differenzaresa = c(106, -20, 101, -33, 72, -36, 62, 38, -70, 127, 24)
mean(differenzaresa)



t.test(differenzaresa)$estimate	
t.test(differenzaresa)$null.value	




(mean(differenzaresa) - 0) /(sd(differenzaresa)/sqrt(11))
t.test(differenzaresa)$statistic









par(mfrow = c(1,2))
x = seq(from = -2.5, to = 2.5, by = .01)
y = dnorm(x)
plot(x, y,  "l", ylim = c(0, 0.4), main = "distribuzione normale", lty = 2)
tright = seq(1.690476, 3,  by = 0.01)
yright = dnorm(tright)
xx = c(1.690476, tright, 3, 3, 1.690476 )
yy = c(0, yright, dnorm(3),0, 0)
polygon(xx, yy, col = "violet", density = 20, angle = -60)
points(1.690476, 0, pch =19)
text(1.6, 0, "1.69", 1)
tleft = seq( -3, -1.690476, by = 0.01)
yleft = dnorm(tleft)
xx = c(-3, tleft, -1.690476, -1.690476, -3 )
yy = c(0, yleft, dnorm(-1.690476),0, 0)
polygon(xx, yy, col = "violet", density = 20, angle = -60)
points(-1.690476, 0, pch =19)
text(-1.4, 0, "-1.69")
x = seq(from = -2.5, to = 2.5, by = .01)
y = dnorm(x)
plot(x, y,  "l", ylim = c(0, 0.4), main = "distribuzione t di Student", lty = 2)
yt = dt(x, df = 10)
lines(x, yt, lwd = 2, col = "orange")
tright = seq(1.690476, 3,  by = 0.01)
yright = dt(tright, df = 10)
xx = c(1.690476, tright, 3, 3, 1.690476 )
yy = c(0, yright, dt(3, df = 10),0, 0)
polygon(xx, yy, col = "orange", density = 20, angle = -30)
points(1.690476, 0, pch =19)
text(1.6, 0, "1.69", 1)
tleft = seq( -3, -1.690476, by = 0.01)
yleft = dt(tleft, df = 10)
xx = c(-3, tleft, -1.690476, -1.690476, -3 )
yy = c(0, yleft, dt(-1.690476, df = 10),0, 0)
polygon(xx, yy, col = "orange", density = 20, angle = -30)
points(-1.690476, 0, pch =19)
text(-1.4, 0, "-1.69")






2 * (1 -  pnorm(1.690476))  ## 0.09



length(differenzaresa) - length(mean(differenzaresa))
t.test(differenzaresa)$parameter




2 * (1 -  pt(q = 1.690476, df = 10))
t.test(differenzaresa)$p.value	



##  raul = read.csv(file.choose(), header = TRUE)
www = "http://www.biostatisticaumg.it/dataset/raul.csv"
raul = read.csv(www, header = TRUE)
attach(raul)
names(raul)
table(Esito)

2018/2
1278/2

verde = split(Ca125, Esito)[[1]]
rosso = split(Ca125, Esito)[[2]]
t.test(verde, rosso)


###t.test(Ca125[Esito == "benigno"], Ca125[Esito == "maligno"], var.equal = TRUE)


t.test(Ca125[Esito == "benigno"], Ca125[Esito == "maligno"])
t.test(Ca125 ~ Esito)


verde = split(Ca125, Esito)[[1]]
rosso = split(Ca125, Esito)[[2]]
boxplot(verde, rosso, col = c("green", "red"), horizontal = TRUE)

summary(verde)
summary(rosso)


boxplot(verde, rosso, col = c("green", "red"), horizontal = TRUE)
quantile(rosso, .2)
quantile(verde, .9)


sum(rosso < 28)
sum(rosso < 16)
sort(rosso)
sum(rosso > 100)





cov(Ldhuno, Ldhtre)
cor(Ldhuno, Ldhtre)



attach(airquality)
cor(Temp, Ozone)
cor(Temp, Ozone, use = "complete.obs")

lm(Ldhtre ~ Ldhuno)





-0.223 * sd(Ldhuno) / sd(Ldhtre)
cor(Ldhuno, Ldhtre) 



summary(lm(Ldhtre ~ Ldhuno))
summary(lm(Ldhtre ~ Ldhuno * Esito))