The rules behind the statistics

This section shows the three rules that decide what is computed and what is caveated on this page: the minimum count a test needs before it runs, the count below which a test carries a note that one company can move the result, and the denominators the sample statistics use.

The case is the revenue-against-hashrate fit. The universe holds 18 miners. The fit uses 11 of them as points. The annualized revenue distribution covers 16 miners.

We check the first rule. A test runs only when its point count meets 3. The fit's count, 11, is at or above that floor, so the test is computed.

We check the second rule. When a test's point count falls below 8, the result carries a caveat: one company in the sample can shift the estimate. The fit's count, 11, is compared against 8 to decide whether that note appears beside the result.

The third rule sets the denominators. The fit estimates two parameters, a slope and an intercept. The degrees of freedom is the point count with those two subtracted.

Point count: 11

Degrees of freedom: 9

The difference between them names the parameters the fit holds:

2

That is the two parameters, the slope and the intercept, estimated from the points before the spread is measured.

The sample standard deviation of the revenue distribution uses a different denominator. It divides the sum of squared deviations by the count minus one:

Denominator for the sample standard deviation: 16 minus one

The minus-one and the minus-two look arbitrary, but they do the same job. They correct for the fact that we are estimating from a sample rather than measuring the whole population. The degrees of freedom is smaller because the fit spends two of the points' information on the slope and intercept before measuring the residual spread.

The rules do three things. They gate which tests appear at all. They flag the tests where a single company can sway the number. They set the denominators so the sample statistics describe the spread of the observed points.