How Many Subjects Constitute a Study?

“Voxelwise random-effects analyses [5] for musicians, non-musicians, and all subjects combined, were performed in order to determine clusters of significant group activation, based on extent threshold of activated voxels and Gaussian Random Field theory.”

“Next, a random effects model was performed to make group statistical inferences (Friston et al., 1999a), and contrasts (described below) were applied using a false detection rate correction (Genovese et al., 2002) at p b 0.05.”

“In order to create activation maps representing the main effects of movement rates (0th order), as well as the linear (1st order) and non-linear (2nd, 3rd and 4th order) changes in signals in relation to movement rates, random-effect analysis was performed (Friston et al., 1999).”

“Firstly, to investigate the behaviour of the fMRI response in patients and controls, one-sample t tests were performed for each contrast in each group using a random-effects approach [21, 22].”

“Statistical inferences In order to compare the generic activations associated with each of the three groups, a two-stage random effects analysis was used for each hypothesis tested (Friston et al., 1999).”

“Second, to make inferences at a population level, individual data were summarized into a random effect model (Friston et al., 1999).”

“Data of the ten participants were averaged in a group analysis using the random effects model approach (second level analysis; (Friston et al. 1999).”

“A GLM corrected for first-order serial correlation was applied (Friston et al., 1999).”

“A General Linear Model (GLM) corrected for first-order serial correlation was applied [Friston et al., 1999].”

“Second, the summary data of each individual were incorporated into the second-level analysis using a random effects model [27]; this was used to make inferences at a population level regarding the task-related activation within each group and the differences between the groups.”

“The weighted sum of the parameters estimated in the individual analyses consisted of “contrast” images, which were used for the group analyses [21].”

“…the effect of the number of subjects (N-sub) necessary in a functional study to make inferences about the typical activation in a given task and population [Desmond and Glover, 2002; Friston et al., 1999b; Grabowski et al., 1996; Kiehl et al., 2005; Murphy and Garavan, 2004; Strother et al., 1997].”

“Significant signal changes for each contrast were assessed by means of t statistics on a voxel-byvoxel basis (Friston et al., 1999).”

“Fixed-effect analyses allow limited inference, as they do not permit findings to be generalized from a sample to a population of subjects (Friston et al., 1999; Holmes and Friston, 1998).”

“Data were analyzed using a random-effects model (Friston et al., 1999), implemented in a two-level procedure.”

“The GLM framework has been used to explore group effects by combining the single-subject analyses using spatial normalization [Penny and Holmes, 2004] for the purpose of making population level inferences [Friston et al., 1999; Worsley et al., 2002].”

“Statistical maps were generated using a random-effect model, implemented in a 2-levels procedure [33].”

“These dSPM maps were averaged across subjects after aligning their cortical surfaces, resulting in dynamic activation maps which can be interpreted as estimates of the of signal-to-noise at each point on the cortical surface, and thus analogous to the ‘‘z-score maps’’ often displayed in fMRI analyses (Friston et al. 1…”

“These interpretations should be seen in light of the fact that the PPI analysis was exploratory in nature and that our two key amygdala findings were not consistent as the correlation between condition-specific differences in BOLD activity and pain-related fear was observed in the right amygdala whereas the condition-…”

“A conjunction analysis across tasks (or subjects) may be another option but should be used carefully since it requires quite conservative statistical thresholding (Price and Friston, 1997; Friston et al., 1999a; 1999b).”

“This two-stage random effects analysis enables inferences based on these contrasts to be extended to the general population from which the subjects were drawn (Friston, Holmes, & Worsley, 1999 ).”

“Activations at the group level were obtained using a fixed-effect analysis following guidelines provided in (Friston et al., 1999).”

“For the group data, a random effects analysis was performed (Friston et al. 1999).”

“Using group analysis according to a random effect model that allowed inference to the general population (Friston et al, 1999), we first identified brain regions that showed a significantly greater response to unpleasant word sets in comparison with the response to neutral word sets among 4…”

“…size was chosen for two main reasons: firstly, a typical neuroimaging study of regional differences includes 12–16 subjects per experimental group (Friston et al., 1999); secondly, a recent analysis of effect size in classical inference has suggested that, in order to optimize the sensitivity to…”

“The Talairach transformed contrast images were entered into a group-level random-effect analysis (Friston et al., 1999), i.”

“…prescribed medication that may alter brain function), 3) fewer than 8 female and 8 male participants were included in the analysis (c.f., Friston et al., 1999), 4) female and male brain activity was not directly compared, 5) there were any confounds, or 6) a whole-brain analysis was not…”

“The PET images were preprocessed including anatomical standardization and global normalization to 50 ml/100 g/min, using the SPM2 statistical package (Wellcome Foundation, London), [Frackowiak, 2004; Friston et al., 1999; Savic et al., 2000, 2001].”

“Group analyses were investigated using fixed-effect analysis (FFX) (recommended by Friston et al., 1999a), which infers ''typical'' characteristics about the sample of participants.”

“The number of subjects in the study was relatively large (n1⁄433) and considerably above the number considered sufficient for fMRI studies of this nature [13], suggesting that the lack of strong significant differences is unlikely to be due to lack of statistical power.”

“Differently our study involved a larger sample, possibly allowing more sensitivity (Friston, Holmes, & Worsley, 1999).”

