How jackknifing works

The jackknife method uses less computational effort than a bootstrap analysis and is thus often quicker and easier to undertake. However, it cannot be used to estimate confidence intervals.

The general scheme is as follows:

1.        Consider a situation where a parameter is to be estimated from n samples, e.g. a species diversity index from 10 kicknet samples from a stream.

2.        Use all n samples to calculate the parameter of interest, E, the diversity index.

3.        Now remove one of the samples at a time and recalculate the parameter of interest, Ei.

4.        Calculate the pseudovalues for the parameter of interest :

where  n = the total number of replicates, E = the estimate for all n samples, Ei = the estimate with sample i removed.

5.        Estimate the mean and standard error of the parameter of interest from the n pseudovalues. The jackknife estimate of bias is E - the mean of the pseudovalues and the estimate of the standard error of the sample is simply the standard error of the pseudovalues:

where

is the mean of the pseudovalues.