Work out reliability of a test instantly with clear inputs, formula shown and shareable results.
The Spearman-Brown prophecy formula predicts reliability after changing test length: k.r/(1 + (k-1)r). Doubling a test at reliability 0.72 lifts it to 0.837, a gain of 0.117. Reaching 0.90 would need 3.5 times the length, which shows the sharply diminishing returns of simply adding items.
Spearman-Brown formula
r(new) = k x r / (1 + (k - 1) x r)
Length required
k = target(1 - r) / (r(1 - target))
Only if they are of comparable quality and measure the same construct. Adding poor items can lower reliability rather than raise it.
Because reliability is bounded at one. Each extra item reduces the remaining error variance by a smaller absolute amount.