc.)"),
hr(),
checkboxInput("popsd_twomeanspaired", "Se conoce la \\( \\sigma^2_D \\)", FALSE),
conditionalPanel(
condition = "input.popsd_twomeanspaired == 1",
numericInput("sigma2_twomeanspaired", "\\(\\sigma^2_D = \\)",
value = 1, min = 0, step = 1
)
)
),
#### Una proporción ---------
conditionalPanel(
condition = "input.inference == 'Una proporción'",
tags$b("Tamaño muestral"),
numericInput("n_oneprop", "\\(n = \\)",
value = 30, min = 0, step = 1
),
hr(),
radioButtons(
inputId = "propx_oneprop",
label = NULL,
choices = c(
"Proporción de éxitos \\(P_1\\)" = "prop_true",
"Número de éxitos \\(n_1\\)" = "prop_false"
)
),
conditionalPanel(
condition = "input.propx_oneprop == 'prop_true'",
tags$b("Proporción de éxitos"),
numericInput("p_oneprop", "\\(P_1 = \\)",
value = 0.2, min = 0, max = 1, step = 0.01
)
),
conditionalPanel(
condition = "input.propx_oneprop == 'prop_false'",
tags$b("Número de éxitos"),
numericInput("x_oneprop", "\\(n_1\\)",
value = 10, min = 0, step = 1
)
)
),
#### Dos proporciones ---------
conditionalPanel(
condition = "input.inference == 'Dos proporciones'",
tags$b("Tamaño muestral de la muestra 1"),
numericInput("n1_twoprop", "\\(n_1 = \\)",
value = 30, min = 0, step = 1
),
tags$b("Tamaño muestral de la muestra 2"),
numericInput("n2_twoprop", "\\(n_2 = \\)",
value = 30, min = 0, step = 1
),
hr(),
radioButtons(
inputId = "propx_twoprop",
label = NULL,
choices = c(
"Proporción de éxitos \\(\\hat{p}\\)" = "prop_true",
"Número de éxitos \\(x\\)" = "prop_false"
)
),
conditionalPanel(
condition = "input.propx_twoprop == 'prop_true'",
tags$b("Proporción de éxitos"),
numericInput("p1_twoprop", "\\(P_1 = \\)",
value = 0.2, min = 0, max = 1, step = 0.01
),
numericInput("p2_twoprop", "\\(P_2 = \\)",
value = 0.3, min = 0, max = 1, step = 0.01
)
),
conditionalPanel(
condition = "input.propx_twoprop == 'prop_false'",
tags$b("Número de éxitos"),
numericInput("x1_twoprop", "\\(x_1 = \\)",
value = 10, min = 0, step = 1
),
numericInput("x2_twoprop", "\\(x_2 = \\)",
value = 12, min = 0, step = 1
)
)
),
#### Una varianza ---------
conditionalPanel(
condition = "input.inference == 'Una varianza' & input.inference2 == 'Un conjunto de datos de forma manual'",
textInput("muestra_onevar", "Muestra", value = "0.9, -0.8, 0.1, -0.3, 0.2", placeholder = "Introduzca valores separados por una coma con decimales como puntos (p. ej., 0.9, -0.8, 0.1, -0.3, 0.2, etc.)")
),
conditionalPanel(
condition = "input.inference == 'Una varianza' & input.inference2 == 'Valores poblaciones y muestrales'",
tags$b("Datos muestrales"),
numericInput("unavarianza_S2", "\\(S^2 = \\)",
value = 0.397, step = 0.01, min = 0),
numericInput("unavarianza_n", "\\(n = \\)",
value = 5, step = 1, min = 0)
),
#### Dos varianzas ---------
conditionalPanel(
condition = "input.inference == 'Dos varianzas' & input.inference2 == 'Un conjunto de datos de forma manual'",
textInput("muestra1_twovar", "Muestra 1", value = "0.9, -0.8, 0.1, -0.3, 0.2, 0.7, -0.8, 0.1, -0.3, 0.2", placeholder = "Introduzca valores separados por una coma con decimales como puntos (p. ej., 0.9, -0.8, 0.1, -0.3, 0.2, etc.)"),
textInput("muestra2_twovar", "Muestra 2", value = "0.4, -0.3, -0.1, 0.4, 0.1, 0.2, -0.1, -0.1, 0.4, 0.1", placeholder = "Introduzca valores separados por una coma con decimales como puntos (p. ej., 0.9, -0.8, 0.1, -0.3, 0.2, etc.)")
