Understanding Confidence Intervals to Reach Significance My question is in regards to whether you can use confidence intervals to claim statistical significance?  For example, if I calculate the CI at 95% for weekly sales to be between $100–$200 and one week I reach sales of $250, is this a significant result?  If not, how exactly would you describe the effect in relation to the CI we calculated?
 A: Sometimes you can interpret CI coverage in terms of significance testing, and sometimes you cannot depending on the specific test and null hypothesis. There's a literature on the issues that arise which is sometimes termed 'visual hypothesis testing', a brief bibliography of which is presented here (I might start with the article by Geoff Cumming):
Afshartous, D. and Preston, R. (2010). Confidence intervals for dependent data: Equating non-overlap with statistical significance. Computational Statistics & Data Analysis, 54(10):2296–2305.
Browne, R. H. (1979). On visual assessment of the significance of a mean difference. Biometrics, 35(3):657–665.
Cumming, G. (2009). Inference by eye: reading the overlap of independent confidence intervals. Statistics In Medicine, 28(2):205–220.
Goldstein, H. and Healy, M. J. R. (1995). The graphical presentation of a collection of means. Journal of the Royal Statistical Society. Series A (Statistics in Society), 158(1):175– 177.
Payton, M. R., Miller, A., and Raun, W. (2000). Testing statistical hypotheses using standard error bars and confidence intervals. Communications in soil science and plant analysis, 31(5):547–551.
Payton, M. E., Greenstone, M. H., and Schenker, N. (2003). Overlapping confidence intervals or standard error intervals: What do they mean in terms of statistical significance? Journal of Insect Science, 3(34):1–6.
Smith, R. W. (1997). Visual hypothesis testing with confidence intervals. In Proceedings of the Twenty-Second Annual SAS® Users Group International Conference.
Tryon, W. W. and Lewis, C. (2008). An inferential confidence interval method of establishing statistical equivalence that corrects Tryon’s (2001) reduction factor. Psychological Methods, 13(3):272–277.
