Unfortunately for the standard approach, the real relationship is radically different from a threshold, instead having a concave shape that continually flattens, reflecting diminishing marginal returns. This characteristic shape was recently verified for a wide variety of measures of projected value that have been proposed for use in sample size planning, including power . Falling short of any particular arbitrary goal, notably 80% power, is therefore not the calamity presumed by conventional thinking. The lack of any threshold undercuts the foundation of current standards--they guard against a non-existent danger.Figure 1. Qualitative depiction of how sample size influences a study's projected scientific and/or practical value. A threshold shaped relationship (dashed line) would create a meaningful distinction between adequate and inadequate sample sizes, but such a relation does not exist. The reality (solid line) is qualitatively different, exhibiting diminishing marginal returns. Under the threshold myth, cutting a sample size in half could easily change a valuable study into an inadequate one, but in reality such a cut will always preserve more than half of the projected value.
Table 1. Sample layout of sensitivity analysis. Shown are possible study results with a given sample size (935 per group, based on the vitamin study discussed above ), for a yes or no outcome. Rows have differing assumptions concerning precision of the estimates, ranging from high precision (top row) to low precision (bottom row). For a continuous outcome, the rows would instead be for optimistic (small), expected, and pessimistic (large) standard deviations.The entries in the table are exactly the key results that interpretation should focus on when the study is completed, so this properly aligns planning with eventual use. The middle row can be a best guess such as would be used for conventional calculations; the other rows should reflect a reasonable range of uncertainty, which will depend on what is already known about the topic being studied. For the columns, inclusion of the intermediate case is important, because this will often include the most problematic or disappointing potential results. The vitamin study  paired a safe and inexpensive intervention with a severe outcome, so even results in the middle column would be regarded as encouraging; the actual completed study landed essentially in box 7, which should have been interpreted as very encouraging even though not definitive. Boxes 8 and 9 will usually be the least useful, but as noted above (False assurance), the risk of disappointing results is always present and should not be considered a flaw in study design.