Hartley's test

In statistics, Hartley's test, also known as the "F"_max test or Hartley's "F"_max, is used in the analysis of variance to verify that different groups have a similar variance, an assumption needed for other statistical tests.

It was developed by H. O. Hartley, who published it in 1950.

The test involves computing the ratio of the largest group variance, max(s_j²) to the smallest group variance, min(s_j²). The resulting ratio, F_max, is then compared to a critical value from a table of the sampling distribution of F_max [1] . If the computed ratio is less than the critical value, the groups are assumed to have similar or equal variances.

Hartley's test assumes that data for each group are normally distributed. This test, although convenient, is quite sensitive to violations of the normality assumption [2] . Alternatives to Hartley's test that are robust to violations of normality are O'Brien's procedure [3] , and the Brown-Forsythe test [4] .

ee also

Bartlett's test

References

*1. David, H.A. (1952). "Upper 5 and 1% points of maximum F-ratio." "Biometrika" 39:422-424.
*2. O'Brien, R.G. (1981). A simple test for variance effects in experimental designs. "Psychological Bulletin", 89:570-574.
*3. Ibid.
*4. Keppel, G. and Wickens, T.D. (2004). Design and analysis (4th ed.). Englewood Cliffs, NJ: Prentice-Hall.