A p-value is the probability of seeing a result at least as extreme as yours if the null hypothesis were true. Enter a z-score directly, or an observed value with the mean and standard deviation, and choose a one- or two-tailed test. The result comes with the tail area it represents and what it does and does not let you conclude.
A p-value is a conditional probability: assuming the null hypothesis is true, how likely is a result at least this extreme? Nothing more. It is not the probability that the null hypothesis is true, not the probability your result is a fluke, and not a measure of effect size. Those three misreadings account for most of the trouble p-values cause.
A two-tailed test asks whether the result differs from the null in either direction. A one-tailed test asks only about one direction and puts the whole 5% in that tail, which makes significance easier to reach. That is legitimate only if you committed to the direction before seeing the data. Choosing the tail afterwards halves your p-value for free and is a well-documented way to manufacture a finding.
With a large enough sample, a trivial difference will clear any threshold. With a small one, a large effect can miss it. Always report the effect size and a confidence interval alongside the p-value; on their own, significance stars say very little about whether a result matters.
If the null hypothesis were true, there is a 3% chance of observing data at least this extreme. It is not the probability that the null hypothesis is true, and it is not the probability that your finding is a fluke.
Use two-tailed unless you have committed in advance to testing a direction and genuinely do not care about an effect the other way. Switching to one-tailed after seeing the data halves the p-value for no good reason and is a well-known way to manufacture significance.
No. 0.05 is a convention, not a law of nature, and a p-value says nothing about effect size or practical importance. Report the effect and a confidence interval alongside the p-value.
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