Logarithmic transformation for high-field BOLD fMRI data

Scott M. Lewis, Trenton A. Jerde, Haris Tzagarakis, Pavlos Gourtzelidis, Maria Alexandra Georgopoulos, Nikolaos Tsekos, Bagrat Amirikian, Seong Gi Kim, Kamil Ugurbil, Apostolos P Georgopoulos

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9 Scopus citations


Parametric statistical analyses of BOLD fMRI data often assume that the data are normally distributed, 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 logarithmic 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.

Original languageEnglish (US)
Pages (from-to)447-453
Number of pages7
JournalExperimental Brain Research
Issue number4
StatePublished - Aug 2005

Bibliographical note

Funding Information:
Acknowledgements This work was supported by United States Public Health Service grant NS32919 and P41 RR08079 (National Center for Research Resource (NCRR), the University of Minnesota Graduate School (T.A.J.), the United States Department of Veterans Affairs, and the American Legion Chair in Brain Sciences.


  • BOLD
  • Brain
  • Logarithmic transformation
  • fMRI


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