Capítulo 9 Práctica 5
9.2 Intervalo de cofianza
\(X /leadsto N(/mu, /sigma)\) \(/mu: /overline{X} /pm z_{/alpha/2} /cdot /frac{/alpha}{/sqrt{n}}\)
alpha<- .05 # nivel de confianza
fsd <- 18 # sd
n <- nrow(Framingham) # tamaño muestral
media <- mean(Framingham$FRW, na.rm = T)
cuantil <- qnorm(1-alpha/2) # valor tipificada a ña normal que deja a la dcha alpha
# calcular intervalo de confianza para esa población
lim_inf <- round(media - cuantil*fsd/sqrt(n), 3)
lim_sup <- round(media + cuantil*fsd/sqrt(n), 3)
# Nurstro intervalo de confianza para la media de población:
# el 95% de las veces acierto (va a contener el verdadero valor del parámetro)
c(lim_inf, lim_sup)## [1] 104.518 106.4009.3 Desviación T-destudent
# cuasi desviaión típica
# a mayor n, t se acerca a distribución normal
## RCMDR
# with(Framingham, (t.test(FRW,
# Rcmdr+ alternative='two.sided', mu=0.0, conf.level=.95)))
## RCMDR LOG
# data: FRW
# t = 220.06, df = 1394, p-value < 2.2e-16
# alternative hypothesis: true mean is not equal to 0
# 95 percent confidence interval:
# 104.5187 106.3989
# sample estimates:
# mean of x
# 105.4588 9.3.1 Ej.: Intervalo de confianza en DBP
alpha<- .01 # nivel de confianza
fsd <- sqrt(200) # sd
n <- nrow(Framingham) # tamaño muestral
media <- mean(Framingham$DBP, na.rm = T)
cuantil <- qnorm(1-alpha/2)
lim_inf <- round(media - cuantil*fsd/sqrt(n), 3)
lim_sup <- round(media + cuantil*fsd/sqrt(n), 3)
c(lim_inf, lim_sup)## [1] 89.176 91.1199.4 ej 2
## RCMDR
# Rcmdr> with(Framingham, (t.test(DBP,
# Rcmdr+ alternative='two.sided', mu=0.0, conf.level=.95)))
## RCMDR LOG
# One Sample t-test
#
# data: DBP
# t = 237.85, df = 1405, p-value < 2.2e-16
# alternative hypothesis: true mean is not equal to 0
# 95 percent confidence interval:
# 89.40444 90.89144
# sample estimates:
# mean of x
# 90.14794 9.5 Test de proporciones para una muestra
# Esta>prop>Test 1 muestra [hip p = .5]
# Frequency counts (test is for first level):
# SEX
# Hombre Mujer
# 669 737
# 1-sample proportions test without continuity
# correction
# data: rbind(.Table), null probability 0.5
# X-squared = 3.2888, df = 1, p-value = 0.06976
# alternative hypothesis: true p is not equal to 0.5
# 95 percent confidence interval:
# 0.4498147 0.5019529
# sample estimates:
# p
# 0.4758179 9.5.1 ej.: CHOL2
# Esta>prop>Test 1 muestra [xonf = .5]
# RCMDR OUTPUT
# Frequency counts (test is for first level):
# CHOL2
# Hipercolesterolemia Normocolesterolemia
# 1081 325
#
# 1-sample proportions test without continuity
# correction
#
# data: rbind(.Table), null probability 0.5
# X-squared = 406.5, df = 1, p-value < 2.2e-16
# alternative hypothesis: true p is not equal to 0.5
# 90 percent confidence interval:
# 0.7498492 0.7868137
# sample estimates:
# p
# 0.7688478 9.6 ej.: Calcular para hipercolesterolemia (hay que reordenar)
# datos>modificar>reordernar niveles
# Rcmdr> local({
# Rcmdr+ .Table <- xtabs(~ CHOL2 , data= Framingham )
# Rcmdr+
# Rcmdr+ cat("/nFrequency counts (test is for first level):/n")
# Rcmdr+ print(.Table)
# Rcmdr+ prop.test(rbind(.Table), alternative='two.sided',
# Rcmdr+ p=.5, conf.level=.90, correct=FALSE)
# Rcmdr+ })
#
# Frequency counts (test is for first level):
# CHOL2
# Normocolesterolemia Hipercolesterolemia
# 325 1081
#
# 1-sample proportions test without continuity
# correction
#
# data: rbind(.Table), null probability 0.5
# X-squared = 406.5, df = 1, p-value < 2.2e-16
# alternative hypothesis: true p is not equal to 0.5
# 90 percent confidence interval:
# 0.2131863 0.2501508
# sample estimates:
# p
# 0.2311522 9.7 Salimos y guardamos
Al no cerrar la consola, el paquete Rcmdr (la GUI) sigue cargado, por lo que simplemente tenemos que llamar a Commander() para crear una nueva ventana.
