df <- read.csv("dataset1.csv")
x <- df$Height[df$Group == "Treatment"]
y <- df$Height[df$Group == "Control"]

ftest <- var.test(x, y)   # F-test for equality of variances (reported for reference)
ftest

alpha <- 0.05

# --- Unpaired / independent groups (default) ---
mwtest <- wilcox.test(x, y,
                      alternative = "two.sided",   # or "less", "greater"
                      conf.int    = TRUE,
                      conf.level  = 1 - alpha,      # default 95%
                      paired      = FALSE,
                      exact       = FALSE)          # normal approximation
mwtest

# reported quantities
mean(x); mean(y)                                    # group means
median(x); median(y)                                # group medians
IQR(x); IQR(y)                                       # group interquartile ranges
mwtest$statistic                                     # W (U) statistic
mwtest$p.value                                       # p-value
mwtest$conf.int                                      # Hodges-Lehmann confidence interval
mwtest$estimate                                      # Hodges-Lehmann location-shift estimate

# --- Paired design (paired = TRUE) ---
# x[i] and y[i] are the two measurements on the same unit; this runs the
# Wilcoxon signed-rank test on the paired differences and the statistic is
# reported as "V value" in the app
wilcox.test(x, y,
            alternative = "two.sided",
            conf.level  = 1 - alpha,
            paired      = TRUE,
            exact       = FALSE)

vars <- c("Height", "Weight", "Yield")
digits <- 3

result_rows <- do.call(rbind, lapply(vars, function(v) {
  x <- df[df$Group == "Treatment", v]
  y <- df[df$Group == "Control",   v]
  wt <- wilcox.test(x, y, alternative = "two.sided",
                     conf.int = TRUE, conf.level = 0.95,
                     paired = FALSE, exact = FALSE)
  data.frame(
    Variable   = v,
    Mean_Trt   = round(mean(x), digits),
    Mean_Ctrl  = round(mean(y), digits),
    W_value    = round(unname(wt$statistic), digits),
    p_value    = format.pval(wt$p.value, digits = 4, eps = 1e-4)
  )
}))
result_rows
# Expected: Height W=225 p<0.0001 ; Weight W=225 p<0.0001 ; Yield W=225 p<0.0001