url <- "https://raw.githubusercontent.com/jbrownlee/Datasets/master/pima-indians-diabetes.data.csv"
data <- read.csv(url)
summary(data)## X6 X148 X72 X35
## Min. : 0.000 Min. : 0.0 Min. : 0.0 Min. : 0.00
## 1st Qu.: 1.000 1st Qu.: 99.0 1st Qu.: 62.0 1st Qu.: 0.00
## Median : 3.000 Median :117.0 Median : 72.0 Median :23.00
## Mean : 3.842 Mean :120.9 Mean : 69.1 Mean :20.52
## 3rd Qu.: 6.000 3rd Qu.:140.0 3rd Qu.: 80.0 3rd Qu.:32.00
## Max. :17.000 Max. :199.0 Max. :122.0 Max. :99.00
## X0 X33.6 X0.627 X50
## Min. : 0.0 Min. : 0.00 Min. :0.0780 Min. :21.00
## 1st Qu.: 0.0 1st Qu.:27.30 1st Qu.:0.2435 1st Qu.:24.00
## Median : 32.0 Median :32.00 Median :0.3710 Median :29.00
## Mean : 79.9 Mean :31.99 Mean :0.4717 Mean :33.22
## 3rd Qu.:127.5 3rd Qu.:36.60 3rd Qu.:0.6250 3rd Qu.:41.00
## Max. :846.0 Max. :67.10 Max. :2.4200 Max. :81.00
## X1
## Min. :0.0000
## 1st Qu.:0.0000
## Median :0.0000
## Mean :0.3481
## 3rd Qu.:1.0000
## Max. :1.0000print(data)## X6 X148 X72 X35 X0 X33.6 X0.627 X50 X1
## 1 1 85 66 29 0 26.6 0.351 31 0
## 2 8 183 64 0 0 23.3 0.672 32 1
## 3 1 89 66 23 94 28.1 0.167 21 0
## 4 0 137 40 35 168 43.1 2.288 33 1
## 5 5 116 74 0 0 25.6 0.201 30 0
## 6 3 78 50 32 88 31.0 0.248 26 1
## 7 10 115 0 0 0 35.3 0.134 29 0
## 8 2 197 70 45 543 30.5 0.158 53 1
## 9 8 125 96 0 0 0.0 0.232 54 1
## 10 4 110 92 0 0 37.6 0.191 30 0
## 11 10 168 74 0 0 38.0 0.537 34 1
## 12 10 139 80 0 0 27.1 1.441 57 0
## 13 1 189 60 23 846 30.1 0.398 59 1
## 14 5 166 72 19 175 25.8 0.587 51 1
## 15 7 100 0 0 0 30.0 0.484 32 1
## 16 0 118 84 47 230 45.8 0.551 31 1
## 17 7 107 74 0 0 29.6 0.254 31 1
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## 25 10 125 70 26 115 31.1 0.205 41 1
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## 29 5 117 92 0 0 34.1 0.337 38 0
## 30 5 109 75 26 0 36.0 0.546 60 0
## 31 3 158 76 36 245 31.6 0.851 28 1
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## 37 9 102 76 37 0 32.9 0.665 46 1
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## 49 7 105 0 0 0 0.0 0.305 24 0
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## 56 7 187 68 39 304 37.7 0.254 41 1
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## 758 1 106 76 0 0 37.5 0.197 26 0
## 759 6 190 92 0 0 35.5 0.278 66 1
## 760 2 88 58 26 16 28.4 0.766 22 0
## 761 9 170 74 31 0 44.0 0.403 43 1
## 762 9 89 62 0 0 22.5 0.142 33 0
## 763 10 101 76 48 180 32.9 0.171 63 0
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## 765 5 121 72 23 112 26.2 0.245 30 0
## 766 1 126 60 0 0 30.1 0.349 47 1
## 767 1 93 70 31 0 30.4 0.315 23 0Se plantea una hipótesis para comparar los niveles de glucosa entre personas con y sin diabetes. Mediante una prueba t de muestras independientes se encontró una diferencia significativa entre ambos grupos (p < 0.05), lo que indica que los niveles promedio de glucosa son distintos según la condición de diabetes.
# Asignar nombres de columnas
colnames(data) <- c("Pregnancies", "Glucose", "BloodPressure", "SkinThickness",
"Insulin", "BMI", "DiabetesPedigreeFunction", "Age", "Outcome")
# Verificar estructura
str(data)## 'data.frame': 767 obs. of 9 variables:
