. Comparing a Single Patient versus a Group of Controls (and Spm)

1.1 Z-scores versus one-sample T-tests If we knew the mean, µ , and standard deviation, σ , of the control "population", we could construct the "Z-score": σ µ p Z − = where p is the single patient score, and determine the probability of obtaining a Z-score this large from the "Z-distribution" (or "normal" or "Gaussian" distribution). In practice, Z-scores are often tested this way when the group of controls is large, such that one has very reliable estimates of the population mean and standard deviation (e.g, when using "norm-based" tests). However, when we estimate µ and σ from a small sample of the population, we need to acknowledge that our values of µ and σ are estimated quantities that have associated errors. Firstly, we need to take into account the distribution of the mean (i.e, the range of values of the mean that would obtain if we took many samples from the population).