I'm comparing the means of two groups--A and B, using t-test. Can I say a larger p-value (e.g. 0.94) suggests higher tendencies towards similarity than a smaller p-value (e.g. 0.08)? I understand that the p-value is the probability of the observing the data when the null is true (A=B), but not sure if I can infer that from this statement. Thanks!
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1$\begingroup$ What are "higher tendencies towards similarity" supposed to be when you are comparing two means? Please note that the p-value is not as you have characterized it. For more information, please search our site. $\endgroup$– whuber ♦Commented Oct 30, 2016 at 17:40
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$\begingroup$ If the null hypothesis is true then a high $p$-value simply tells you that the two samples are similar, indeed if it greater than $0.5$ then the samples are more similar than would happen half the time. There is not much special about this: it happens half the time. $\endgroup$– HenryCommented Oct 30, 2016 at 17:42
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If the P-value is small then either the Null Hypothesis is True and you have observed a rare event, or the Null Hypothesis is False.
If the P-value is less than significance level (alpha) you reject the null hypothesis · If the P-value is more than significance level (alpha) you fail to reject the null hypothesis.
A low p-value is a low probability. This means your data is unusual and is closer to the alternative hypothesis than the null.
As whuber suggests, "higher tendencies towards similarity" is not meaningful in this context.
