Precision and consistency of treatment effects
95% confidence intervals are dependent upon sample size
Also, 95% confidence intervals act as the primary inference associated with unadjusted odds ratios, relative risk, hazard ratios, and adjusted odds ratios. If the confidence interval crosses over 1.0, there is a non-significant effect. Wide 95% confidence intervals are indicative of small sample sizes and lead to decreased precision of the effect. Constricted or narrow 95% confidence intervals reflect increased precision and consistency of a treatment effect.
In essence, p-values should not be what people get excited about when it comes to statistical analyses. The interpretation of your findings within the context of the subsequent population means, odds, risk, hazard, and 95% confidence intervals IS the real "meat" of applied statistics.