),
conditionalPanel(
condition = "input.inference == 'Dos varianzas' & input.inference2 == 'Valores poblaciones y muestrales'",
tags$b("Datos muestrales"),
numericInput("dosvarianzas_n1", "\\(n_1 = \\)",
value = 10, step = 1, min=2),
numericInput("dosvarianzas_s21", "\\(S^2_1 = \\)",
value = 0.318, step = 0.1, min=0),
numericInput("dosvarianzas_n2", "\\(n_2 = \\)",
value = 10, step = 1, min=2),
numericInput("dosvarianzas_s22", "\\(S^2_2 = \\)",
value = 0.062, step = 0.1, min=0)
),
hr(),
tags$b("Hipótesis nula"),
conditionalPanel(
condition = "input.inference == 'Una media'",
sprintf("\\( H_0 : \\mu = \\)")
),
conditionalPanel(
condition = "input.inference == 'Dos medias (independientes)'",
sprintf("\\( H_0 : \\mu_1 - \\mu_2 = \\)")
),
conditionalPanel(
condition = "input.inference == 'Dos medias (relacionadas)'",
sprintf("\\( H_0 : \\mu_D = \\)")
),
conditionalPanel(
condition = "input.inference == 'Una proporción'",
sprintf("\\( H_0 : \\pi_1 = \\)")
),
conditionalPanel(
condition = "input.inference == 'Dos proporciones'",
sprintf("\\( H_0 : P_1 - P_2 = \\)")
),
conditionalPanel(
condition = "input.inference == 'Una varianza'",
sprintf("\\( H_0 : \\sigma^2 = \\)")
),
conditionalPanel(
condition = "input.inference == 'Dos varianzas'",
sprintf("\\( H_0 : \\sigma^2_1 = \\sigma^2_2 \\)")
),
conditionalPanel(
condition = "input.inference != 'Dos varianzas'",
numericInput("h0",
label = NULL,
value = 0.3, step = 0.1
)
),
conditionalPanel(
condition = "input.inference == 'Dos varianzas'",
br()
),
conditionalPanel(
condition = "input.inference != 'Dos varianzas'",
radioButtons(
inputId = "Alternativa",
label = "Alternativa",
choices = c(
"\\( \\neq \\)" = "two.sided",
"\\( > \\)" = "greater",
"\\( < \\)" = "less"
)
)
),
conditionalPanel(
condition = "input.inference == 'Dos varianzas'",
radioButtons(
inputId = "Alternativa_twovar",
label = "Alternativa",
choices = c(
"\\( \\sigma^2_1 \\neq \\sigma^2_2 \\)" = "two.sided",
"\\( \\sigma^2_1 > \\sigma^2_2 \\)" = "greater",
"\\( \\sigma^2_1 < \\sigma^2_2 \\)" = "less"
)
)
),
hr(),
sliderInput("alpha",
"Nivel de significación \\(\\alpha = \\)",
min = 0.01,
max = 0.20,
value = 0.05
),
width = 4),
mainPanel(
br(),
conditionalPanel(
condition = "input.inference == 'Una media' && input.inference2 == 'Un conjunto de datos de forma manual'",
uiOutput("results_onemean")
),
conditionalPanel(
condition = "input.inference == 'Una media' && input.inference2 == 'Valores poblaciones y muestrales'",
uiOutput("results_onemean2")
),
conditionalPanel(
condition = "input.inference == 'Dos medias (independientes)' && input.inference2 == 'Un conjunto de datos de forma manual'",
uiOutput("results_twomeans")
),
conditionalPanel(
condition = "input.inference == 'Dos medias (independientes)' && input.inference2 == 'Valores poblaciones y muestrales'",
uiOutput("results_twomeans2")
),
conditionalPanel(
condition = "input.inference == 'Dos medias (relacionadas)' && input.inference2 == 'Un conjunto de datos de forma manual'",
uiOutput("results_twomeanspaired")
),
conditionalPanel(
condition = "input.inference == 'Dos medias (relacionadas)' && input.inference2 == 'Valores poblaciones y muestrales'",
uiOutput("results_twomeanspaired2")
),
