4 ms·
Your analysis tells nothing about whether the model of fair coin being flipped is confirmed. You see a deviation of 0.06 in the mean and 0.47 in the variance. I
by ssivark 8y ago
Your analysis tells nothing about whether the model of fair coin being flipped is confirmed. You see a deviation of 0.06 in the mean and 0.47 in the variance. Is that negligible? Imagine you had much less data i.e. nDays=5 — What if your sample had a mean of 10.6 and a variance of 4.8? Could you confirm or rule out the fair coin model? Or confirm/ rule out the 0.6-heads-0.4-tails model? Within the frequenting framework, you’d need a null hypothesis to answer that question.
Regarding p-value, I agree I could have phrased my comment better.
In the frequentist framework, there is no way to confirm a model. The only way to arrive at a model is to falsify all “simpler” models one can think of, that might possibly have explained the data.
- nonbel 8y ago>"Your analysis tells nothing about whether the model of fair coin being flipped is confirmed. You see a deviation of 0.06 in the mean and 0.47 in the variance. Is that negligible?" Th easiest way is to just run a simulation thousands or millions of times then check how often the observed results occurred. Eg, using R again to get distributions for the mean and sd for the model and getting the one sided p-value: p = 0.5 nDays = 365 nPerDay = 20 obs = rbinom(nDays, nPerDay, p) sim = replicate(1e3, rbinom(nDays, nPerDay, p)) stats = apply(dat, 2, function(x) c(mean(x), var(x))) mean(stats[1,] > mean(obs)) mean(stats[2,] > var(obs)) >"In the frequentist framework, there is no way to confirm a model. The only way to arrive at a model is to falsify all “simpler” models one can think of, that might possibly have explained the data." That isn't frequestist. Its the so-called "NHST hybrid" which it seems confused stats 101 authors in the 1930-1940s cobbled together from the ideas of Ronald Fisher, Jerzy Neyman, and Egon Pearson. This is a decent intro to that topic, but there are thousands of papers on this: http://library.mpib-berlin.mpg.de/ft/gg/GG_Mindless_2004.pdf http://library.mpib-berlin.mpg.de/ft/gg/GG_Mindless_2004.pdf
- ssivark 8y agoThanks for the Gigerenzer article. While he points out unfortunate problems with the way NHST is commonly/mindlessly used, none of that changes the fact that in many cases, there is a natural null hypothesis from an application of Occam's razor. (which was the point of the response to OP's question)
- nonbel 8y agoGreat to hear! Here is another you may find interesting: Meehl, Paul E (1967). Theory-testing in psychology and physics: A methodological paradox. Philosophy of Science, 34(2), 103–115. http://www.jstor.org/stable/10.2307/186099 http://www.jstor.org/stable/10.2307/186099