---
title: "ADA1 hw3"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```


```{r}
d2 <- read.table("http://math.unm.edu/~luyan/ADA117/acid.txt",header=T)
head(d2)
nrow(d2)
dnew1<-d2[which(d2[,2]=="Acid1"),]
dnew2<-d2[which(d2[,2]=="Acid2"),]
nrow(dnew1)
nrow(dnew2)

#### Visual comparison of whether sampling distribution is close to Normal via Bootstrap
# a function to compare the bootstrap sampling distribution
#   of the difference of means from two samples with
#   a normal distribution with mean and SEM estimated from the data
bs.two.samp.diff.dist <- function(dat1, dat2, N = 1e4) {
  n1 <- length(dat1);
  n2 <- length(dat2);
  # resample from data
  sam1 <- matrix(sample(dat1, size = N * n1, replace = TRUE), ncol=N);
  sam2 <- matrix(sample(dat2, size = N * n2, replace = TRUE), ncol=N);
  # calculate the means and take difference between populations
  sam1.mean <- colMeans(sam1);
  sam2.mean <- colMeans(sam2);
  diff.mean <- sam1.mean - sam2.mean;
  # save par() settings
  old.par <- par(no.readonly = TRUE)
  # make smaller margins
  par(mfrow=c(3,1), mar=c(3,2,2,1), oma=c(1,1,1,1))
  # Histogram overlaid with kernel density curve
  hist(dat1, freq = FALSE, breaks = 6
      , main = paste("Sample 1", "\n"
                    , "n =", n1
                    , ", mean =", signif(mean(dat1), digits = 5)
                    , ", sd =", signif(sd(dat1), digits = 5))
      , xlim = range(c(dat1, dat2)))
  points(density(dat1), type = "l")
  rug(dat1)

  hist(dat2, freq = FALSE, breaks = 6
      , main = paste("Sample 2", "\n"
                    , "n =", n2
                    , ", mean =", signif(mean(dat2), digits = 5)
                    , ", sd =", signif(sd(dat2), digits = 5))
      , xlim = range(c(dat1, dat2)))
  points(density(dat2), type = "l")
  rug(dat2)

  hist(diff.mean, freq = FALSE, breaks = 25
      , main = paste("Bootstrap sampling distribution of the difference in means", "\n"
                   , "mean =", signif(mean(diff.mean), digits = 5)
                   , ", se =", signif(sd(diff.mean), digits = 5)))
  # overlay a density curve for the sample means
  points(density(diff.mean), type = "l")
  # overlay a normal distribution, bold and red
  x <- seq(min(diff.mean), max(diff.mean), length = 1000)
  points(x, dnorm(x, mean = mean(diff.mean), sd = sd(diff.mean))
       , type = "l", lwd = 2, col = "red")
  # place a rug of points under the plot
  rug(diff.mean)
  # restore par() settings
  par(old.par)
}



bs.two.samp.diff.dist(dnew1$conc, dnew2$conc)


```

