Basics of fMRI data analysis

Data in two fMRI time courses are collected, which have been obtained from each voxel in an experiment with two conditions, a control condition (“Rest”) and a main condition (“Stim”). Each condition has been measured several times. Note that in a real experiment, one would not just present the control and main condition only once, but one would design several “on-off” cycles in order to be able to separate task-related responses from potential low-frequency drifts. The data is assessed to find the response values are higher in the main condition than in the control condition. One approach consists in subtracting the mean value of the “Rest” condition, from the mean value of the “Stim” condition, note that one would obtain the same mean values and, thus, the same difference.

Data Processing through Statistical Parametric Mapping (SPM)

The difference in signal from control condition and main condition is very small. So the statistical data analysis helps more than simple subtraction. Statistical analysis essentially asks how likely it is to obtain a certain effect if there would be only noise fluctuations. The Statistical analysis is to obtained, if there are only noise fluctuations. This is formalized by the null hypothesis stating that there is no effect, i.e. no difference between conditions. In the case of comparing the two means (control and main) μ₁ and μ₂, the null hypothesis can be formulated as: H₀: μ₁ = μ₂. Assuming the null hypothesis, it can be calculated how likely it is that an observed effect would have occurred simply by chance. This requires knowledge about the amount of noise fluctuations which can be estimated from the data. By incorporating the variability of measurements, statistical data analysis allows to estimate the uncertainty of effects (e.g. mean differences) in data samples. If an effect is so large that it is very unlikely that it has occurred simply by chance (e.g. the probability is less than p = 0.05), one rejects the null hypothesis and accepts the alternative hypothesis stating that there exists a true effect. The decision to accept or reject the null hypothesis is based on a probability value. This has been accepted widely by the scientific community (p < 0.05). A statistical analysis, does not prove the existence of an effect, but it only suggests an effect. It is very unlikely that the observed effect has occurred by chance. Note that a probability of p = 0.05 means that if we would repeat the experiment 100 times we would accept the alternative hypothesis in about 5 cases although there would be no real effect. Since the chosen probability value thus reflects the likelihood of wrongly rejecting the null hypothesis, it is also called error probability.

The uncertainty of an effect is estimated by calculating the variance of the noise fluctuations from the data. For the case of comparing two mean values, the observed difference of the means is related to the variability of that difference resulting in a t statistic: