The accuracy of four approximations to noncentralF

The accuracy of the two-moment, three-moment, square root, and cube root approximations to the noncentralF distribution was assessed using 7,920 entries from Tiku’s (1967) power tables. Tiku’s tables list exact values of β for α= .005?.05, ν₁ = 1?12, ν₂ = 2?120, and ?= 0.5?3.0. Analysis of the errors showed generally satisfactory performance for all four approximations. The three-moment approximation was most accurate, registering a maximum error of only .009. The other three approximations had maximum errors of ±.02, except for the square root approximation at ν₂ = 2, where maximum errors of .05 occur. Approximation error increased with decreases in ν₁ and, less consistently, with increases in ν2. Error was nonmonotonically related to ?. A second investigation explored the accuracy of the approximations at values of αranging from .10 to .90. All four approximations degraded substantially in this situation, with maximum errors ranging from ?.09 to .05. If the analysis is restricted to cases where ν₁ τ; 1 and ν₂ τ; 2, maximum errors drop to roughly ±.03. We conclude that the approximations perform reasonably well for small αand moderately well for larger values, if certain restrictions are imposed. From a computational standpoint, however, there is little advantage to using approximate as opposed to exact methods unless exact values ofF _α are known in advance.