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In frequentist hypothesis testing, the $p$-value is the probability of a result as extreme (or more) than the observed result, under the assumption that the null hypothesis is true.
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p-values for hypothesis testing
I'm going to focus on what seems to be your question. As you stated: "This implies that we are considering other, more extreme (and irrelevant) values of a test statistic we do not observe. Why is not …
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Do we reject null if we have a pvalue of 0.0503 at alpha = 0.05? What way to validate the re...
Strictly speaking, no. This is a very good question because it strikes at the heart of frequentist hypothesis testing and what it actually means. As the investigator, you decide on alpha before conduc …