“Indeed group analysis can be very informative in identifying common regions of activity for a given task, and there has been much effort in determining the most appropriate method of group analysis for a variety of experimental situations (Friston et al., 1999).”

“At the single subject level, voxel-wise fixed effect contrast analyses were performed followed by random effect analyses at the group level using a general linear model to create SPM contrast maps [15].”

“Despite the small number of ARMS-T subjects available, we note that the use of a random effects approach with small sample sizes typically results in reduced sensitivity rather than false positive results in neuroimaging experiments (Friston et al., 1999).”

“At the group level, a random effects approach was applied ( Friston et al., 1999 ).”

“Images were analyzed using a two-stage random-effects approach (Friston et al. 1999).”

“A randomeffects analysis was used, so that any inferences drawn from the data can be applied to the general population (Friston et al., 1999).”

“Whilst the statistical power of functional magnetic resonance imaging (fMRI) data was shown to be relatively robust with small sample sizes (Friston et al. 1999), this is not the case for neuropsychological data.”

“Data were analyzed using a random-effects model (Friston et al. 1999), implemented in a 2-level procedure.”

“After estimation, beta values were taken to the second level for random effects analysis (Friston et al., 1999).”

“Then, to accommodate interparticipant variability, the images representing preparation-related and execution-related brain activity obtained from all participants were entered into a random effect group analysis with a one-sample t-test (13 degrees of freedom) (Friston et al., 1999).”

“random effects analysis (RFX GLM; (Friston et al., 1999)).”

“For the group, a random-eVects analysis was employed (Friston et al. 1999), so that any inferences drawn from the data can be applied to the general population.”

“Group analysis with a random-effect model The weighted sum of the parameter estimates in the individual analysis constituted ‘‘contrast’’ images, which were used for group analyses (Friston et al., 1999).”

“Normalization of each participant’s MRI to a common spatial framework was performed using SPM99 software (Wellcome Department of Cognitive Neurology, London, UK), implemented in MATLAB (The MathWorks Inc, Natick, Massachusetts, USA), through an automatic nonlinear stereotaxic normalization procedure [12], and restrict…”

“This intersubject variability obviously reduces the sensitivity of conventional intersubject analyses [Friston et al., 1999; Holmes and Friston, 1998; Wei et al., 2004] because these between-subject effects are treated as noise.”

“It has long been known, that FFX suffers from a high susceptibility to outliers, that is, single subjects with strong activations, as it only accounts for within-subject variance [38].”

“…in animal studies on whether the cortical motor system has evolved primarily for the organization of different actions rather than for movement control [Gallese et al., 1996; Graziano and Aflalo, 2007; Kohler et al., 2002; Rizzolatti et al., 1988; see, for a review, Fernandino and Iacoboni, 2010].”

“Given the relatively small sample size of the study, random-effects (‘second-level’) analyses were not appropriate (Friston, Holmes, & Worsley, 1999 ), thus, strictly speaking, our inferences relate only to the seven participants sampled (Penny, Holmes, & Friston, 2003 ).”

“Previous imaging investigations of pattern encoding have reported similar premotor cortex activity, and it has been proposed that this activity may subserve short-term maintenance of visuospatial in-”

“Group analyses were conducted according to a random effect model that permitted inferences to the general population (Friston et al., 1999).”

“Data were analyzed using a random-effects model (Friston et al., 1999), implemented in a two-level procedure.”

“The total score for the 11-item fatigue scale ranges from 0 to 33, with higher scores indicating greater fatigue.”

“Images were analyzed using a two-stage approach based on a random-effect model (Friston et al. 1999).”

“After the fMRI measurements, the subjects were moved outside of the MRI room, where they were again asked to match their force of grasping to the required % MVC for five trials with a hand dynamometer.”

“A general linear model (GLM) corrected for first-order serial correlation was applied (Friston et al., 1999).”

“…images for each comparison or effect were entered into second-level random effects analyses — these take into account intersubject variability, eliminate the possibility of one subject skewing the results, and allow inferences to be made regarding the population in general (Friston et al., 1999).”

“As we were uncertain whether adaptation effects might be reliably found in individual subjects, we changed our approach from a fixedeffects analysis to a random effects approach (RFX) where activations were assessed in relation to their variability across subjects (Friston et al., 1999).”

“This was computed both at the individual level, as well as in a group analysis (n = 11 for the deaf, n = 15 for the normally hearing) using a GLM in a hierarchical random effects (RFX) analysis 133 .”

“Random effect analysis (Friston et al., 1999) was used for the group-based statistical inference.”

“…inferences, we note that tests of fixed effects analyses can indeed be meaningful in terms of allowing inferences about typical characteristics at the population level, via the use of conjunction (separate subject) analyses for relatively small numbers of subjects (see Friston et al., 1999).”

“For the latter purpose, a randomeffects analysis was carried out, allowing for inference on the population level [Friston et al., 1999a,b].”

“29 Our study lacked power to confirm the mild effects of age and sex on TSPO radioligand binding, 6,30 but we note that the relationship between the PET and CD68 signals was present in all participants, regardless of age and sex.”

“…linear model (GLM), where early fi xed-effects models were soon replaced by random-effects and full mixed-effects approaches that have since become standards in the fi eld (Beckmann et al., 2003; Friston et al., 1999, 2005; Holmes and Friston, 1998; Mumford and Nichols, 2009; Woolrich et al., 2004).”