Resampling / simulation methods: monte carlo, bootstrapping, jackknifing, cross-validation, randomization tests, and permutation tests I am trying to understand difference between different resampling methods (Monte Carlo simulation, parametric bootstrapping, non-parametric bootstrapping, jackknifing, cross-validation, randomization tests, and permutation tests) and their implementation in my own context using R.
Say I have the following situation – I want to perform ANOVA with a Y variable (Yvar) and X variable (Xvar). Xvar is categorical. I am interested in the following things:
(1) Significance of p-values – false discovery rate
(2) effect size of Xvar levels  
Yvar <- c(8,9,10,13,12, 14,18,12,8,9,   1,3,2,3,4)
Xvar <- c(rep("A", 5),  rep("B", 5),    rep("C", 5))
mydf <- data.frame (Yvar, Xvar)

Could you gel me to explain the  sampling differences with explicit worked examples how these resampling method work?
Edits:
Here are my attempts:
Bootstrap 
10 bootstrap samples, sample number of samples with replacement, means that samples can be repeated   
boot.samples <- list()
for(i in 1:10) {
   t.xvar <- Xvar[ sample(length(Xvar), length(Xvar), replace=TRUE) ]
   t.yvar <- Yvar[ sample(length(Yvar), length(Yvar), replace=TRUE) ]
   b.df <- data.frame (t.xvar, t.yvar) 
   boot.samples[[i]] <- b.df 
}
str(boot.samples)
 boot.samples[1]

Permutation:
10 permutation samples, sample number of samples without replacement
 permt.samples <- list()
    for(i in 1:10) {
       t.xvar <- Xvar[ sample(length(Xvar), length(Xvar), replace=FALSE) ]
       t.yvar <- Yvar[ sample(length(Yvar), length(Yvar), replace=FALSE) ]
       b.df <- data.frame (t.xvar, t.yvar) 
       permt.samples[[i]] <- b.df 
    }
    str(permt.samples)
    permt.samples[1]

Monte Caro Simulation 
Although the term "resampling" is often used to refer to any repeated random or pseudorandom sampling simulation, when the "resampling" is done from a known theoretical distribution, the correct term is "Monte Carlo" simulation.
I am not sure about all above terms and whether my above edits are correct. I did find some information on jacknife but I could not tame it to my situation. 
 A: Here's my contribution.
Data
Yvar <- c(8,9,10,13,12,
          14,18,12,8,9,
          1,3,2,3,4)
Xvar <- rep(LETTERS[1:3], each=5)
mydf <- data.frame(Yvar, Xvar)

Monte Carlo
I see Monte Carlo as a method to obtain a distribution of an (outcome) random variable, which is the result of a nontrivial function of other (input) random variables.  I don't immediately see an overlap with the current ANOVA analysis, probably other forum members can give their input here.
Bootstrapping
The purpose is to have an idea of the uncertainty of a statistic calculated from an observed sample.  For example: we can calculate that the sample mean of Yvar is 8.4, but how certain are we of the population mean for Yvar?  The trick is to do as if the sample is the population, and sample many times from that fake population.
n <- 1000
bootstrap_means <- numeric(length=n)
for(i in 1:n){
   bootstrap_sample <- sample(x=Yvar, size=length(Yvar), replace=TRUE)
   bootstrap_means[i] <- mean(bootstrap_sample)
}
hist(bootstrap_means)

We just took samples and didn't assume any parametric distribution.  This is the nonparametric bootstrap.  If you would feel comfortable with assuming for example that Xvar is normally distributed, you can also sample from a normal distribution (rnorm(...)) using the estimated mean and standard deviation, this would be the parametric bootstrap.
Other users might perhaps give applications of the bootstrap with respect to the effect sizes of the Xvar levels?
Jackknifing
The jackknife seems to be a bit outdated.  Just for completeness, you could compare it more or less to the bootstrap, but the strategy is here to see what happens if we leave out one observation (and repeat this for each observation).
Cross-validation
In cross-validation, you split your (usually large) dataset in a training set and a validation set, to see how well your estimated model is able to predict the values in the validation set.  I personally haven't seen yet an application of cross-validation to ANOVA, so I prefer to leave this part to others.
Randomization/permutation tests
Be warned, terminology is not agreed upon.  See Difference between Randomization test and Permutation test.
The null hypothesis would be that there is no difference between the populations of groups A, B and C, so it shouldn't matter if we randomly exchange the labels of the 15 values of Xvar.  If the originally observed F value (or another statistic) doesn't agree with those obtained after randomly exchanging labels, then it probably did matter, and the null hypothesis can be rejected.
observed_F_value <- anova(lm(Yvar ~ Xvar))$"F value"[1]

n <- 10000
permutation_F_values <- numeric(length=n)

for(i in 1:n){
   # note: the sample function without extra parameters defaults to a permutation
   temp_fit <- anova(lm(Yvar ~ sample(Xvar)))
   permutation_F_values[i] <- temp_fit$"F value"[1]
}

hist(permutation_F_values, xlim=range(c(observed_F_value, permutation_F_values)))
abline(v=observed_F_value, lwd=3, col="red")
cat("P value: ", sum(permutation_F_values >= observed_F_value), "/", n, "\n", sep="")


Be careful with the way you reassign the labels in the case of complex designs though.  Also note that in the case of unequal variances, the null hypothesis of exchangeability is not true in the first place, so this permutation test wouldn't be correct.
Here we did not explicitly go through all possible permutations of the labels, this is a Monte Carlo estimate of the P-value.  With small datasets you can go through all possible permutations, but the R-code above is a bit easier to understand.
