What are s-values?

P-values are a common measure of statistical significance that are often misunderstood.

One issue is that the scale of p-values can be difficult to interpret. For example, small p-values such as 0.0001 and 0.00001 are easily confused, and many readers often convert p-values to fractions ($\frac1{100}, \frac1{1,000}, \frac1{10,000}$), rounding them in the process (e.g., $0.0103 \approx 0.01 = \frac1{100}$).

S-values address the issue of interpretability by converting p-values into a more tangible representation of probability: the number of heads in a row on a fair coin.

Figure 1 shows the relationship between s-values and p-values. A p-value of 0.5 corresponds to an s-value of 1, since a probability of 0.5 corresponds to a single successful coin flip. Similarly, the common significance cutoff of 0.05 is equivalent to flipping 4.32 heads in a row.

S-values are particularly convenient when comparing or evaluating p-values that are very small or correspond to difficult fractions. See Table 1 below for some examples.