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I did a Spearman correlation test and I used 14 samples(12 form group 1 and 2 form group 2). P value =0.04. here is the plot: enter image description here

I repeated the analysis for group 1 only (12 samples) and removed group 2 (2 data points). The significant is lost and p value become high p=o.11. here is the second plot: enter image description here

The question is: Is the loss of the significant p value because it was driven by 2 data points from group 2 or there is no enough power for the second analysis?. Can I conclude that there result is not significant as it was driven by 2 points for the first case(group 1 and 2 first plot)? your help is very appreciated.

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    $\begingroup$ Why did you pool the two groups together when estimating a coefficient? Are these two groups comparable? Did you pool them together because you only have two units in the second group? $\endgroup$
    – user2974951
    Jul 25 at 6:36
  • $\begingroup$ Hi @user2974951 we did our analysis for both groups first and for group 1 alone in the second analysis. so we removed the 2 data points just because it belongs to group 2. $\endgroup$
    – Marwah Al-kaabi
    Jul 25 at 7:25
  • $\begingroup$ The 2 groups are related to different genetic background $\endgroup$
    – Marwah Al-kaabi
    Jul 25 at 7:30

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Once you have performed multiple tests, you should really correct for them. Under the standard corrections, all your tests will be non-significant. Which is not surprising, because you have very little data, and the correlation is indeed quite weak.

Then again, this is a bit of a purist position. You would not be the first to report an uncorrected p-value for the overall analysis, and p-values corrected for only two tests on two subgroups. (Or here, an uncorrected p-value for a single subgroup.)

Your results on the total dataset are driven by the two data points. It makes no sense to discuss "post-hoc power" after you have observed the data (Hoenig & Heisey, 2001)).

Finally, note that The Difference Between “Significant” and “Not Significant” is not Itself Statistically Significant (Gelman & Stern, 2006).

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