conditionalPanel(
condition = "input.inference == 'Una proporción'",
uiOutput("results_oneprop")
),
conditionalPanel(
condition = "input.inference == 'Dos proporciones'",
uiOutput("results_twoprop")
),
conditionalPanel(
condition = "input.inference == 'Una varianza'",
uiOutput("results_onevar")
),
conditionalPanel(
condition = "input.inference == 'Dos varianzas'",
uiOutput("results_twovar")
),
br(),
br(),
plotOutput("plot"),
br(),
br()
)
),
)
),
tags$footer(
tags$div(
class = "footer_container",
includeHTML(path = "www/html/footer.html")
)
)
)
server <- function(input, output) {
extract <- function(text) {
text <- gsub(" ", "", text)
split <- strsplit(text, ",", fixed = FALSE)[[1]]
as.numeric(split)
}
###FUNCIONES###
## NUEVO ###
#IC c. una media
t.testIC <- function(mean, sd, n, alfa, varprob = NULL){
IC <- c()
ICInf <- c()
ICSup <- c()
if (is.null(varprob)) {
ICInf <- mean - qt(alfa/2, df = n -1 , lower.tail = FALSE)*sd/sqrt(n)
ICSup <- mean + qt(alfa/2, df = n -1 , lower.tail = FALSE)*sd/sqrt(n)
} else {
ICInf <- mean - qnorm(alfa/2, lower.tail = FALSE)*sqrt(varprob)/sqrt(n)
ICSup <- mean + qnorm(alfa/2, lower.tail = FALSE)*sqrt(varprob)/sqrt(n)
}
IC <- c(ICInf,ICSup)
return(IC)
print(IC)
}
## NUEVO ###
#t test c. una media
t.testv2 <- function(mean, sd, n, alfa, mu, varprob = NULL, alternative){
estadistico <- c()
pvalor <- c()
if(is.null(varprob)){
estadistico <- (mean-mu)/(sd/sqrt(n))
if(alternative == "two.sided"){
if(estadistico > 0) {pvalor <- 2*pt(estadistico, df = n-1, lower.tail = FALSE)}
else {pvalor <- 2*pt(estadistico, df = n-1, lower.tail = TRUE)}
} else if (alternative == "less") {
pvalor <- pt(estadistico, df = n-1, lower.tail = TRUE)
} else { pvalor <- pt(estadistico, df = n-1, lower.tail = FALSE)}
} else {
estadistico <- (mean-mu)/(sqrt(varprob)/sqrt(n))
if(alternative == "two.sided"){
if(estadistico > 0) {pvalor <- 2*pnorm(estadistico, lower.tail = FALSE)}
else {pvalor <- 2*pnorm(estadistico, lower.tail = TRUE)}
} else if (alternative == "less") {
pvalor <- pnorm(estadistico, lower.tail = TRUE)
} else { pvalor <- pnorm(estadistico, lower.tail = FALSE)}
}
datos <- list(Estadistico = estadistico, pvalor = pvalor)
return(datos)
}
t.test2 <- function(x, V, m0 = 0, alpha = 0.05, Alternativa = "two.sided") {
M <- mean(x)
n <- length(x)
sigma <- sqrt(V)
S <- sqrt(V / n)
statistic <- (M - m0) / S
p <- if (Alternativa == "two.sided") {
2 * pnorm(abs(statistic), lower.tail = FALSE)
} else if (Alternativa == "less") {
pnorm(statistic, lower.tail = TRUE)
} else {
pnorm(statistic, lower.tail = FALSE)
}
# p <- (1 - pnorm((M-m0)/S))
LCL <- (M - S * qnorm(1 - alpha / 2))
UCL <- (M + S * qnorm(1 - alpha / 2))
value <- list(mean = M, m0 = m0, sigma = sigma, statistic = statistic, p.value = p, LCL = LCL, UCL = UCL, Alternativa = Alternativa)
# print(sprintf("P-value = %g",p))
# print(sprintf("Lower %.2f%% Confidence Limit = %g",
# alpha, LCL))
# print(sprintf("Upper %.2f%% Confidence Limit = %g",
# alpha, UCL))
return(value)
}
### NUEVO ###
#t.test2_muestrameans
t.test3 <- function(x, y, V1, V2, m0 = 0, alpha = 0.05, Alternativa = "two.sided") {
M1 <- mean(x)
M2 <- mean(y)
n1 <- length(x)
n2 <- length(y)
sigma1 <- sqrt(V1)
sigma2 <- sqrt(V2)