Commander()9.8 Muesta
Dist>continua>normal>muestra de normal
# Rcmdr> Normal01 <- as.data.frame(matrix(rnorm(100*30,
# Rcmdr+ mean=75, sd=11), ncol=30))
#
# Rcmdr> rownames(Normal01) <- paste("sample", 1:100, sep="")
#
# Rcmdr> colnames(Normal01) <- paste("obs", 1:30, sep="")
#
# Rcmdr> Normal01 <- within(Normal01, {
# Rcmdr+ mean <- rowMeans(Normal01[,1:30])
# Rcmdr+ sd <- apply(Normal01[,1:30], 1, sd)
# Rcmdr+ })
# RcmdrMsg: [3] NOTA: El conjunto de datos Normal01 tiene 100
# RcmdrMsg+ filas y 32 columnas.9.9 Representación gráfica
graf>hist [mean]
# Rcmdr> with(Normal01, Hist(mean, scale="frequency",
# Rcmdr+ breaks="Sturges", col="darkgray"))9.10 Resumir
Estadisticos>resumen>resumen numerico
# Rcmdr> with(Normal01, Hist(mean, scale="frequency",
# Rcmdr+ breaks="Sturges", col="darkgray"))
#
# Rcmdr> library(abind, pos=17)
#
# Rcmdr> library(e1071, pos=18)
#
# Rcmdr> numSummary(Normal01[,"mean", drop=FALSE],
# Rcmdr+ statistics=c("mean", "sd", "IQR", "quantiles"),
# Rcmdr+ quantiles=c(0,.25,.5,.75,1))
# mean sd IQR 0% 25% 50%
# 75.11098 2.175502 2.358741 70.63716 73.76057 75.05243
# 75% 100% n
# 76.11931 80.66785 1009.11 Reutiliza codigo
alpha<- .05 # nivel de confianza
fsd <- 11 # sd
n <- ncol(Normal01) - 2 # tamaño muestral (75)
# ^ filas de mean y sd
cuantil <- qnorm(1-alpha/2) # valor tipificada a ña normal que deja a la dcha alpha
# calcular intervalo de confianza para esa población
Normal01$lim_inf <- round(Normal01$mean - cuantil*fsd/sqrt(n), 3)
Normal01$lim_sup <- round(Normal01$mean + cuantil*fsd/sqrt(n), 3)9.12 Amplitud de intervalos
diferencia entre límite superior e inferior
Normal01$diff <- Normal01$lim_sup-Normal01$lim_inf9.14 Comparamos datos
Estadistico > resumen numericos [mean]
# Rcmdr> numSummary(Normal02[,"mean", drop=FALSE],
# Rcmdr+ statistics=c("mean", "sd", "IQR", "quantiles"),
# Rcmdr+ quantiles=c(0,.25,.5,.75,1))
# mean sd IQR 0% 25% 50%
# 75.01775 0.3668131 0.5178061 74.12818 74.77113 75.01862
# 75% 100% n
# 75.28894 75.88728 100
n2 <- ncol(Normal02)-2
Normal02$lim_inf <- round(Normal02$mean - cuantil*fsd/sqrt(n2), 3)
Normal02$lim_sup <- round(Normal02$mean + cuantil*fsd/sqrt(n2), 3)