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Apr 24, 2015 at 23:34 comment added Nick Cox For example, a set of quantile-quantile plots could be a sampling distribution. You don't need to quantify a P-value for the idea of "more extreme" to be useful. Several statisticians have used the analogy of a police line-up. If one graph leaps out at you as different, you are on to something. See e.g. Buja et al. rsta.royalsocietypublishing.org/content/367/1906/4361
Apr 24, 2015 at 20:37 comment added amoeba @Nick, if test statistic is not scalar, then what is the meaning of "more extreme" in the p-value definition? It seems to me that it must take values at least in a partially ordered set... But I don't think I have ever encountered non-scalar test statistic.
Apr 24, 2015 at 15:58 history edited Jessica CC BY-SA 3.0
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Apr 24, 2015 at 15:39 comment added Nick Cox This looks a good introductory outline. I would want to quibble that a test statistic is not necessarily a scalar (single number). For example, a plot from one sample could be a test statistic.
Apr 24, 2015 at 15:38 comment added Nick Cox Note for people new to statistics: The last point qualifies as a statistical joke. Some would want to add that the methodology makes more sense than zero: you should want to worry that you are looking at something that might be a sampling fluke, but opinions differ on how to do that. Others would want to add that they don't do this any way: Bayesians would certainly deny that everyone uses it.
Apr 24, 2015 at 15:27 history answered Jessica CC BY-SA 3.0