S <- sqrt((V1 / n1) + (V2 / n2))
statistic <- (M1 - M2 - m0) / S
p <- if (Alternativa == "two.sided") {
2 * pnorm(abs(statistic), lower.tail = FALSE)
} else if (Alternativa == "less") {
pnorm(statistic, lower.tail = TRUE)
} else {
pnorm(statistic, lower.tail = FALSE)
}
# p <- (1 - pnorm((M-m0)/S))
LCL <- (M1 - M2 - S * qnorm(1 - alpha / 2))
UCL <- (M1 - M2 + S * qnorm(1 - alpha / 2))
value <- list(mean1 = M1, mean2 = M2, m0 = m0, sigma1 = sigma1, sigma2 = sigma2, S = S, statistic = statistic, p.value = p, LCL = LCL, UCL = UCL, Alternativa = Alternativa)
# print(sprintf("P-value = %g",p))
# print(sprintf("Lower %.2f%% Confidence Limit = %g",
# alpha, LCL))
# print(sprintf("Upper %.2f%% Confidence Limit = %g",
# alpha, UCL))
return(value)
}
prop.z.test <- function(x, n, p0 = 0.5, conf.level = 0.95, Alternativa = "two.sided") {
ts.z <- NULL
cint <- NULL
p.val <- NULL
phat <- x / n
qhat <- 1 - phat
SE.phat <- sqrt((phat * qhat) / n)
if (x<(n*p0)) {
ts.z <- ((phat+0.5/n) - p0) / SE.phat
} else if (x>(n*p0)) {
ts.z <- ((phat-0.5/n) - p0) / SE.phat
} else {
ts.z <- (phat - p0) / SE.phat }
p.val <- if (Alternativa == "two.sided") {
2 * pnorm(abs(ts.z), lower.tail = FALSE)
} else if (Alternativa == "less") {
pnorm(ts.z, lower.tail = TRUE)
} else {
pnorm(ts.z, lower.tail = FALSE)
}
cint <- c(phat - (abs((qnorm(p = (1-conf.level)/ 2))) * SE.phat),
phat + (abs((qnorm(p = (1-conf.level)/ 2))) * SE.phat))
return(list(x = x, n = n, estimate = phat, null.value = p0, stderr = SE.phat, statistic = ts.z, p.value = p.val, conf.int = cint))
}
prop.z.test2 <- function(x1, x2, n1, n2, p0 = 0, pooled.stderr = TRUE, conf.level = 0.95, Alternativa = "two.sided") {
ts.z <- NULL
cint <- NULL
p.val <- NULL
phat1 <- x1 / n1
qhat1 <- 1 - phat1
phat2 <- x2 / n2
qhat2 <- 1 - phat2
pooled.phat <- ((n1 * phat1) + (n2 * phat2)) / (n1 + n2)
pooled.qhat <- 1 - pooled.phat
if (pooled.stderr == FALSE) {
SE.phat <- sqrt((phat1 * qhat1) / n1 + (phat2 * qhat2) / n2)
} else {
SE.phat <- sqrt(pooled.phat * pooled.qhat * (1 / n1 + 1 / n2))
}
ts.z <- (phat1 - phat2 - p0) / SE.phat
p.val <- if (Alternativa == "two.sided") {
2 * pnorm(abs(ts.z), lower.tail = FALSE)
} else if (Alternativa == "less") {
pnorm(ts.z, lower.tail = TRUE)
} else {
pnorm(ts.z, lower.tail = FALSE)
}
cint <- (phat1 - phat2) + c(
-1 * ((qnorm(((1 - conf.level) / 2) + conf.level)) * SE.phat),
((qnorm(((1 - conf.level) / 2) + conf.level)) * SE.phat)
)
return(list(x1 = x1, x2 = x2, n1 = n1, n2 = n2, estimate1 = phat1, estimate2 = phat2, null.value = p0, stderr = SE.phat, pooled.phat = pooled.phat, statistic = ts.z, p.value = p.val, conf.int = cint))
}
prop.z.test3 <- function(x, n, p0 = 0.5, conf.level = 0.95, Alternativa = "two.sided") {
ts.z <- NULL
cint <- NULL
p.val <- NULL
phat <- x / n
qhat <- 1 - phat
SE.phat <- sqrt((p0 * (1-p0)) / n)
if (x<(n*p0)) {
ts.z <- ((phat+0.5/n) - p0) / SE.phat
} else if (x>(n*p0)) {
ts.z <- ((phat-0.5/n) - p0) / SE.phat
} else {
ts.z <- (phat - p0) / SE.phat }
p.val <- if (Alternativa == "two.sided") {
2 * pnorm(abs(ts.z), lower.tail = FALSE)
} else if (Alternativa == "less") {
pnorm(ts.z, lower.tail = TRUE)
} else {
pnorm(ts.z, lower.tail = FALSE)
}
