### Useful Papers - P-thresholds

**Primary**:

Genovese et. al (2002), "Thresholding of statistical maps in functional neuroimaging using the false discovery rate," NeuroImage 15, 870-878 PDF

Summary: Landmark paper applying Benjamini and Hochberg's original concepts (below) specifically to neuroimaging. Briefly reviews the concept of FDR, its mathematical background, and methods to control it, then demonstrates its use on sample and real fMRI datasets. Extremely readable and short - should be required reading for anyone using FDR control.

Bottom line: Indispensable citation for anyone interested in using FDR - and you should be.

Friston et. al (1996), "Detecting activations in PET and fMRI: levels of inference and power," (first couple of pages, at least) NeuroImage 4, 223-235 PDF

Summary: A good reference on Gaussian RFT methods in neuroimaging; reviews some of the ideas of FWE control in general and has a little bit of math, but not too much, on how Gaussian methods work. Set-, cluster- and voxel-level inferences are introduced, with power analyses for all and some discussion of when each is appropriate.

Bottom line: The voxel-level info is useful, as is the Gaussian RFT review.

Nichols & Holmes (2001), "Nonparametric permutation tests for functional neuroimaging: a primer with examples," (first ten pages) Human Brain Mapping 15, 1-25 PDF

Summary: A specific attempt to bring permuation tests to the masses, this is a clear and comprehensive introduction to permutation testing, with a concise but thorough review of the concepts, and, crucially, three fully worked-out examples showing how permutation testing is applied to PET and fMRI data.

Bottom line: Also indispensable, this time for anyone interested in using permutation testing.

**Supplementary**:

Nichols & Hayasaka (2003), "Controlling the familywise error rate in functional neuroimaging: a comparative review," Statistical Methods in Medical Research 12, 419-446 PDF

Summary: The best overview of FWE correction (with an excellent section on FDR) I've seen. Somewhat technical, but comprehensive. The authors review the mathematical background for several FWE correction methods (RFT, permutation, Bonferroni, etc.), and then, crucially, perform a variety of tests comparing the different methods in simulated and real data with various characteristics.

Bottom line: Comprehensive look at the advantages and disadvantages of every major method of p-threshold control, demonstrating the usefulness of FDR in low-smoothness data, the excellent performance of permutation testing, and the troubles of RFT methods outside high smoothness. Tremendously useful.

Benjamini & Hochberg (1995), "Controlling the false discovery rate: a practical and powerful approach to multiple testing," Journal of the Royal Statistical Society Series B 57, 289-300 PDF

Summary: The original paper describing the current method of FDR control. Authors review the concepts of FWE correction and discuss why they're not always appropriate, then describe a simple mathematical procedure to control FDR, using some examples to show how it may be used. They use simulations to show that the gain in power over FWE methods may be substantial.

Bottom line: Good background on FDR - the original paper introducing the concept.

Worsley et. al (1996), "A unified statistical approach for determining significant signals in images of cerebral activation," Human Brain Mapping 4, 58-73 (see Jeff for paper copies - PDF coming soon)

Summary: Not the first paper applying Gaussian RFT methods to neuroimaging data, but one of the most important ones. Worsley et. al bring together several lines of research on Gaussian RFT methods and tie up a number of loose threads to create a single statistical system for correcting FWE in neuroimaging (at the time, generally PET) data. This paper's approach is the foundation of SPM96 and SPM99's FWE correction.

Bottom line: A landmark in Gaussian RFT methods as applied to neuroimaging.

Bullmore et. al (1999), "Global, voxel, and cluster tests, by theory and permutation, for a difference between two groups of structural MR images of the brain," IEEE Transactions on Medical Imaging 18, 32-42 PDF

Summary: An experimental paper showing the viability of permutation testing for a variety of different statistics in a group-analysis setting. Bullmore et. al look at practical issues surrounding permutation testing of various different statistics in real structural data.

Bottom line: Nice look at permuation testing in a practical setting.