## $ Pregnancies : int 1 8 1 0 5 3 10 2 8 4 ...
## $ Glucose : int 85 183 89 137 116 78 115 197 125 110 ...
## $ BloodPressure : int 66 64 66 40 74 50 0 70 96 92 ...
## $ SkinThickness : int 29 0 23 35 0 32 0 45 0 0 ...
## $ Insulin : int 0 0 94 168 0 88 0 543 0 0 ...
## $ BMI : num 26.6 23.3 28.1 43.1 25.6 31 35.3 30.5 0 37.6 ...
## $ DiabetesPedigreeFunction: num 0.351 0.672 0.167 2.288 0.201 ...
## $ Age : int 31 32 21 33 30 26 29 53 54 30 ...
## $ Outcome : int 0 1 0 1 0 1 0 1 1 0 ...# Dividir en dos grupos: con diabetes y sin diabetes
diabetes_yes <- subset(data, Outcome == 1)
diabetes_not <- subset(data, Outcome == 0)
# Prueba de hipótesis: comparar la media de glucosa entre los grupos
test_ <- t.test(diabetes_yes$Glucose, diabetes_not$Glucose,
alternative = "two.sided", conf.level = 0.95)
# Mostrar el resultado del test
print(test_)##
## Welch Two Sample t-test
##
## data: diabetes_yes$Glucose and diabetes_not$Glucose
## t = 13.703, df = 458.37, p-value < 2.2e-16
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## 26.77046 35.73396
## sample estimates:
## mean of x mean of y
## 141.2322 109.9800Puesto que los valores de P en ambos casos son mucho menores que
0.05, se rechaza la hipótesis nula de normalidad.
Por tanto, la variable GLUCOSE no sigue una distribución normal en
ninguno de los dos grupos.
datos_glucosa <- data[, c("Glucose", "Outcome")]
# Crear los dos grupos
grupo_0 <- datos_glucosa$Glucose[datos_glucosa$Outcome == 0]
grupo_1 <- datos_glucosa$Glucose[datos_glucosa$Outcome == 1]
# Prueba de Shapiro-Wilk
cat("\nNormalidad para el grupo SIN diabetes (Outcome = 0):\n")##
## Normalidad para el grupo SIN diabetes (Outcome = 0):print(shapiro.test(grupo_0))##
## Shapiro-Wilk normality test
##
## data: grupo_0
## W = 0.96795, p-value = 5.447e-09cat("\nNormalidad para el grupo CON diabetes (Outcome = 1):\n")##
## Normalidad para el grupo CON diabetes (Outcome = 1):print(shapiro.test(grupo_1))##
## Shapiro-Wilk normality test
##
## data: grupo_1
## W = 0.95852, p-value = 6.323e-07En los dos grupos (con y sin diabetes), se observa una correlación positiva moderada entre Glucose y Insulin, lo cual sugiere que a mayor nivel de glucosa, tiende a haber mayor nivel de insulina. Sin embargo, esta relación es más fuerte en el grupo con diabetes. Además, variables como BMI y SkinThickness también presentan correlaciones moderadas, especialmente en el grupo con diabetes. Estas asociaciones pueden indicar patrones metabólicos alterados en personas con diabetes.
# Seleccionar variables numéricas
variables <- c("Glucose", "BloodPressure", "SkinThickness", "Insulin", "BMI",
"DiabetesPedigreeFunction", "Age")
# Correlación para grupo sin diabetes (Outcome = 0)
cat("\n--- Correlación (Pearson) para grupo SIN diabetes (Outcome = 0) ---\n")##
## --- Correlación (Pearson) para grupo SIN diabetes (Outcome = 0) ---grupo_0 <- data[data$Outcome == 0, variables]
cor_0 <- cor(grupo_0, use = "complete.obs", method = "pearson")
print(cor_0)## Glucose BloodPressure SkinThickness Insulin
## Glucose 1.00000000 0.19279456 0.01601513 0.35295698
## BloodPressure 0.19279456 1.00000000 0.18707162 0.07462648
## SkinThickness 0.01601513 0.18707162 1.00000000 0.41278982
## Insulin 0.35295698 0.07462648 0.41278982 1.00000000
## BMI 0.13174900 0.36317809 0.43860594 0.25420153
## DiabetesPedigreeFunction 0.09554795 0.02729154 0.09518116 0.22738532
## Age 0.22801775 0.21469388 -0.16378832 -0.14923353
## BMI DiabetesPedigreeFunction Age
## Glucose 0.13174900 0.09554795 0.22801775
## BloodPressure 0.36317809 0.02729154 0.21469388
## SkinThickness 0.43860594 0.09518116 -0.16378832
## Insulin 0.25420153 0.22738532 -0.14923353
## BMI 1.00000000 0.07066436 0.03606979
## DiabetesPedigreeFunction 0.07066436 1.00000000 0.04166504
## Age 0.03606979 0.04166504 1.00000000# Correlación para grupo con diabetes (Outcome = 1)
cat("\n--- Correlación (Pearson) para grupo CON diabetes (Outcome = 1) ---\n")##
## --- Correlación (Pearson) para grupo CON diabetes (Outcome = 1) ---grupo_1 <- data[data$Outcome == 1, variables]
cor_1 <- cor(grupo_1, use = "complete.obs", method = "pearson")
print(cor_1)## Glucose BloodPressure SkinThickness Insulin
## Glucose 1.00000000 0.06866161 0.03708161 0.26222185
## BloodPressure 0.06866161 1.00000000 0.22532254 0.08960419
## SkinThickness 0.03708161 0.22532254 1.00000000 0.45943977
## Insulin 0.26222185 0.08960419 0.45943977 1.00000000
## BMI 0.05059491 0.13400675 0.31297470 0.05459284
## DiabetesPedigreeFunction 0.02631528 0.03448306 0.27363213 0.10223248
## Age 0.09789354 0.26313184 -0.09557467 0.02724892
## BMI DiabetesPedigreeFunction Age
## Glucose 0.05059491 0.02631528 0.09789354
## BloodPressure 0.13400675 0.03448306 0.26313184
## SkinThickness 0.31297470 0.27363213 -0.09557467
## Insulin 0.05459284 0.10223248 0.02724892
## BMI 1.00000000 0.13694708 -0.18757696
## DiabetesPedigreeFunction 0.13694708 1.00000000 -0.08927011
## Age -0.18757696 -0.08927011 1.00000000Dado que los datos no cumplían con los supuestos de normalidad en ninguno de los grupos, se decidió utilizar la prueba no paramétrica de Wilcoxon para comparar las diferencias entre ambos grupos de manera más adecuada. Los resultados mostraron una diferencia altamente significativa en los niveles de glucosa entre los grupos, lo que indica que esta variable varía notablemente según o con respecto al Outcome.