return(list(x = x, n = n, estimate = phat, null.value = p0, stderr = SE.phat, statistic = ts.z, p.value = p.val))
}
# ANALISIS UNA MEDIA CON DATOS MANUALES ---------------------------------
output$results_onemean <- renderUI({
dat <- extract(input$muestra_onemean)
if (anyNA(dat) | length(dat) < 2) {
"Entrada no válida o número insuficiente de observaciones"
} else if (input$inference == "Una media" & input$popsd_onemean == FALSE) {
test_confint <- t.test(x = dat, mu = input$h0, Alternativa = "two.sided", conf.level = 1 - input$alpha)
test <- t.test(x = dat, mu = input$h0, Alternativa = input$Alternativa, conf.level = 1 - input$alpha)
withMathJax(
tags$b("Datos:"),
br(),
paste(c(paste(dat, collapse = ", ")), collapse = " "),
br(),
paste0("\\(n =\\) ", length(dat)),
br(),
paste0("\\(\\bar{X} =\\) ", round(mean(dat), 3)),
br(),
paste0("\\(S_x =\\) ", round(sd(dat), 3)),
br(),
br(),
tags$b("Intervalo de confianza"),
tags$em("(Bilateral)"),
br(),
paste0(
"IC al ", (1 - input$alpha) * 100, "% para \\(\\mu = \\bar{X} \\pm t_{\\alpha/2, n - 1} \\dfrac{S_x}{\\sqrt{n}} = \\) ",
round(test_confint$estimate, 3), " \\( \\pm \\) ", "\\( ( \\)", round(qt(input$alpha / 2, df = test_confint$parameter, lower.tail = FALSE), 3), " * ", round(test_confint$stderr * sqrt(length(dat)), 3), " / ", round(sqrt(length(dat)), 3), "\\( ) \\) ", "\\( = \\) ",
"[", round(test_confint$conf.int[1], 3), "; ", round(test_confint$conf.int[2], 3), "]"
),
br(),
br(),
tags$b("Contraste de la hipótesis:"),
br(),
paste0("1. \\(H_0 : \\mu = \\) ", test$null.value, " y \\(H_1 : \\mu \\) ", ifelse(input$Alternativa == "two.sided", "\\( \\neq \\) ", ifelse(input$Alternativa == "greater", "\\( > \\) ", "\\( < \\) ")), test$null.value),
br(),
paste0(
"2. Estadístico de contraste : \\(T = \\dfrac{\\bar{X} - \\mu_0}{S_x / \\sqrt{n}} = \\) ",
"(", round(test$estimate, 3), ifelse(test$null.value >= 0, paste0(" - ", test$null.value), paste0(" + ", abs(test$null.value))), ") / ", round(test$stderr, 3), " \\( = \\) ",
round(test$statistic, 3)
),
br(),
paste0(
"3. Valor crítico :", ifelse(input$Alternativa == "two.sided", " \\( \\pm t_{\\alpha/2, n - 1} = \\pm t(\\)", ifelse(input$Alternativa == "greater", " \\( t_{\\alpha, n - 1} = t(\\)", " \\( -t_{\\alpha, n - 1} = -t(\\)")),
ifelse(input$Alternativa == "two.sided", input$alpha / 2, input$alpha), ", ", test$parameter, "\\()\\)", " \\( = \\) ",
ifelse(input$Alternativa == "two.sided", "\\( \\pm \\)", ifelse(input$Alternativa == "greater", "", " -")),
ifelse(input$Alternativa == "two.sided", round(qt(input$alpha / 2, df = test$parameter, lower.tail = FALSE), 3), round(qt(input$alpha, df = test$parameter, lower.tail = FALSE), 3))
),
br(),
paste0("4. Conclusión/Decisión : ", ifelse(test$p.value < input$alpha, "Rechazar \\(H_0\\)", "No rechazar \\(H_0\\)")),
br(),
br(),
tags$b("Intepretación"),
br(),
paste0("Considerando un nivel de significación del ", input$alpha * 100, "%",
ifelse(test$p.value < input$alpha, " debemos rechazar la hipótesis nula que afirma que la verdadera media es ",
" NO debemos rechazar la hipótesis nula que afirma que la verdadera media es "),
input$h0, " \\((p\\)-value ",
ifelse(test$p.value < 0.001, "< 0.001", paste0("\\(=\\) ", round(test$p.value, 3))), ")", ".")
