# Contents

- Introduction
- User Guide
- Theory
- FAQ

**randomise** is FSL's tool for nonparametric permutation inference on neuroimaging data.

If you use **randomise** in your research please cite this article:

Winkler AM, Ridgway GR, Webster MA, Smith SM, Nichols TE. Permutation inference for the general linear model. NeuroImage, 2014;92:381-397. (Open Access)

Permutation methods (also known as randomisation methods) are used for inference (thresholding) on statistic maps when the null distribution is not known. The null distribution is unknown because either the noise in the data does not follow a simple distribution, or because non-statandard statistics are used to summarize the data. **randomise** allows modelling and inference using standard GLM design setup as used for example in FEAT. It can output voxelwise, cluster-based and TFCE-based tests, and also offers variance smoothing as an option.

# Test Statistics in Randomise

**randomise** produces a test statistic image (e.g., `ADvsNC_tstat1`, if your chosen output rootname is `ADvsNC`) and sets of P-value images (stored as 1-P for more convenient visualization, as bigger is then "better"). The table below shows the filename suffices for each of the different test statistics available.

Voxel-wise uncorrected P-values are generally only useful when a single voxel is selected *a priori* (i.e., you don't need to worry about multiple comparisons across voxels). The significance of suprathreshold clusters (defined by the cluster-forming threshold) can be assessed either by cluster size or cluster mass. Size is just cluster extent measured in voxels. Mass is the sum of all statistic values within the cluster. Cluster mass has been reported to be more sensitive than cluster size (Bullmore et al, 1999; Hayasaka & Nichols, 2003).

# Accounting for Repeated Measures

Permutation tests do not easily accommodate correlated datasets (e.g., temporally smooth timeseries), as such dependence violates null-hypothesis exchangeability. However, the case of "repeated measurements", or more than one measurement per subject in a multisubject analysis, can sometimes be accommodated.

**randomise** allows the definition of exchangeability blocks, as specified by the group_labels option. If specfied, the program will only permute observations within block, i.e., only observations with the same group label will be exchanged. See the repeated measures example in the Guide below for more detail.

# Confound Regressors

Unlike with the previous version of **randomise**, you no longer need to treat confound regressors in a special way (e.g. putting them in a separate design matrix). You can now include them in the main design matrix, and **randomise** will work out from your contrasts how to deal with them. For each contrast, an "effective regressor" is formed using the original full design matrix and the contrast, as well as a new set of "effective confound regressors", which are then pre-removed from the data before the permutation testing begins. One side-effect of the new, more powerful, approach is that the full set of permutations is run for each contrast separately, increasing the time that **randomise** takes to run.

More information on the theory behind **randomise** can be found in the Theory section below.

# REFERENCES

The primary reference for **randomise**, which describes the algorithm for creating permutation tests with the GLM, is:

Winkler AM, Ridgway GR, Webster MA, Smith SM, Nichols TE. Permutation inference for the general linear model. NeuroImage, 2014;92:381-397. (Open Access)

For a gentle introduction to permutation inference, see:

Nichols TE, Holmes AP. Nonparametric permutation tests for functional neuroimaging: a primer with examples. Hum Brain Mapp. 2002 Jan;15(1):1-25.

For more details, see:

Anderson MJ, Robinson J. Permutation Tests for Linear Models. Aust New Zeal J Stat Stat. 2001;43(1):75-88.

Bullmore ET, Suckling J, Overmeyer S, Rabe-Hesketh S, Taylor E, Brammer MJ. Global, voxel, and cluster tests, by theory and permutation, for a difference between two groups of structural MR images of the brain. IEEE Trans Med Imaging. 1999;18(1):32-42.

Freedman D, Lane D. A Nonstochastic Interpretation of Reported Significance Levels. J Bus Econ Stat. 1983;1(4):292. doi:.

Hayasaka S, Nichols TE. Validating cluster size inference: random field and permutation methods. Neuroimage. 2003;20(4):2343-2356.

Holmes AP, Blair RC, Watson JD, Ford I. Nonparametric analysis of statistic images from functional mapping experiments. J Cereb Blood Flow Metab. 1996 Jan;16(1):7-22.

Kennedy PE. Randomization Tests in Econometrics. J Bus Econ Stat. 1995;13(1):85–94.

Salimi-Khorshidi G, Smith SM, Nichols TE. Adjusting the effect of nonstationarity in cluster-based and TFCE inference. Neuroimage. 2011;54(3):2006-2019.

Smith SM, Nichols TE. Threshold-free cluster enhancement: addressing problems of smoothing, threshold dependence and localisation in cluster inference. Neuroimage. 2009;44(1):83-98.

Copyright © 2004-2014, University of Oxford. Written by T. Behrens, S. Smith, M. Webster and T. Nichols.