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Use of significance tests is often misleadingly oversimplified by putting too much emphasis on whether p is above or below 0.05. A p < 0.05 means the result is statistically significant at the 5% level, but is an arbitrary guideline. It does not mean one has firm proof of an effect. By definition, even if two treatments are truly identical there is a 1 in 20 chance of reaching p < 0.05. Also, p > 0.05, not statistically significant (or n.s.), does not necessarily imply that a clinically meaningful difference does not exist.

This concept is illustrated graphically in Figure 6.1. In the left hand panel of this figure, similar treatment effects are obtained from two different studies, one of which is significant and one is not. The lack of significance alone should not be the sole metric on which to interpret the findings, particularly as the effect size appears to be large, albeit imprecise. In contrast, in the right‐hand panel, a p‐value of 0.05 is obtained with two very different effect sizes, one which is large and another that is much smaller. Again, focusing on the p‐value alone as the sole discriminator of importance in treatment effect would ignore the very large and perhaps clinically relevant gradient of effect between the treatments.

Figure 6.1 Interpreting p‐values.