)
} else if (input$inference
== "Una media" & input$popsd_onemean == TRUE) {
test <- t.test2(x = dat, V = input$sigma2_onemean, m0 = input$h0, alpha = input$alpha, Alternativa = input$Alternativa)
withMathJax(
tags$b("Datos:"),
br(),
paste(c(paste(dat, collapse = ", ")), collapse = " "),
br(),
paste0("\\(n =\\) ", length(dat)),
br(),
paste0("\\(\\bar{x} =\\) ", round(mean(dat), 3)),
br(),
paste0("\\(\\sigma =\\) ", round(sqrt(input$sigma2_onemean), 3)),
br(),
br(),
tags$b("Intervalo de confianza"),
tags$em("(Bilateral)"),
br(),
paste0(
"IC al ", (1 - input$alpha) * 100, "% para \\(\\mu = \\bar{x} \\pm z_{\\alpha/2} \\dfrac{\\sigma}{\\sqrt{n}} = \\) ",
round(test$mean, 3), " \\( \\pm \\)", " \\( ( \\)", round(qnorm(input$alpha / 2, lower.tail = FALSE), 3), " * ", round(test$sigma, 3), " / ", round(sqrt(length(dat)), 3), "\\( ) \\) ", "\\( = \\) ",
"[", round(test$LCL, 3), "; ", round(test$UCL, 3), "]"
),
br(),
br(),
tags$b("Contraste de la hipótesis:"),
br(),
paste0("1. \\(H_0 : \\mu = \\) ", input$h0, " y \\(H_1 : \\mu \\) ", ifelse(input$Alternativa == "two.sided", "\\( \\neq \\) ", ifelse(input$Alternativa == "greater", "\\( > \\) ", "\\( < \\) ")), input$h0),
br(),
paste0(
"2. Estadístico de contraste : \\(z_{obs} = \\dfrac{\\bar{x} - \\mu_0}{\\sigma / \\sqrt{n}} = \\) ",
"(", round(test$mean, 3), ifelse(input$h0 >= 0, paste0(" - ", input$h0), paste0(" + ", abs(input$h0))), ") / ", round(test$sigma / sqrt(length(dat)), 3), " \\( = \\) ",
round(test$statistic, 3)
),
br(),
paste0(
"3. Valor crítico :", ifelse(input$Alternativa == "two.sided", " \\( \\pm z_{\\alpha/2} = \\pm z(\\)", ifelse(input$Alternativa == "greater", " \\( z_{\\alpha} = z(\\)", " \\( -z_{\\alpha} = -z(\\)")),
ifelse(input$Alternativa == "two.sided", input$alpha / 2, input$alpha), "\\()\\)", " \\( = \\) ",
ifelse(input$Alternativa == "two.sided", "\\( \\pm \\)", ifelse(input$Alternativa == "greater", "", " -")),
ifelse(input$Alternativa == "two.sided", round(qnorm(input$alpha / 2, lower.tail = FALSE), 3), round(qnorm(input$alpha, lower.tail = FALSE), 3))
),
br(),
paste0("4. Conclusión/Decisión : ", ifelse(test$p.value < input$alpha, "Reject \\(H_0\\)", "Do not reject \\(H_0\\)")),
br(),
br(),
tags$b("Interpretation"),
br(),
paste0("Considerando un nivel de significación del ", input$alpha * 100, "%",
ifelse(test$p.value < input$alpha, " debemos rechazar la hipótesis nula que afirma que la verdadera media es ",
" NO debemos rechazar la hipótesis nula que afirma que la verdadera media es "),
input$h0, " \\((p\\)-value ",
ifelse(test$p.value < 0.001, "< 0.001", paste0("\\(=\\) ", round(test$p.value, 3))), ")", ".")
)
} else {
print("loading...")
