What are s-values?

Mon, 25 May 2026 00:00:00 +0000

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.

Figure 1: The relationship between s-values and p-values.

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.

Table 1: Example conversions from p-values to their equivalent simplest fractions and (rounded) s-values.
P-value	Fraction	S-value
0.5000000	1 / 2	1.00
0.2500000	1 / 4	2.00
0.1000000	1 / 10	3.32
0.0625000	1 / 16	4.00
0.0500000	1 / 20	4.32
0.0100000	1 / 100	6.64
0.0058366	3 / 514	7.42
0.0010000	1 / 1000	9.97
0.0001000	1 / 10000	13.30
0.0000010	1 / 1e+06	19.90

Statistics | Poisson Consulting

What are s-values?