I was carrying out a Pearson correlation with Bootstrapping and have issues understanding when to accept the p value and when not to depending on the 95% Bootstrapping confidence interval.

I have read that if both the bounds are positive or negative, you can accept the conclusion that the p value gives. However, if one bound is positive and one negative, the conclusion given by the p value is wrong and you just need to negate that conclusion and accept the other one.

I am unable to understand why do we negate when one is negative and one positive? How does that matter? Or is there something that I am missing?

Also this rule of accepting and rejecting depending on the signs of the bounds, does it apply even when we bootstrap with T-test, ANOVA, etc.?

This is no different from any other confidence interval. If the confidence interval contains zero, then the correlation is not significant, and the sig level will be large.

So you mean to say, that if it contains a zero, we say that we accept the null hypothesis (they are same) in all case?

Or do you mean that if it contains a zero, we negate what the p value told us.

For example, p value is 0.06 which tells us that the 2 groups are same. However, the confidence intervals include a 0 between them.

So in such a case, do we say that the conclusion that they are same is wrong, and we accept the alternate hypothesis that they are different.

I just wish to know that if there is a 0 between the CI interval, we believe the opposite conclusion given by p value right?

a p value tells you the probability of a difference that large or greater if the null hypothesis is true. A CI at a given confidence level tells you the range of differences under H0 that lie within that interval. It is not a statement that the p value is wrong.

Okay I got it. But I am still confused as to how should I interpret the conclusion of the p value if there is a 0 between confidence interval.

So I'll attach 2 references from where I get the doubt.

https://methods.sagepub.com/dataset/howtoguide/bootstrapping-ehs-2009

The link above shows an example and conclusion when both CI are positive.

https://www.youtube.com/watch?v=P3T96y3wijg&ab_channel=how2stats

The above video shows an example when there is a 0 in between and in this he concludes that the conclusion acc to the p value can be wrong. Hence, the actual conclusion is the opposite of what the p value gave