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I have a question that if a p value less than 0.05 in wilcox test means that the two data are significantly different and the p-value of 1 means that are exactly same, then what is the meaning of a p-value, say 0.6 or 0.7. Is it like there is a small difference between the two data? But the null hypothesis is already rejected when we have a value of more than 0.05 and null hypothesis means the data are different?

I am getting a p-value of 0.7, though there is a difference in my data.

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First of all, p-values are nos strictly defined as a measure of the effect size.

  • If the p-value is lower the significance level (usually 0.05) then we can say that we have statistically significant evidences to reject the null hypothesis, and thus to accept that the data are different in your case.

  • On the other hand, if the p-value is above 0.05, we can not say that H0 is true, that is, we can not say that the data are equal. We can just say that we have not enough evidences to reject H0.

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  • $\begingroup$ and can we take the threshold value (mu) other than 0.05? Is it depend on the kind/size of data or it should be exactly 0.05 for all kind of data? My data is very large, say 300 values in column A and 300 values in column B, with positive and negative signs? $\endgroup$ – Khan Mar 12 '19 at 9:04
  • $\begingroup$ Yes, you can take other significant levels. The significant levels depends on "how sure/confident" you will be with your result. The lower the the significant level is the more restrictive is your approach. In fact, the 0.05 confidence level is a "rule of thumb". $\endgroup$ – Leibnitz Crew Mar 12 '19 at 9:12
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I think there are a couple of points of hypothesis testing that may be helpful. First, review the definition of p value: It's the probability of getting data as extreme as the observed values assuming that the null hypothesis is true. Conceptually, one could stop at this point, without moving on to making a hard decision about whether the null hypothesis can be "rejected." Second is the idea that the observed values you are examining are sampled from some populations. You can't examine the populations; you just have these samples to consider. So, it may be that your samples are not identical (and perhaps your test returns a p value: 0.05 < p < 1). But the question the hypothesis test is trying to address is, Is this good evidence against the populations from which the samples were drawn being identical? It's not addressing hypotheses about the observed data. In fact, it would be trivially easy to address some question about the observed data. For example, we could calculate the exact mean of the observed data, and so on. But that's not the question of interest. When you are looking up the hypotheses tested by a statistical test, you should be finding the hypotheses stated in terms of the populations from which the samples are drawn, but often authors use simple or imprecise language.

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