APG-4.r

# uji satu sampel
ujiSatuSampel <- function(data_1, miu, sigma = NULL, alpha = 0.05){
  X_bar = apply(data_1, 2, mean)
  n = nrow(data_1)
  p = ncol(data_1)
  
  hasSigma = !is.null(sigma)
  
  if(length(miu) != p) stop("data tidak sama")
  
  if (!hasSigma) sigma = cov(data_1)
  
  stat = n*(t(X_bar - miu)%*%solve(sigma)%*%(X_bar - miu))
  
  if (hasSigma) {
    criticalPoint = qchisq((1-alpha), p)
  } else {
    stat = ((n-p)/(p*(n-1)))*stat
    criticalPoint = qf((1-alpha),p,n-p)
  }
  
  cat("\nStatistics : ", stat)
  cat("\nCritical   : ", criticalPoint)
  
  if (stat >= criticalPoint) {
    cat("\n::Reject null hyphothesis with alpha",alpha)
  } else {
    cat("\n::Failed to reject null hyphothesis with alpha",alpha)
  }
}

# uji dua sampel independet
ujiDuaSampel <- function(data_1, data_2, alpha = 0.05, isSigmaEqual = TRUE){
  if(ncol(data_1) != ncol(data_2)) stop("number of column different")
  
  p = ncol(data_1)
  n_1 = nrow(data_1)
  n_2 = nrow(data_2)
  X_bar_1 = apply(data_1, 2, mean)
  X_bar_2 = apply(data_2, 2, mean)
  
  # asumsi varians sama
  sig_1 = cov(data_1)
  sig_2 = cov(data_2)
  
  if(isSigmaEqual){
    cat("Asumsi varians sama")
    S_pool = ((n_1 - 1)*sig_1 + (n_2 - 1) *sig_2)/(n_1 + n_2 - 2)
    stats = ((n_1 * n_2) / (n_1 + n_2))* (t(X_bar_1 - X_bar_2)%*%solve(S_pool)%*%(X_bar_1 - X_bar_2))
  } else {
    cat("Asumsi varians tidak sama")
    S_pool = sig_1 / n_1 + sig_2 / n_2
    stats = (t(X_bar_1 - X_bar_2)%*%solve(S_pool)%*%(X_bar_1 - X_bar_2))
  }
  
  # convert to F
  stats = ((n_1+n_2-p-1)/((n_1+n_2-2)*p))*stats
  criticalPoint = qf((1-alpha),p,n_1+n_2-p-1)
  
  cat("\nStatistics   : ", stats)
  cat("\nCritical (F) : ", criticalPoint)
  
  if (stats >= criticalPoint) {
    cat("\n::Reject null hyphothesis with alpha",alpha)
  } else {
    cat("\n::Failed to reject null hyphothesis with alpha",alpha)
  }
}

# uji dua sampel dependent
ujiDuaSampelDependen <- function(data_1, data_2, alpha = 0.05){
  data = data_1 - data_2
  n = nrow(data)
  p = ncol(data)
  avg = apply(data_1 - data_2, 2, mean)
  S_d = cov(data)
  
  T_squre = n*t(avg)%*%solve(S_d)%*%avg
  F_obs = ((n-p)/(p*(n-1)))*T_squre
  criticalPoint = qf((1-alpha),p,n-p)
  
  cat("\nF obs    : ", F_obs)
  cat("\nCritical : ", criticalPoint)
  
  if (F_obs >= criticalPoint) {
    cat("\n::Reject null hyphothesis with alpha",alpha)
  } else {
    cat("\n::Failed to reject null hyphothesis with alpha",alpha)
  }
}

# versi gabungan simpel
ujiSampel <- function(data_1, data_2 = NULL, miu = NULL, sigma = NULL, alpha = 0.05, type = "independent", isSigmaEqual = TRUE){
  
  if(!is.null(data_2) && type == "independent"){
    cat("\n2 populasi test independent")
    return(ujiDuaSampel(data_1, data_2, alpha = alpha, isSigmaEqual = isSigmaEqual))
  }
  
  if(!is.null(data_2) && type == "dependent"){
    cat("\n2 populasi test dependent")
    return(ujiDuaSampelDependen(data_1, data_2, alpha))
  }
  
  if(is.null(data_2)){
    cat("\n1 populasi test")
    return(ujiSatuSampel(data_1, miu, sigma, alpha))
  }
  return(NULL)
}


ujiDuaSampelModified <- function(sd_1, r_1, X_bar_1, n_1, sd_2, r_2, X_bar_2, n_2, p, alpha = 0.05, isSigmaEqual = TRUE){  
  sig_1 = diag(sd_1) %*% r_1 %*% diag (sd_1)
  cat(sig_1)
  sig_2 = diag(sd_2) %*% r_2 %*% diag (sd_2)
  if(isSigmaEqual){    
    cat("\nAsumsi varians sama\n")    
    S_pool = ((n_1 - 1)*sig_1 + (n_2 - 1)*sig_2)/(n_1 + n_2 - 2)    
    stats = (t(X_bar_1 - X_bar_2)%*%solve(S_pool)%*%(X_bar_1 - X_bar_2))    
    stats = ((n_1 * n_2) / (n_1 + n_2))*stats  
  } else {    
    cat("\nAsumsi varians tidak sama\n")    
    S_pool = sig_1 / n_1 + sig_2 / n_2    
    stats = (t(X_bar_1 - X_bar_2)%*%solve(S_pool)%*%(X_bar_1 - X_bar_2))  
  } 
  # convert to F  
  stats = ((n_1+n_2-p-1)/((n_1+n_2-2)*p))*stats  
  criticalPoint = qf((1-alpha),p,n_1+n_2-p-1)  
  cat("\nF obs        : ", stats)  
  cat("\nCritical (F) : ", criticalPoint)  
  if (stats >= criticalPoint) {    
    cat("\n::Reject null hyphothesis with alpha",alpha)  
  } else {    
    cat("\n::Failed to reject null hyphothesis with alpha",alpha)  
  }
}


plotKontur <- function(data, x = NaN, alpha = 0.05){
  if (is.matrix(data) && ncol(data) != 2) stop("matrix bukan bivariat")
  if (is.data.frame(data) && length(data) != 2) stop("data bukan bivariat")
  library(mixtools)
  plot(data, xlab = "X1", ylab = "X2")
  miu = apply(data, 2, mean)
  sigma = cov(data)
  ellipse(miu, sigma, alpha, col = "red")
  if(!is.na(x) && length(x) == 2){
    points(x[1], x[2], pch=19, cex=1, col="blue")
  }
}

p = 3

n_1 = 20
r_1 = matrix(c(1.00, 0.79,  0.84,
               0.79, 1.00,  0.84,
               0.84, 0.84,  1.00), nrow =3)
sd_1 = c(31.30, 18.86, 19.12)
Y_1 = c(1433.52, 860.22, 2478.05)

n_2 = 20
r_2 = matrix(c(1.00, 0.54, 0.57,
               0.79, 1.00, 0.78,
               0.84, 0.78, 1.00), nrow = 3)

sd_2 = c(28.60, 18.87, 28.77)
Y_2 = c(1217.16, 691.04, 2394.62)
ujiDuaSampelModified(sd_1, r_1, Y_1, n_1, sd_2, r_2, Y_2, n_2, p)