How many days a blind diary needs to detect a link

What the diary does

The blind diary hides every forecast. Each evening you rate your day from 1 to 5. At the end, each system's daily scores are compared with your ratings using Spearman's rank correlation, and a permutation test (5,000 shuffles of your ratings across the days) gives the p-value. A system counts as lining up with your days, or running against them, only at p below 0.05 ÷ 3.

Power

Power is the chance that a test detects a link that is really there. It depends on how strong the link is, measured by rho (0 for none, 1 for perfect), and on the number of days. The figures below use Fisher's z transformation with the Bonett–Wright variance for Spearman's rho, at the 0.05 ÷ 3 threshold.

Worked figures

A weak link, rho = 0.2: detected 19% of the time after 60 days, 30% after 90 and 41% after 120. Reaching 80% takes about 263 days.

A moderate link, rho = 0.3: detected 46% of the time after 60 days, 67% after 90 and 81% after 120. Reaching 80% takes about 118 days.

For rho = 0.2 at 60 days: z = atanh(0.2) = 0.203; its standard error is √((1 + 0.2² ÷ 2) ÷ (60 − 3)) = 0.134; 0.203 ÷ 0.134 = 1.52, against a critical value of 2.39 for p = 0.05 ÷ 3, two-sided. The chance of clearing it is about 19%.

Reading a result

Read the other way round, 60 days reliably pick up only a strong link (rho around 0.4, detected about three times in four). A result that isn't significant after 60 days is weak evidence: it argues against a strong link much more than against a weak one. Many days rated 3 create ties, which make these figures slightly optimistic.

Why blind

Seeing a forecast can colour how a day is remembered. Hiding the forecasts until the end removes that influence. Controlled tests of astrology, such as Shawn Carlson's double-blind study published in Nature in 1985, are built the same way, and have not found predictive power.

How Jyotishya uses it

The diary offers fixed lengths and reports which systems, if any, lined up with your ratings or ran against them more than shuffling usually manages. Before 20 rated days it reports nothing, and it says plainly that even 60 days can only pick up a strong link.