# Tag Info

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Note that the t-distribution becomes closer to the normal distribution as degree of freedom increases. When df approaches 30, it will be practically the same as normal distribution. The figures on t-distribution Wiki page clearly shows the process. So basically "t-test is used when the samples are less than 30", just because there is no need to use is ...

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You can certainly use a two sample proportions test. Indeed, since it sounds like your alternative is one tailed, that's probably what you want; the other common choice - the chi-square - doesn't do one-tailed alternatives. For small samples, you could use the fact that (given the usual assumptions, at least) the proportions are discrete. Depending on ...

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1) I found this pre-print paper by @Michael Lew to clarify many things for me. In terms of calculating a p-value under the null hypothesis, it can be seen as more of a matter of convenience than anything else: the null hypothesis serves as little more than an anchor for the calculation|a landmark in parameter space To P or not to P: on the ...

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The test statistic is chosen to be a measure of the discordance of the data with the null hypothesis, in some direction of interest (e.g. the difference of sample means between two groups, the correlation between successive observations in time, &c.). The bigger it gets, the more evidence against the null hypothesis. Well, we don't always. Sometimes the ...

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One quick remark: I assume that you want to know if the variances of the two population are equal (if you want to compare population means an F-test is not the correct choice). The ratio of the variance estimations is F-distributed (given normality of the data) and we are interested if the variance in one population is bigger or smaller than in the other, ...

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The p-value applies to upper, lower, and double tailed tests. It is the probability that the test statistic would be at least as contradictory to your null hypothesis as you currently observe assuming your null hypothesis is true. So, for upper tail tests, you are comparing $H_o: a = b$ vs. $H_a: a>b$, in this case, the p-value is the probability that the ...

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You could do an Ansari-Bradley test or a Siegel-Tukey test ... or indeed almost any suitable scale test. To estimate the scale, you can scale one sample until the test statistic reaches its expected value under the null hypothesis, and you can get an interval for the scale by the same method as generating an interval for the shift parameter in the ...

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