I have performed a meta-analysis and found a certain pooled effect with 95% CI that was

**not**statistically significant (p>0.05). Consequently, I have done a sensitivity analysis for which I have excluded studies that contributed most to heterogeneity.

In order to do so I used the Leave-one-out method to determine which studies contributed most and have excluded studies so heterogeneity (I^2) would decrease to 35% or less.

However, the pooled effect remained nearly the same but the 95% CI became narrower and my result is now statistically significant (p<0.05).

I think this is because heterogeneity is linked to the standard error of each study, and when excluding studies with large standard errors the overall 95% CI becomes narrower to the point where zero is no longer included in the confidence interval making the result statistically significant.

Is my rationale correct?

Thanks in advance,

Tom