OpenEpi is a Javascript stats library, is open source, and has ANOVA and t-tests. I've not tried it (it's a bit too focused on epidemiology for my needs) but it might be useful.
jStat is a javascript statistical library project, and it looks like it's got a great future, but it might not have all you need right now. Edit: as of Dec 2012 it looks like the jStat project page is no longer maintained but the project is continuing to be developed. There's more up to date documentation on github. It now does have anova tests and varieties of t-test. No sign of Wilcoxon signed-rank though.
If you need very specific statistical processing in javascript urgently, you might have most success by browsing Omegahat who have various little tools that bridge the established stats language R with others including javascript.
It'll depend on the details of exactly what you want to do, but you might have some success with packages such as RJavascript - a code translator which aims to help turn existing R features into Javascript (just don't expect quality results first time). Also, SpiderMonkey builds on R for browsers, so it might be useful for internal or personal uses (but it's unlikely to be suitable for public publishing).
