What does p-value mean ? What and how can i interpret the results

Question

[sushumitha6]

out of 27464 with nonzero total read count
adjusted p-value < 0.1
LFC > 0 (up)       : 0, 0%
LFC < 0 (down)     : 0, 0%
outliers [1]       : 0, 0%
low counts [2]     : 0, 0%
(mean count < 0)
[1] see 'cooksCutoff' argument of ?results
[2] see 'independentFiltering' argument of ?results

[i.sudbery]

As well as discussing the attempts you have made to investigate this yourself before post here (as discussed by @ATPoint below). Can you please elaborate some of the context for your question? Why is the experiment, why are you conducting this analysis? Otherwise one cannot interpret the result. Further, a question like yours, without context, could be mistaken for someone asking for help with a homework or exam question.

[Kevin Blighe]

• p-value: The probability that we can reject the NULL hypothesis when the NULL hypothesis is TRUE.
• power: The probability that we can reject the NULL hypothesis when the NULL hypothesis is FALSE.

Answer 1

[i.sudbery]

The p-value is the probability (hence "p"-value) of the obtaining this data or more extreme data assuming the null hypothesis is true. (definition of "more extreme" is dependent on the null and alternative hypotheses)

Answer 2

[Istvan Albert]

There is a tradeoff. When we try to be precise, the explanations become a little unwieldy and make the definition hard to remember. When we make the explanation simple, the wording is ambiguous.

Here is a definition that I like, tries to reconcile the two extremes:

The p-value is the probability that the observed difference between two groups is due to chance.

[i.sudbery]

I don't agree with this, because while a low p-value makes it unlikely that a difference is due to chance, a high p-value does not make it likely that a difference is due to chance, it just means we have insufficient evidence to say anything either way.

[Jeremy Leipzig]

I find this just as succinct and less easily misinterpreted: The p-value is the probability that random chance could produce the observed difference

[i.sudbery]

The random chance if the null is true

[Istvan Albert]

the phrase "due to chance" has no connection to the magnitude of the p-values at all. Observing smaller or larger probability does not affect the interpretation of the second part of the sentence.

"due to chance" is just a succinct way to say "caused by random chance while the null hypothesis is true".

I like Jeremy Leipzig formulation as well:

The p-value is the probability that random chance could produce the observed difference

We have here a formulation that, while incomplete, captures the salient points. On the other hand, we could also use seemingly precise, words that, in turn, need to be defined separately, and remain hard to recall and interpret correctly. In my opinion, using words like null hypothesis is true is the primary reason that most people don't know what p-values are even at a simpler level.

Let me also posts the Biostar Handbook's theorem on p-values:

Nobody understands p-values. We only differ in the degree of our misinterpretation.