# Question about interpreting change in significance of correlation analysis when removing several subjects

Hypothetical example: Let's say someone is interested in the correlation of two continuous variables; let's say the correlation between test scores (specifically test scores on a math test and a verbal test) with cortisol levels in people with depression. They calculate Spearman's rho for 12 subjects and they find a strong and significant negative correlation between verbal test score and cortisol (rho = -.65, p = .045) and they also find a strong and significant negative correlation between math test score and cortisol (rho = -.75, p = .035). Now let's say that four of the subjects with a particular subtype of depression are removed from the group of 12 (so now there are 8 participants), and the same correlations are calculated for the remaining 8 participants. Let's say that size/strength of the correlations are virtually identical or very similar, but let's say that the results are no longer significant: let's say specifically that for the correlation between verbal test score and cortisol rho = -.63 and p = .115 and for the correlation between math test score and cortisol rho = -.77 and p = .105. My interpretation here is as follows: Given that larger sample sizes are better at finding true effects, and also given that the strength of the correlation was virtually identical in both the group of 12 and group of 8 and also since the p values in the group of 8 only increased by .07 compared to the group of 12, then it appears to me that since the sample size was so small to begin with (n = 12) and was even smaller after the removal of 4 subjects (n = 8) it was likely simply the reduction of the sample size by 4 subjects that caused the loss of significance and the loss of significance had nothing to do with removing subjects with the particular subtype of depression. And it's unlikely that the the particular subtype of depression of the four subjects that were removed was what was driving the effects that were seen when the correlations were calculated for the full group of 12. Does that sound like a reasonable interpretation of what is likely going on here?

Thanks!