Hold on a second, you originally wrote, "if the p-value is less than .05 (by an arbitrary and accidental custom) the model is rejected." Usually by model we mean an alternative to null hypothesis. So essentially you said, if p < .05, alternative model is rejected and null hypothesis is accepted. Well that's a contradiction to what you just stated in your second post (and to what we both agree on).
Nah, you fit the null hypothesis, and if it fails you reject it. You never, ever accept the null hypothesis; there might just not be enough power in the test.
My goof, of course you don't accept the null model (you generally never accept any models -- you only eliminate ones that are worse at explaining the data).
In basic frequentist stats, you usually have two models -- a simpler one (usually called the null hypothesis), and a more complex one called an alternative model (what makes it more complex is usually one or more extra parameters), and you're usually interested in testing whether the more complex model holds up when compared to the more simple one. You do this most often by a likelihood ratio test: you divide the probability of data given null hypothesis by the probability of data given alternative model, and then you compare the value of the negative log of the resulting ratio to an expected distribution of said statistic assuming the alternative model is false and taking into account degrees of freedom (how many more parameters the alternative model contains). If it turns out that, under the null hypothesis, the probability of the ratio statistic being larger or equal to the one at hand is <= 0.05, the null hypothesis is rejected. The alternative hypothesis is not automatically accepted yet but it is said to explain the data better than the null model.
Basically everything you wrote is correct, it's just that I misinterpreted what you referred to as "model" to mean "alternative model," while you actually meant "null hypothesis" or "null model." Now you should have been more clear on that, otherwise you can confuse people new to this subject (you already confused me!)
Ha ha. I used to repeat the p value interpretation over and over in different ways to the class in the hopes of eventually explaining what it is not. I did dare you to wrap your head around it, so you were warned!! It is an upside down concept.
You know the value is 0.05 because fisher had a tabulation of the zeta function lying around with 0.05, 0.025, and 0.01 in it when he was writing the paper?
