# Fallacy in p-value definition

I have two more questions. Why Statsoft's textbook says that

the p-value represents the probability of error that is involved in accepting our observed result as valid

whereas Wikipedia gives a slightly different definition:

p-value is the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true

Wikipedia warns us against confusing Fisher's p-value criteria with Pearson's Type I error (probability of taking a wrong decision). I read that statsoft's definition falls into the Type I fallacy. Am I wrong? Can you explain how these definitions related?

## 2 Answers

The StatSoft definition is incorrect. (I know, a short answer, but sometimes there is no long answer).

• It's also really only centered on two population t-tests somehow. This whole explanation seems to be wrong and misleading. In fact I would stop using that textbook and probably the software as well. ugh – IMA Jun 5 '13 at 15:44

This is a helpful link.

More formally, if you observed a p-value that was less than 5%, you could say: "The probability of the available (or of even less likely) data, given that the null hypothesis is true, is less than 5%.

• It is a convention that you post useful links in comments (I have upvoted you so that you can do that). In the answers, you extranct the information and answer question. that you fall into the same fallacy as StatSoft definition and confirm that definition whereas the first answer says it is false? Do you see any contradicitons? – Val Jun 5 '13 at 19:40
• I'm not sure I exactly understand your query. Are you asking me if I am contradicting StatSoft? Their answer is wrong, as Peter has mentioned above. Edit: The reason the StatSoft definition is wrong is because it is trying to get at the Neymen-Pearson approach to significance, which is different than the Fisherian approach (P-values). The correct, formal definition is the one I indicated above and the one by Wikipedia. (The papers elaborate more on this, definitely worth reading). – Francisco Arceo Jun 5 '13 at 20:45
• Ok, excuse me for misreading it the first time. – Val Jun 6 '13 at 11:30