I quantified a statistics that measure the percentage of covariation between set of variables, lets say Int, across 3 groups (for each group Int was calculated). Int ranges from 0 to 100.
Afterwards I used bootstrap in order to obtain some measure of variability of the Int within each group (resampling was with replacement within each group).
Because I can not pass all the data and complex cod for the Int, below I generated (mimic) the pattern of the results that I obtained after bootstrap:
set.seed (50) # here "Int.boot.dist" mimic bootstrap distribution that I obtained Int.boot.dist <- rnorm (n = 100, mean = 50, sd = 15) # boxplot boxplot (Int.boot.dist, main = "Boxplot of bootstrapped distribution of the Int", ylab = "integration", ylim = c (0, 100)) # mimic observed mean obs.mean <- sample [order (sample, decreasing = T)] points (obs.mean, cex = 2.5, lwd = 3, pch = 4, col = "red") legend ("topleft", legend = "observed mean", cex = 1, col = "red", pch = 4)
As you can note, observed Int is almost like outlier and considerably far away from bootstrapped mean or median.
## plot (as a bar where height correspond to the observed Int) along with standard error plot (Int.boot.dist, type = "n", xlim = c(0, 2), ylim = c (0, 100), xlab = "group1", ylab = "integration") x <- c (0.5, 1.5, 1.5, 0.5) y <- c (0, 0, obs.mean, obs.mean) polygon (x, y, border = "black", col = "gray") ## calculate standard error sd <- sqrt(var(sample)) y0 <- obs.mean-sd y1 <- obs.mean+sd segments (1, y0, 1, y1, col = "red", lwd = 2) legend ("topleft", legend = "SDM", lwd = 2, col = "red")
Second graph shows bar that corresponds to the observed Int value and red line shows standard error obtained by bootstrap.
Q1: Is it appropriate to report standard error (e.g. second graph) when observed statistics depart from mean or median of bootstrapped distribution?
Q2: What does such pattern tell us about the data and is it appropriate to compare such statistics at all?