## Sunday, 13 December 2009

### Jacknife Test

Miller (1968) introduced a test based on the jacknife technique for testing the null hypothesis (F 2.1) in two-sample examples. This test used the value which is defined as:

(F 2.13)

In the equation above, is defined as follows (being the ith sample mean excluding the jth observation) :

Based on the conjecture by Turkey (1962) that are distributed approximately independently, this lead Miller to use the values which are defined as:

(F 2.14)

Miller proposed testing the null hypothesis (F 2.1) using a two-sample t-test derived from the . Miller demonstrated that:

(F 2.15)

And that the convergence in probability can be shown to be,

(F 2.16)

Miller demonstrates that this test asymptotically robust. The Monte Carlo simulations have validated that Miller’s Jacknife robust with a diverse assortment of population distributions.

Layard (1973) proposed a K-sample generalisation of the Miller two-sample jacknife test based on a one-way analysis F test. This test was derived using the values as follows:

(F 2.17)

Using the Layard variation of the Jacknife test, the null hypothesis (F 2.1) will be rejected were the J statistic exceeds the percentile of an F-distribution with (K-1) and (n-K) degrees of freedom.