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+#' One-way ANOVA (from scratch)
+#'
+#' @description
+#' Computes a one-way Analysis of Variance (ANOVA) to test whether k group means
+#' are equal. Implements sums of squares, F statistic, and p-value without using \code{aov()}.
+#'
+#' @param x Numeric vector of observations.
+#' @param g Factor or character vector of group labels (same length as \code{x}).
+#'
+#' @return A list with:
+#' \item{df_between}{Degrees of freedom between groups (k - 1).}
+#' \item{df_within}{Degrees of freedom within groups (n - k).}
+#' \item{ss_between}{Between-group sum of squares.}
+#' \item{ss_within}{Within-group sum of squares.}
+#' \item{ms_between}{Between-group mean square.}
+#' \item{ms_within}{Within-group mean square.}
+#' \item{F}{F-statistic.}
+#' \item{p_value}{Right-tail p-value from F distribution.}
+#'
+#' @details
+#' One-way ANOVA partitions total variance into between-group and within-group components:
+#' \deqn{SS_T = SS_B + SS_W.}
+#' The test statistic \eqn{F = MS_B / MS_W} follows an F distribution under H0 (equal means).
+#'
+#' @examples
+#' set.seed(0)
+#' x <- c(rnorm(20, 0, 1), rnorm(22, 0.2, 1), rnorm(18, -0.1, 1))
+#' g <- factor(rep(c("A", "B", "C"), times = c(20, 22, 18)))
+#' res <- anova_oneway(x, g)
+#' res$F; res$p_value
+#'
+#' @export
+anova_oneway <- function(x, g) {
+  if (!is.numeric(x)) stop("`x` must be numeric.")
+  if (length(x) != length(g)) stop("`x` and `g` must have the same length.")
+  if (!is.factor(g)) g <- factor(g)
+
+  n <- length(x)
+  k <- nlevels(g)
+  if (k < 2L) stop("Need at least 2 groups.")
+  if (n <= k) stop("Total observations must exceed number of groups.")
+
+  grand_mean <- mean(x)
+
+  # group stats
+  group_means <- tapply(x, g, mean)
+  group_sizes <- tapply(x, g, length)
+
+  # SS_between = sum_{groups} n_j * (mean_j - grand_mean)^2
+  ss_between <- sum(group_sizes * (group_means - grand_mean)^2)
+
+  # SS_within = sum over groups of sum (x_ij - mean_j)^2
+  ss_within <- sum(unlist(tapply(x, g, function(v) sum((v - mean(v))^2))))
+
+  df_between <- k - 1L
+  df_within  <- n - k
+
+  ms_between <- ss_between / df_between
+  ms_within  <- ss_within  / df_within
+
+  F_stat <- ms_between / ms_within
+  p_val  <- stats::pf(F_stat, df_between, df_within, lower.tail = FALSE)
+
+  list(
+    df_between = df_between,
+    df_within  = df_within,
+    ss_between = ss_between,
+    ss_within  = ss_within,
+    ms_between = ms_between,
+    ms_within  = ms_within,
+    F = F_stat,
+    p_value = p_val
+  )
+}
+
+# --- Simple self-test (uncomment to run locally) ---
+# set.seed(1)
+# x <- c(rnorm(15, 0, 1), rnorm(15, 0.5, 1), rnorm(15, 1, 1))
+# g <- factor(rep(c("A","B","C"), each = 15))
+# res <- anova_oneway(x, g)
+# stopifnot(res$F > 0, res$p_value >= 0, res$p_value <= 1)