RESEARCH ARTICLE Scott M. Lewis Æ Trenton A. Jerde Charidimos Tzagarakis Æ Pavlos Gourtzelidis Maria-Alexandra Georgopoulos Æ Nikolaos Tsekos Bagrat Amirikian Æ Seong-Gi Kim Kaˆmil Ug˘urbil Æ Apostolos P. Georgopoulos Logarithmic transformation for high-field BOLD fMRI data Received: 27 August 2004 / Accepted: 22 February 2005 / Published online: 15 July 2005 Ó Springer-Verlag 2005 Abstract Parametric statistical analyses of BOLD fMRI data often assume that the data are normally distrib- uted, the variance is independent of the mean, and the effects are additive. We evaluated the fulfilment of these conditions on BOLD fMRI data acquired at 4 T from the whole brain while 15 subjects fixated a spot, looked at a geometrical shape, and copied it using a joystick. We performed a detailed analysis of the data to assess (a) their frequency distribution (i.e. how close it was to a normal distribution), (b) the dependence of the standard deviation (SD) on the mean, and (c) the dependence of the response on the preceding baseline. The data showed a strong departure from normality (being skewed to the right and hyperkurtotic), a strong linear dependence of the SD on the mean, and a proportional response over the baseline. These results suggest the need for a loga- rithmic transformation. Indeed, the log transformation reduced the skewness and kurtosis of the distribution, stabilized the variance, and made the effect additive, i.e. independent of the baseline. We conclude that high-field BOLD fMRI data need to be log-transformed before parametric statistical analyses are applied. Keywords Logarithmic transformation Æ fMRI Æ BOLD Æ Brain Introduction Traditionally, BOLD fMRI data are analyzed using parametric statistical analyses without any transforma- tion. However, such analyses (e.g. t-test, ANOVA, linear regression, etc.) typically assume that the data are nor- mally distributed, the variance is independent of the mean, and the effects are additive, i.e. independent of the baseline. However, departures from these assumptions, especially the heteroskedasticity (i.e. inequality of the variances) and nonadditivity are likely to have serious effects on the results (Snedecor and Cochran 1989, pp. 273–296). Such violations could be due to physio- logical factors that underlie the measurements. For example, many functional maps in the fMRI literature are presented as percentage changes from the baseline, which assumes that the effect depends on the baseline; in S. M. Lewis (&) Æ T. A. Jerde Æ C. Tzagarakis P. Gourtzelidis Æ M.-A. Georgopoulos B. Amirikian Æ A. P. Georgopoulos Veterans Affairs Medical Center, Brain Sciences Center, One Veterans Drive, Minneapolis, MN 55417, USA E-mail: lewis093@umn.edu S. M. Lewis Æ A. P. Georgopoulos Department of Neurology, University of Minnesota Medical School, Minneapolis, MN 55455, USA S. M. Lewis Æ T. A. Jerde Æ S.-G. Kim K. Ug˘urbil Æ A. P. Georgopoulos Graduate Program in Neuroscience, University of Minnesota, Minneapolis, MN 55455, USA T. A. Jerde Æ A. P. Georgopoulos Center for Cognitive Sciences, University of Minnesota, Minneapolis, MN 55455, USA C. Tzagarakis Æ P. Gourtzelidis Æ B. Amirikian A. P. Georgopoulos Department of Neuroscience, University of Minnesota Medical School, Minneapolis, MN 55455, USA M.-A. Georgopoulos Æ N. Tsekos Æ S.-G. Kim Æ K. Ug˘urbil Department of Radiology, University of Minnesota Medical School, Minneapolis, MN 55455, USA N. Tsekos Æ S.-G. Kim Æ K. Ug˘urbil Center for Magnetic Resonance Research, University of Minnesota Medical School, Minneapolis, MN 55455, USA A. P. Georgopoulos Department of Psychiatry, University of Minnesota Medical School, Minneapolis, MN 55455, USA E-mail: omega@umn.edu Tel.: +1-612-7252282 Fax: +1-612-7252291 Exp Brain Res (2005) 165: 447–453 DOI 10.1007/s00221-005-2336-4