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I was new in using t-test I got p-value 2.6293E-109 is this statistically significant how to represent in article results

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  • $\begingroup$ By itself the numerical value is meaningless. $\endgroup$ – Xi'an Apr 22 at 7:30
  • $\begingroup$ What is your question (hyphotesis)? $\endgroup$ – oszkar Apr 22 at 7:30
  • $\begingroup$ I recommend you do further research on the principles behind hypothesis testing, what are p-values and how the sampling distributions with which these tests are based on work. I recommend Khan Academy's series on AP Statistics which has good introductory statistical theory. $\endgroup$ – ajax2112 Apr 22 at 8:38
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The p-value represents the probability of seeing a result as extreme as the result you got, assuming the null hypothesis is true (that there is no difference). Whether or not your p-value is significant is determined by your statistical significance threshold, which can be any value but is commonly set to 0.05. Since your p-value is far less than this (like by a lot) you can safely say your results are significant.

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  • $\begingroup$ How to represent P vale sir $\endgroup$ – Yemineni. Gopi Apr 22 at 7:23
  • $\begingroup$ A bit pedantic: The p-value represents the probability of seeing a result as extreme as the result you got, assuming the null hypothesis is true and assuming the statistical model is true. (and actually no model is true, but some models are sufficiently accurate) This means that the p-value, a computation of a probability, does not incorporate uncertainty about the computation/model itselve. Normally it is assumed that these effects are negligible, but for such small number like p-values of the order of $10^{-109}$, details like the tails of the distribution are important. $\endgroup$ – Sextus Empiricus Apr 22 at 7:48
  • $\begingroup$ So that is probably why many people, in sciences with uncertainty about the used statistical model, just stick to p<0.001 and consider any differentiation below it as not meaningful (it is sort of like saying that there is a one in thousand probability of a black swan or that there was some sampling error). In physics, it is often more easy to describe the system and model it accurately, and people tend to use smaller p-values. But even in physics the p-values must be considered with some skepticism (e.g. the observation of faster than light neutrino's in 2011 with 6.2 sigma significance). $\endgroup$ – Sextus Empiricus Apr 22 at 7:55
  • $\begingroup$ What small p-values mean is that an anomaly has been observed. But such anomalies can have two reasons: either (or both) the null-hypothesis is wrong, or the statistical analysis is wrong (or three reasons, anomalies also happen by chance). $\endgroup$ – Sextus Empiricus Apr 22 at 7:57
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Whether the result is "significant" depends on your significance level, which, in turn, depends on the chance of obtaining the test statistics by pure chance, which, in turn, depends on many things, including the number of tests you perform. Even if you do only a single test, I'd like to warn that it can still be some convoluted hidden effect you haven't thought about. For an example, see my question here.

How you report it, depends on the community. In some communities it is common to report almost exact, rounded to the next highest power of ten, e.g. $p < 10^{-108}$. In other communities, they prefer a more readable variant, $p < 0.001$ (which they tend to interpret as "highly significant").

But, the use of p-values has been criticised for years by statisticians for being unreliable, unsuitable for making decisions, and misleading. You shouldn't concentrate on the p-value, but on your hypothesis. The p-value is just a supporting evidence, among many other things, starting with the prior knowledge and experiment design.

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