Vice versa, if p is sufficiently small, the probability of the *null* *hypothesis* being *true* is minimal enough as to reject the *null* and accept our alternative *hypothesis*. The smaller the p-**value**, the more evidence we have against H0. In the world of the __null__ __hypothesis__ fetish, the p-__value__ (p) is the most revered number. The p-__value__ is the probability, assuming the __null__ __hypothesis__ is __true__, of obtaining a test statistic at least as extreme as the one calculated from the sample data.

## P value null hypothesis is true

: Researcher 1 conducts a clinical trial to test a drug for a certain medical condition on 30 patients all having that condition. The patients are randomly assned to either the drug or a look-alike placebo (15 each).

I argued that (despite our long pedagogical practice) there are, in fact, many situations where this interpretation of the p-

valueis actually the correct one (or at least close: it’s our rational belief about this probability, given the observed evidence). Under the prior belief that allvaluesof are equally likely a priori, this expression reduces to ; this is just the p-value(where we consider starting with the likelihood density conditional on with a horizontal line at , and then sliding the entire distribution to the left adding up the area swept under the likelihood by that line).

### P value null hypothesis is true

#### P value null hypothesis is true

As I also explained in the earlier post, everything about my training and teaching experience tells me that this way lies madness. Neither patients nor medical personnel know which patient takes which drug.

Last week, I posted about statisticians’ constant battle against the belief that the p-**value** associated (for example) with a regression coefficient is equal to the probability that the **null** **hypothesis** is **true**, for a **null** **hypothesis** that beta is zero or negative. HOW TO WRITE A GOOD AP EURO THESIS If p is hh, there is a hh likelihood of obtaining said result when the __null__ is actually __true__, therefore we would choose not to reject the __null__ __hypothesis__.

P value null hypothesis is true:

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