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#              EXEMPLO AULA 21 - Pratica de teste de hipotes                  #
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rm(list = ls()); cat('\014')

setwd(dirname(rstudioapi::getActiveDocumentContext()$path))

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dados = read.table("Dados_ALAT.csv", sep = ",", header = T)
head(dados)


x = dados[, 1]
y = dados[, 2]


######################################
# Abordagem usando teste de hipóteses


# (a) Teste considerando amostras independentes
t.test(x, y)

# valor-p<0.05 Há diferências


# (b) Teste considerando amostras pareadas
D = y - x
XD = mean(D)
SD = sd(D)

t.test(y, x, mu = 0, paired = TRUE)
t.test(D)

# Ambos resultados são equivalentes e mostram
# que há diferências nos métodos



###############################
# Abordagem usando correlação

cor.test(x, y)
plot(x, y)

sxy = cov(x,y)
sx = sd(x)
sy = sd(y)
xbarra = mean(x)
ybarra = mean(y)
conc = 2*sxy/(sx^2 + sy^2 + (xbarra - ybarra)^2)
conc



#################################################
# Terceira abordagem (Analise de regressão linear)

output = lm(y ~ x)
summary(output)