Consider for a moment that you may be comparing datasets (and results from them) incorrectly. "Significance" or rather the power is not independent of design. If Study A is done on 1,000 people but Study B is identical but includes only 100 volunteers, Study A is much more powerful, so (statistically) significant findings from A and (statistically) non-significant findings from B are non-surprising. There are better methods for comparing two studies, like a forest plot.
I only mention this because it all depends on the "you" you are trying to sell for this application. An undergraduate level sociologist doesn't need to have a graduate level statistics education, but if you are boasting it as a strength, you should be sure that you are correctly interpreting a set of findings.
The word "negative" (result or study) is an abuse of statistical terminology. There are issues of power, context, and precision; but adept researchers are readily throwing the baby out with the bathwater. Stop for a moment and think:
"Do not reject H_0" means that the confidence limits include the null hypothesized value(s): 0 for differences or 1 for ratios. So what?
1) Was this study sufficiently powered or is it a complete shot-in-the-dark? Large, untenable confidence intervals can represent a crappy study or it can reflect substantial heterogeneity in the population. Were there issues with recruitment or compliance? Did you need to compensate people better? Did you administer an existing instrument and if so, did you assess yourself or the patients to be sure the wording is clear? If it's a trainwreck study you can focus on lessons learned. E.g.
we recruited 30 people based on an incorrect power calculation, our effect estimate had a much smaller magnitude than was noted in previous literature. This is a cause for some concern given our calculation was based on previous research which claimed that...
2) Is the CI narrowly on 0 or 1 excluding all other research? This is a significant finding because it is inconsistent with other literature. There's a whole field of research devoted to determining the effects of publication bias. Funnel Plots show the expected distribution of effects from meta-analyses. If the distribution is shifted with a gap at H0 it gives some pause as to whether the state of evidence is exaggerated by filtering out null findings? Important landmark research has been able to conclusively say, "No. A certain treatment does not / cannot cause a difference.
3) Is the CI wide but centered on a result which confirms previous research. For instance:
A 5,000 person study of salt reduction found that the HR for MI was 0.95 95%CI 0.92, 0.99 (p < 0.05). A confirmation study of 100 found a HR for MI of 0.95 95% CI 0.5, 1.45. (p > 0.05).
Importantly these studies agree 100%.