using shapiro wilk test to explain p-values I have a result of p-value = 1.439e-05 and I don't understand what this means? does this mean the p-value is less than 0.05? or it is greater? and what does the result say about the Shapiro-Wilk test?
 A: A p-value of 1.439e-05 equals to 1.429*10^(-5), which is less than 0.05. A Shapiro-Wilk test is the test to check the normality of the data. The null hypothesis for Shapiro-Wilk test is that your data is normal, and if the p-value of the test if less than 0.05, then you reject the null hypothesis at 5% significance and conclude that your data is non-normal. Hope this helps
A: 1.439e-05 equals 1.439 * 10^-5. The null hypothesis for a Shapiro Wilk test is that there is no difference between your distribution and a normal distribution. The alternative hypothesis is that there is a difference. If your p value is less than 0.05, which it is, then you reject the null hypothesis and conclude that your data is nonormal. How large is your sample size? If you're trying to meet the assumptions for a parametric test, the assumption is that the sampling distribution is normal and usually large sample sizes will allow you to assume that. 
A: Complementing what was mentioned above: "p-values ​​can indicate how incompatible the data is with a specified statistical model." In summary, p-value is the probability that in a specified statistical model that your test statistic assumes values ​​equal to or greater than the observed value.
In your case (the Shapiro test), assume that your data (the sample) comes from a normal distribution (null hypothesis or specified model). When performing the test or obtaining a P value <0.001, what you have is that the test statistic used, almost never assumes values ​​higher than what it pointed out and, therefore, you have evidence against the null hypothesis (or against the specification of the your model). Note that if your P-value was very high, that is, if your test statistic almost always assumed values ​​higher than that observed by it, your model would be well specified, and therefore, you would have no evidence against the null hypothesis. This division of the P <0.05 value is what some members of the scientific community have been adopting and many others criticizing. Personally, I prefer Fischer's optics, which is more or less what was explained above.
Hope this helps!
