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The t-test assumes a normal distribution which, is rarely true, especially when the number of runs is under 100. A better test is the Mann-Whitney U test which
by frozenport 10y ago
The t-test assumes a normal distribution which, is rarely true, especially when the number of runs is under 100. A better test is the Mann-Whitney U test which is applicable for a wider category of distributions.
- platz 10y agoCentral limit theorem means there are lots of cases where normal distributions are directly applicable.
- ekianjo 10y agoThe central limit theorem applies to independent variables only. If you are not sure your variables are independent you cannot rely on that assumption.
- platz 10y agoGood to know!
- ronald_raygun 10y agoThat's not 100% true. There are lots of different theorems that are "central limit theorems", and that work across different cases. You can have CLT's with non-iid variables (either the aren't identically distributed or aren't independent). The math just becomes much harder, and you have to assume specific dependence structures. For example https://en.wikipedia.org/wiki/Martingale_central_limit_theorem https://en.wikipedia.org/wiki/Martingale_central_limit_theor...
- ekianjo 10y agoThanks for the reference - can you provide an example where one would use the Martingale CLT, if you are aware of any ?
- srean 10y agoLook for any estimation or inference problems in the context of stochastic processes. For a simpler example you can take a look at sequential test of hypothesis. It is quite ubiquitous, but not always called out by its name.
- srean 10y agoSomeone ought to formulate the Godwin's law analogue for CLT. Hint 1: what happens when variance does not exist or is too large to be considered finite for any practical purposes. Hint 2: Levy processes, stable distributions
- platz 10y agoToo cryptic to be helpful, sorry..
- srean 10y agoAh I see, my apologies, I assumed Googling those keywords would be sufficient to connect the dots. The main thing that I wanted to convey is that the consequences of CLT does not come for free. It is not remotely as widely applicable as it is made out to be. CLT is also not so narrow that you need IID random variables as is often claimed. Those assumptions can be relaxed substantially. What gets in the way in obtaining a Gaussian distribution in the limit is the requirement that the original distribution(s) have a finite variance. The (averaging) process may still converge to some limiting distribution but it would not be a Gaussian one. Levy measures, more precisely stable measures are that class and Gaussian is but one member of that class, the only one that has finite variance. It is slowly getting acknowledged that many natural processes in fact do not have a finite variance. Fractals are one such process
- platz 10y agoI wasn't aware of the idea that natural processes might not have a finite variance, or what implications that would have. Thanks for clarifying!
- willhslade 10y agoI've seen variations of this comment in multiple threads, and have to ask: is there a good paper or textbook that spells this out?
- srean 10y ago
- rcthompson 10y agoI think the t-test is conceptually easier to understand, which is important since the target audience for this article is people who know next to nothing about statistics. The t-test might not be the best test for every situation, but if the alternative is no test at all, I'll take it.