}
})
# ANALISIS UNA MEDIA CON VALORES ---------------------------------
output$results_onemean2 <- renderUI({
if (input$n_onemean < 2) {
"Entrada no válida o número insuficiente de observaciones"
}
#Sin varianza poblacional
else if (input$inference == "Una media" & input$inference2 == "Valores poblaciones y muestrales" & input$popsd_onemean2 == FALSE) {
IC <- t.testIC(mean = input$smean_onemean, sd = input$sd_onemean, n = input$n_onemean, alfa = input$alpha)
test <- t.testv2(mean = input$smean_onemean, n = input$n_onemean, sd = input$sd_onemean, alternative = input$Alternativa, mu = input$h0)
#test_confint <- t.test(x = dat, mu = input$h0, Alternativa = "two.sided", conf.level = 1 - input$alpha)
#test <- t.test(x = dat, mu = input$h0, Alternativa = input$Alternativa, conf.level = 1 - input$alpha)
withMathJax(
tags$b("Datos:"),
br(),
br(),
paste0("\\(n =\\) ", input$n_onemean),
br(),
paste0("\\(\\bar{X} =\\) ", input$smean_onemean),
br(),
paste0("\\(S_x =\\) ", input$sd_onemean),
br(),
br(),
tags$b("Intervalo de confianza"),
tags$em("(Bilateral)"),
br(),
paste0(
"IC al ", (1 - input$alpha) * 100, "% para \\(\\mu = \\bar{X} \\pm t_{\\alpha/2, n - 1} \\dfrac{S_x}{\\sqrt{n}} = \\) ",
input$smean_onemean, " \\( \\pm \\) ", "\\( ( \\)", round(qt(input$alpha / 2, df = input$n_onemean - 1, lower.tail = FALSE), 3), " * ", round(input$sd_onemean,3),
" / ", round((sqrt(input$n_onemean)), 3), "\\( ) \\) ", "\\( = \\) ",
"[", round(IC[1], 3), "; ", round(IC[2], 3), "]"),
br(),
br(),
tags$b("Contraste de la hipótesis:"),
br(),
paste0("1. \\(H_0 : \\mu = \\) ", input$h0, " y \\(H_1 : \\mu \\) ", ifelse(input$Alternativa == "two.sided", "\\( \\neq \\) ", ifelse(input$Alternativa == "greater", "\\( > \\) ", "\\( < \\) ")), input$h0),
br(),
paste0(
"2. Estadístico de contraste : \\(T = \\dfrac{\\bar{X} - \\mu_x}{S_x / \\sqrt{n}} = \\) ",
"(", round(input$smean_onemean, 3), ifelse(input$h0 >= 0, paste0(" - ", input$h0), paste0(" + ", abs(input$h0))), ") / ", round((input$sd_onemean/sqrt(input$n_onemean)), 3),
" \\( = \\) ",
round((input$smean_onemean-(input$h0))/(input$sd_onemean/sqrt(input$n_onemean)), 3)),
br(),
paste0(
"3. Valor crítico :", ifelse(input$Alternativa == "two.sided", " \\( \\pm t_{\\alpha/2, n - 1} = \\pm t(\\)",
ifelse(input$Alternativa == "greater", " \\( t_{\\alpha, n - 1} = t(\\)", " \\( -t_{\\alpha, n - 1} = -t(\\)")),
ifelse(input$Alternativa == "two.sided", input$alpha / 2, input$alpha), ", ", input$n_onemean-1, "\\()\\)", " \\( = \\) ",
ifelse(input$Alternativa == "two.sided", "\\( \\pm \\)", ifelse(input$Alternativa == "greater", "", " -")),
ifelse(input$Alternativa == "two.sided", round(qt(input$alpha / 2, df = input$n_onemean-1, lower.tail = FALSE), 3), round(qt(input$alpha, df = input$n_onemean-1, lower.tail = FALSE), 3))
),
br(),
paste0("4. Conclusión/Decisión : ", ifelse(test$pvalor < input$alpha, "Rechazar \\(H_0\\)", "No rechazar \\(H_0\\)")),
br(),
br(),
tags$b("Interpretación"),
br(),
paste0("Considerando un nivel de significación del ", input$alpha * 100, "%",
ifelse(test$pvalor < input$alpha, " debemos rechazar la hipótesis nula que afirma que la verdadera media es ",
" NO debemos rechazar la hipótesis nula que afirma que la verdadera media es "),
input$h0, " \\((p\\)-value ",
ifelse(test$pvalor < 0.001, "< 0.001", paste0("\\(=\\) ", round(test$pvalor, 3))), ")", ".")
