Fig. 2.

Flowchart of Bootstrap algorithm.

Because the distribution of signal intensity in a given voxel over repeated measurements cannot be assumed to be normal the parametric F-test may not provide accurate p-values. This bootstrap procedure is the non-parametric equivalent of the parametric F-test and provides unbiased p values. Step 1) Obtain data with (blue, n^T = 20) and without triggering (red, n^N = 20). Step 2) Pool the triggered and non-triggerred data Step 3) randomly draw (with replacement) N = n^T + n^N = 40 images from the pooled data. Consider the first 20 images as a pseudo dataset with triggering, the other 20 as a pseudo dataset without triggering. Repeat this re-sampling procedure 10,000 times, calculate the variance for each of the resamples of pseudo triggered (σ_b1^T, σ_b2^T,…, σ_b10000^T) and pseudo non–triggered data (σ_b1^N, σ_b2^N,…, σ_b10000^N) and their respective ratios (F₁^b, F₂^b, … F₁₀₀₀₀^b) and store the results. Step 4), calculate the variance of the original triggered (σ^T) and the original non-triggered (σ^N) dataset and their ratio $F=\raisebox{1ex}{${\sigma }^N$}\!\left/ \!\raisebox{-1ex}{${\sigma }^T$}\right.$. Step 5), compare the F value of the original data (F) to the distribution of 10,000 pseudo F^b values obtained from the bootstrap re-sampling procedure. Step 6), identify voxels where fewer than 5 of the 10,000 pseudo F^b values are larger than the original F value. This corresponds to p < 0.0005 meaning that if the triggered and non-triggered data were drawn from the same distribution, there is less than 5 in 10,000 chance to obtain an F value that is as large; i.e. in a given voxel where there is no difference in variance there is only a 5/10000 chance that we would say there is.