Does “Not Different” Equal “The Same”? Nadia Huancahuari, MD, David L. Schriger, MD, MPH  Annals of Emergency Medicine  Volume 57, Issue 2, Pages 175-181 (February 2011) DOI: 10.1016/j.annemergmed.2010.10.001 Copyright © 2011 American College of Emergency Physicians Terms and Conditions

Figure 1 This graphic shows 3 possible distributions representing prior belief about a treatment effect. The lavender curve suggests that we believe that there is no difference between antibiotic and placebo and we are fairly certain that if there is an effect, it is not greater than 2% in either direction. The blue curve suggests that we believe that antibiotic is better by 2% but that we have little certainty about our belief. The curve is consistent with a wide range of differences, some favoring placebo and others, antibiotic. The green curve suggests that we are quite certain that there is 2% less treatment failure when antibiotics are provided. Annals of Emergency Medicine 2011 57, 175-181DOI: (10.1016/j.annemergmed.2010.10.001) Copyright © 2011 American College of Emergency Physicians Terms and Conditions

Figure 2 This figure depicts a Bayesian analysis of this study's data. The black distribution shows the prior belief, an estimate of our state of knowledge about this issue (largely drawn from the article by Duong et al8). The distribution shows that our best guess is that there is 1.2% less treatment failure when antibiotics are used and that it is unlikely that this number exceeds 10% or is less than 0% (implying that there are more treatment failures when antibiotics are used). The red distribution shows the results of the study by Schmitz et al.9 Although the study suggests that there is 9.1% less failure when antibiotics are provided, the study is consistent with a wide range of values. The blue distribution is derived by combining the experimental results with prior belief. It suggests that there are 3% to 4% less treatment failures when antibiotics are used and this number is unlikely to be higher than 8%. Annals of Emergency Medicine 2011 57, 175-181DOI: (10.1016/j.annemergmed.2010.10.001) Copyright © 2011 American College of Emergency Physicians Terms and Conditions