# Aplicar la prueba estadística correctamente
for (var in variables) {
cat("\n=== Análisis de variable:", var, "===\n")
grupo_0 <- data[data$Outcome == 0, var]
grupo_1 <- data[data$Outcome == 1, var]
# Validar normalidad con Shapiro-Wilk
p_norm_0 <- shapiro.test(grupo_0)$p.value
p_norm_1 <- shapiro.test(grupo_1)$p.value
cat(sprintf("p normalidad (Outcome=0): %.4f | p normalidad (Outcome=1): %.4f\n", p_norm_0, p_norm_1))
# Elegir prueba según normalidad
if (p_norm_0 > 0.05 & p_norm_1 > 0.05) {
cat("=> Usando t-test (ambos normales)\n")
prueba <- t.test(grupo_0, grupo_1, var.equal = FALSE)
} else {
cat("=> Usando Wilcoxon test (alguno NO normal)\n")
prueba <- wilcox.test(grupo_0, grupo_1)
}
# Mostrar resultados
print(prueba)}##
## === Análisis de variable: Glucose ===
## p normalidad (Outcome=0): 0.0000 | p normalidad (Outcome=1): 0.0000
## => Usando Wilcoxon test (alguno NO normal)
##
## Wilcoxon rank sum test with continuity correction
##
## data: grupo_0 and grupo_1
## W = 28353, p-value < 2.2e-16
## alternative hypothesis: true location shift is not equal to 0
##
##
## === Análisis de variable: BloodPressure ===
## p normalidad (Outcome=0): 0.0000 | p normalidad (Outcome=1): 0.0000
## => Usando Wilcoxon test (alguno NO normal)
##
## Wilcoxon rank sum test with continuity correction
##
## data: grupo_0 and grupo_1
## W = 55195, p-value = 7.568e-05
## alternative hypothesis: true location shift is not equal to 0
##
##
## === Análisis de variable: SkinThickness ===
## p normalidad (Outcome=0): 0.0000 | p normalidad (Outcome=1): 0.0000
## => Usando Wilcoxon test (alguno NO normal)
##
## Wilcoxon rank sum test with continuity correction
##
## data: grupo_0 and grupo_1
## W = 59734, p-value = 0.015
## alternative hypothesis: true location shift is not equal to 0
##
##
## === Análisis de variable: Insulin ===
## p normalidad (Outcome=0): 0.0000 | p normalidad (Outcome=1): 0.0000
## => Usando Wilcoxon test (alguno NO normal)
##
## Wilcoxon rank sum test with continuity correction
##
## data: grupo_0 and grupo_1
## W = 61545, p-value = 0.05837
## alternative hypothesis: true location shift is not equal to 0
##
##
## === Análisis de variable: BMI ===
## p normalidad (Outcome=0): 0.0000 | p normalidad (Outcome=1): 0.0000
## => Usando Wilcoxon test (alguno NO normal)
##
## Wilcoxon rank sum test with continuity correction
##
## data: grupo_0 and grupo_1
## W = 41701, p-value < 2.2e-16
## alternative hypothesis: true location shift is not equal to 0
##
##
## === Análisis de variable: DiabetesPedigreeFunction ===
## p normalidad (Outcome=0): 0.0000 | p normalidad (Outcome=1): 0.0000
## => Usando Wilcoxon test (alguno NO normal)
##
## Wilcoxon rank sum test with continuity correction
##
## data: grupo_0 and grupo_1
## W = 52670, p-value = 1.459e-06
## alternative hypothesis: true location shift is not equal to 0
##
##
## === Análisis de variable: Age ===
## p normalidad (Outcome=0): 0.0000 | p normalidad (Outcome=1): 0.0000
## => Usando Wilcoxon test (alguno NO normal)
##
## Wilcoxon rank sum test with continuity correction
##
## data: grupo_0 and grupo_1
## W = 41906, p-value < 2.2e-16
## alternative hypothesis: true location shift is not equal to 0