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Why increasing the sample size increase statistical significance? How to mathematically show that when we get more samples, the small difference would become statistically significant easier?

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    You might want to read about power analysis. It would be more correct to state that increasing the sample size increases the power of a statistical test. If a null hypothesis is truly correct then nothing changes in the probability of rejecting the hypothesis. – Sextus Empiricus Oct 10 '22 at 14:10
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    See also https://stats.stackexchange.com/questions/279162/unbiased-hypothesis-test-what-does-it-mean-actually/279199#279199. Although the plot in the answer is about the "left tail", the "right tail" provides an illustration regarding your question. – Christoph Hanck Oct 10 '22 at 14:13
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    Another example https://stats.stackexchange.com/questions/374031/help-calculating-the-power-function-at-a-point-mu-0-5-for-the-normal-distribu – Sextus Empiricus Oct 10 '22 at 14:15

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