)
#Con la varianza poblacional
} else if (input$inference == "Una media" & input$inference2 == "Valores poblaciones y muestrales" & input$popsd_onemean2 == TRUE) {
IC <- t.testIC(mean = input$smean_onemean, sd = input$sd_onemean, n = input$n_onemean, alfa = input$alpha, varprob = input$sigma2_onemean)
test <- t.testv2(mean = input$smean_onemean, n = input$n_onemean, sd = input$sd_onemean, alternative = input$Alternativa, mu = input$h0, varprob = input$sigma2_onemean)
#test_confint <- t.test(x = dat, mu = input$h0, Alternativa = "two.sided", conf.level = 1 - input$alpha)
#test <- t.test(x = dat, mu = input$h0, Alternativa = input$Alternativa, conf.level = 1 - input$alpha)
withMathJax(
tags$b("Datos:"),
br(),
br(),
paste0("\\(n =\\) ", input$n_onemean),
br(),
paste0("\\(\\bar{X} =\\) ", input$smean_onemean),
br(),
paste0("\\(\\sigma =\\) ", round(sqrt(input$sigma2_onemean), 3)),
br(),
br(),
tags$b("Intervalo de confianza"),
tags$em("(Bilateral)"),
br(),
paste0(
"IC al ", (1 - input$alpha) * 100, " % para \\(\\mu = \\bar{X} \\pm z_{\\alpha/2} \\dfrac{\\sigma}{\\sqrt{n}} = \\) ",
input$smean_onemean, " \\( \\pm \\) ", "\\( ( \\)", round(qnorm(input$alpha / 2, mean = 0, sd=1, lower.tail = FALSE), 3),
" * ", round(sqrt(input$sigma2_onemean),3),
" / ", round((sqrt(input$n_onemean)), 3), "\\( ) \\) ", "\\( = \\) ",
"[", round(IC[1], 3), "; ", round(IC[2], 3), "]"),
br(),
br(),
tags$b("Contraste de la hipótesis:"),
br(),
paste0("1. \\(H_0 : \\mu = \\) ", input$h0, " y \\(H_1 : \\mu \\) ", ifelse(input$Alternativa == "two.sided", "\\( \\neq \\) ", ifelse(input$Alternativa == "greater", "\\( > \\) ", "\\( < \\) ")), input$h0),
br(),
paste0(
"2. Estadístico de contraste : \\(Z = \\dfrac{\\bar{X} - \\mu}{\\sigma / \\sqrt{n}} = \\) ",
"(", round(input$smean_onemean, 3), ifelse(input$h0 >= 0, paste0(" - ", input$h0), paste0(" + ", abs(input$h0))), ") / ",
round((sqrt(input$sigma2_onemean)/sqrt(input$n_onemean)), 3),
" \\( = \\) ",
round((input$smean_onemean-(input$h0))/(sqrt(input$sigma2_onemean)/sqrt(input$n_onemean)), 3)),
br(),
paste0(
"3. Valor crítico :", ifelse(input$Alternativa == "two.sided", " \\( \\pm z_{\\alpha/2} = \\pm z(\\)", ifelse(input$Alternativa == "greater", " \\( z_{\\alpha} = z(\\)", " \\( -z_{\\alpha} = -z(\\)")),
ifelse(input$Alternativa == "two.sided", input$alpha / 2, input$alpha), "\\()\\)", " \\( = \\) ",
ifelse(input$Alternativa == "two.sided", "\\( \\pm \\)", ifelse(input$Alternativa == "greater", "", " -")),
ifelse(input$Alternativa == "two.sided", round(qnorm(input$alpha / 2, lower.tail = FALSE), 3), round(qnorm(input$alpha, lower.tail = FALSE), 3))
),
br(),
paste0("4. Conclusión/Decisión : ", ifelse(test$pvalor < input$alpha, "Rechazar \\(H_0\\)", "No rechazar \\(H_0\\)")),
br(),
br(),
tags$b("Interpretación"),
br(),
paste0("Considerando un nivel de significación del ", input$alpha * 100, "%",
ifelse(test$pvalor < input$alpha, " debemos rechazar la hipótesis nula que afirma que la verdadera media es ",
" NO debemos rechazar la hipótesis nula que afirma que la verdadera media es "),
input$h0, " \\((p\\)-value ",
ifelse(test$pvalor < 0.001, "< 0.001", paste0("\\(=\\) ", round(test$pvalor, 3))), ")", ".")
)}
})
# ANALISIS DOS MEDIAS INDEPENDIENTES CON VALORES ---------------------------------
## Función ---------------------------------
t.2indemeans <- function(M1, M2, s1, s2, n1, n2, m0 = 0, alpha = 0.05, Alternativa = "two.sided", Varpob1, Varpob2, IgualVar = NULL, Varpob = "FALSE") {
varmuestral1 <- s1^2
varmuestral2 <- s2^2
ICInf <- c()
ICSup <- c()
estadistico <- c()
pvalor <- c()
v <- c()
## ASUMIENDO VARIANZAS NO IGUALES
if (IgualVar == "TRUE" & Varpob == "FALSE") {
sp <- sqrt((((n1 - 1) * varmuestral1 + (n2 - 1) * varmuestral2) / (n1 + n2 - 2)) * ((1/n1)+(1/n2)))
estadistico <- (M1 - M2 - m0) / sp
if (Alternativa == "two.sided") {
if (estadistico > 0) {
pvalor <- 2 * pt(estadistico, df = n1 + n2 - 2, lower.tail = FALSE)
} else {
pvalor <- 2 * pt(estadistico, df = n1 + n2 - 2, lower.tail = TRUE)
}
} else if (Alternativa == "less") {
pvalor <- pt(estadistico, df = n1 + n2 - 2, lower.tail = TRUE)