### Useful Papers - Contrasts

**Primary**:

Ward, AFNI 3dDeconvolve manual (in particular, pages 5-16 and 43-47) PDF

Summary: An excellent overview of the basic statistical model and the difference between F- and t-tests. Some good examples (p.43-47) of how to design contrasts to test particular questions about the differences between two or more impulse functions. Also contains a good overview of the deconvolution model and its derivation from the basic statistical model.

Bottom line: F-tests simultaneously test several linear contrasts; t-tests only test one at a time.

Veltman & Hutton, SPM99 Manual (in particular, pages 65-80 - some about PET and a lot of junk in there, but some good clean summaries of how to make F-contrasts or conjunction tests and what they mean (e.g., p. 73)) PDF

Summary: Some nice walk-throughs of how to design conjunction contrasts, F-contrasts, and other somewhat advanced techniques in SPM. Some particularly good points are made about F-contrast construction - how to make them for several basis functions at once, for example, their relation to t-contrasts, and other points.

Bottom line: Describes F-contrasts as an OR-ing of linear constraints and conjunctions as a conjunction of 'em.

Friston, "Statistical Parametric Mapping", chapter to appear in *Human Brain Function II* (pages 19-23, and 24-26 to a lesser degree) PDF

Summary: Further, quite concise, overview of the GLM and what contrasts mean. A nice breakdown of how the various ways of testing for activity (correlation coefficient, ANOVA, etc.) all break down to the GLM, and explanation of why the T-contrast (and hence F-contrast) supersede those ways generally. Some description of the 'basis function' model of HRF that transitions between the canonical and the FIR model.

Bottom line: The T-contrast serves as a more versatile version of the correlation coefficient, and the F-contrast tests a combination of T-contrasts.

Friston et. al, "Event-related fMRI: characterizing differential responses," NeuroImage 7, 30-40 PDF

Summary: Introduction of the basis-function approach to event-related analysis, where the design matrix is convolved with a non-Fourier basis function set, designed to span the space of reasonable responses in a compact way. The set introduced here separately models the magnitude and latency of a canonical HRF, and experimental evidence shows different areas differ on those two different metrics.

Bottom line: The basis-function approach can be an effective way to analyze event-related data and can shed light on otherwise difficult-to-interpret questions about the impulse response function

Price & Friston, "Cognitive conjunction: a new approach to brain activation experiments," NeuroImage 5, 261-270 PDF

Summary: The original paper describing conjunction designs as an alternative to subtraction designs. The difference from subtractions is outlined, as are the important ways conjunction analyses fit in well with factorial designs. A primitive way of doing a conjunction analysis (since discarded) is laid forth, and some PET data analyzed with these methods is examined.

Bottom line: Conjunction experiments can test for conjunctions of linear constraints - an important set of questions that hadn't been examined up to this point.

Price et. al, "Subtractions, conjunctions and interactions in experimental design of activation studies," Human Brain Mapping 5, 264-272 PDF

Summary: A follow-up to the Price & Friston paper above, this paper more explicitly describes the difference between conjunction and subtraction analyses in terms of how the former takes account of the interaction term (should there be one). Factorial designs used with conjunction analyses allow a much more explicit treatment of those interactions. Some PET data is examined.

Bottom line: Follow-up to above; more detailed in its treatment of interaction terms.

Friston et. al, "Multisubject fMRI studies and conjunction analyses," NeuroImage 10, 385-396 PDF

Summary: Attempts to get by one big hurdle of the standard conjunction analysis, which is that it's only available in fixed-effect fashion, preventing that style of analysis from being used in a true random-effects group model. The authors suggest a formula that allows one to used a fixed-effect conjunction group model and calculate a reasonable confidence interval of the population that might share such an effect.

Bottom line: Extension (slightly shaky) of the conjunction-analysis model to the group level.