Search Results

Your data are apparently not paired. You should not be attempting to pair unpaired data. With (presumably) independent samples, the usual form of permutation test simply permutes the group labels. W …

While you could certainly use a statistic of the difference in variance to test equality of variance, some people might feel it would make more sense to have a statistic of the ratio of variance (wher …

The pmf that goes with the distribution you give is -3 -2 -1 0 1 2 3 0.05 0.10 0.20 0.30 0.20 0.10 0.05 The cdf is then -3 -2 -1 0 1 2 3 …

Why do we know $X_i$ and $Y_i$ are identically distributed under the null? We don't know it -- it's an assumption -- but it's an easily justifiable one in many situations. For example, imagine …

Often you can use permutation tests to obtain confidence intervals with appropriate coverage, under particular assumptions. For example, consider the signed rank test (which is a permutation test ba …

Generally hypothesis tests are accompanied by extra assumptions that will need to hold (at least when the null is true), so that the null distribution of the test statistic can be obtained; this is as …

You choose a test statistic that measures what you're interested in/has the properties you need. If you want to compare means, you base it on differences of means; if you want a robust comparison of l …

The t-statistic makes a lot of sense as a test statistic; many people find it intuitive. If I quote a t-statistic of 0.5 or 5.5, it tells you something - how many standard errors apart the means are. …

If none the $x$-variables relate to the mean response, then the $y$'s are a set of observations from distributions with the same expectation $E(y|X)=\mu_Y$. The idea of a permutation test is that if w …

If you used a mean-based permutation test it would seem that you regard the mean as informative - an important and relevant feature of the distribution. On the other hand, if you think the quantiles, …

While permutations tests, randomization tests and bootstrapping all fall under the class of resampling procedures, they differ in some important ways. In particular, a permutation test differs in sev …

You can use almost any statistic you like in a randomization test. Some will be more useful than others. So yes, you could put in a t-statistic (but personally I'd tend to just use the difference in …

A problem with doing a permutation test of equality of means occurs if you think that the possible difference in variance of the two groups will remain even if the null of equal means is true. In that …

If it's not quite significant, do you keep simulating? If so, then no, the significance level is no longer the desired level when you do that. It's substantially affected by this checking for signifi …

The conflating of testing for a difference in means with testing for a difference in distributions is, unfortunately, misleading. It's important to focus on the alternatives you're trying to find. Eve …