Lewis Scott M, Jerde Trenton A, Tzagarakis Charidimos, Gourtzelidis Pavlos, Georgopoulos Maria-Alexandra, Tsekos Nikolaos, Amirikian Bagrat, Kim Seong-Gi, Uğurbil Kâmil, Georgopoulos Apostolos P
Veterans Affairs Medical Center, Brain Sciences Center, One Veterans Drive, Minneapolis, MN 55417, USA.
Exp Brain Res. 2005 Sep;165(4):447-53. doi: 10.1007/s00221-005-2336-4. Epub 2005 Jul 15.
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.
对血氧水平依赖性功能磁共振成像（BOLD fMRI）数据进行参数统计分析时，通常假定数据呈正态分布、方差与均值无关且效应具有可加性。我们评估了在4 T磁场下，15名受试者注视一个点、观察一个几何形状并使用操纵杆进行复制时，全脑采集的BOLD fMRI数据是否满足这些条件。我们对数据进行了详细分析，以评估（a）其频率分布（即与正态分布的接近程度），（b）标准差（SD）与均值的相关性，以及（c）响应与先前基线的相关性。数据显示出明显偏离正态分布（向右偏态且峰度较高）、SD与均值之间存在强烈的线性相关性，以及在基线上的比例响应。这些结果表明需要进行对数变换。实际上，对数变换降低了分布的偏度和峰度，稳定了方差，并使效应具有可加性，即与基线无关。我们得出结论，在应用参数统计分析之前，高场BOLD fMRI数据需要进行对数变换。
