The discussion focuses first on methodological contributions of the current study of children with ASD, and second, on results obtained in view of the study's specific goals.
Study goals and findings
The first goal of the study was to determine whether coherence factors, here used as variables, significantly separate ASD- from the control (C)-group populations. As described under Results, when all 40 variables were forced to enter, discriminant function analysis (DFA) produced a highly significant (P < 0.0001) group difference across the full 2- to 12-year-old population and, additionally, for the three separate age group analyses of the 2- to 4-, the 4- to 6-, and the 6- to 12-year-old subjects. These findings establish that the 40 coherence factors significantly separate pediatric ASD-patients from C-subjects.
The second goal was to evaluate the consistency of subject classification by allowing DFA to select the best factors for discrimination. As discussed in Results the average jackknifed classification success for the three separate age-group DFAs was 93.7% for the control- and 97.0% for the ASD-group. When the entire population was subjected to 10 independent split half replications, classification success was on the average 88.5% correct for the C- and 86.0% correct for the ASD-groups. Moreover, when each training-set-generated discriminant function was evaluated against the corresponding test-set by t-test, every one of the 10 control- versus ASD-group comparisons reached probability levels of P < 0.0001 levels. These findings thus establish coherence factors as very useful in subject classification. They, furthermore, establish the substantial stability of the reported coherence findings and argue quite strongly against great inter-subject variability in this study's ASD population. The illustrated factor coherence loading patterns (Figure 2) appear to constitute a potentially useful neurophysiological ASD-phenotype. Furthermore, the demonstrated stability of the above coherence findings argues against marked variability of brain function within the ASD population as postulated by Happé  and Milne .
It is tempting to speculate that the consistency of the classification success reported might point to EEG coherence as a possible future diagnostic test for ASD. However, clinical patients are seldom referred just to confirm that they are either neuro-typical or warranting the diagnosis of ASD. Rather, they are referred to establish a diagnosis from among a wide range of clinical possibilities that may produce clinical presentations superficially similar to ASD, including ASD itself. Before entertaining general clinical applicability, the discriminant process will need to be extended to correctly classify conditions beyond the simple C- versus ASD-group dichotomy. Further analyses must encompass diagnoses often associated with or closely related to classic ASD, such as GDD, Asperger's syndrome, developmental dysphasia, childhood disintegrative disorder and autistic behavior as a presenting symptom of other clinical diagnoses, for example, Rett's syndrome, Angelman's syndrome, tuberous sclerosis and Fragile X syndrome.
The controversy of whether childhood disintegrative disorder and especially Asperger's disorder, should or should not be folded into the ASD-category as DSM-V argues [1, 14, 71], might be answered by similarities and/or differences found on EEG coherence and possibly other neuroimaging tests. Wing et al.  have argued "We, in our many years of clinical diagnostic work have observed how extremely difficult, even impossible, it is to define boundaries of different sub-groups among children and adults with autistic spectrum conditions." The authors' clinical experience parallels this view.
A third goal of the current study was to explore the potential meaning of the 33 factors chosen (as best to discriminate between ASD- and C-group subjects) by the multiple DFAs when variables were allowed to step in and out.
In studies of EEG coherence, careful pre-selection of electrode pairs has been frequently undertaken prior to data analysis, for example, see Coben et al. . This study involved a sample of anterior to posterior intrahemispheric (for example, F3-O1), left to right interhemispheric (for example, C3-C4), and intra-lobar (for example, T7-P7) electrode pairs - see Figure 1 for named electrode locations. Such electrode pair selection facilitates subsequent discussion of coherence increase/decrease in particular frequencies, in different regions, between short and long distance coherence as well as between hemispheres. In contrast, for the current study, channel pairs were not pre-selected; instead exclusively data driven factor loading patterns were used to define coherence pair groupings (Figure 2). As became apparent, none of the factor loading patterns delineated any electrode pairs that reflect simple left-right or anterior-posterior orientations of the sort pre-selected in earlier studies (for example, ). On the one hand, this complicates a direct comparison of the current study's findings with prior studies. On the other hand, since the patterns of coherence pair associations in Figure 2 were driven exclusively by the data structure underlying the large study population's coherence data, they may be taken to represent coherence channel pairs that are the most likely to associate with one another in the larger ASD population and, therefore, the most likely to discriminate ASD- from C- subjects. Despite the complexity of patterns identified none-the-less orderly generalizations about coherence difference in ASD emerge from the results.
Overall, 70% of the factors were associated with reduced coherence for the ASD- population. Furthermore, two of the four most utilized factors by DFA, including the most frequently selected Factor 15, were characterized by reduced ASD coherence. Moreover, seven of the eight factors characterized by short inter-electrode distance and all five of the factors representing a mix of short and long distance coherences were associated with reduced coherence. This study is not, of course, the first to report evidence for reduced coherence in ASD [22, 23, 25, 27, 28]. Such a preponderance of reduced coherence in ASD suggests likely corresponding reduction in cortical connectivity and corresponding lack of interactions between cortical regions. Some authors attribute ASD primarily to reduced integration of brain activity where specialized cortical regions are anatomically and functionally poorly connected with one another [17, 72–76]. Indeed, the most consistently selected factor in the current study (Factor 15) exclusively demonstrated reduced connectivity primarily between the posterior and anterior left temporal regions, and between the left anterior temporal and left frontal regions - and to a degree in the right anterior temporal region. Broadly, left temporal-frontal regions are associated with language function; reduced connectivity in these regions may be associated with the language and communication challenges that are nearly universal in the ASD population. Factor 15 may represent decreased connectivity along the left hemisphere's Arcuate Fasciculus, an anatomical tract important in language and recently shown to be deficient in autism .
On the other hand, 30% of the 33 factors utilized in the current report represented increased ASD-coherence. The current study again is not the first to report evidence for increased coherence in concert with reduced coherence [22, 27, 28] with some studies reporting primarily increased coherence [21, 26]. It is more difficult to interpret increased connectivity in the context of ASD-subjects. Increased connectivity, as seen in this study, is primarily represented by long inter-electrode distance factors. This might represent a failure of developmentally appropriate pruning or die-back and, thereby, constitute a further functional liability. Failure of expected die-back of certain cortical-cortical connections with the attendant, aberrant over-connectivity might interfere with normal cortical processing. An alternative possibility is that the increased coherence may constitute a compensatory attempt of the autistic brain to form atypical, spatially disparate, cortical networks in an attempt to replace function normally subserved by assumed-to-be deficient more localized networks. Additionally, the presence of increased coherence might relate to the known association between autism and epilepsy .
This study identified no evidence for consistent lateralization among the factor loading patterns and no overriding regional involvement. Furthermore, this study identified no clear inter-relationships among spectral bands, number of coherences per factor, nor increased or decreased coherence. A primary spectral finding was the dominance of slow beta across all conditions with the majority of factors manifesting peak loadings in the slow beta range and far fewer in the fast beta, theta, alpha and delta ranges, a finding of uncertain clinical significance. Earlier studies which demonstrated findings specific to differing scalp regions and spectral ranges may largely reflect methodological differences as discussed in the Background.
The most remarkable spectral finding in the current study was the broad, more than 10 Hz wide, average spectral range per factor, with factor spectral bandwidths ranging up to 18 Hz. In other words, within the ASD population coherence patterns tended to be unusually stable across broad spectral ranges, a finding not reported in previously studied non-ASD populations whose ages ranged from infancy to adulthood [53, 57]. The unusually broad spectral ranges in the ASD population, as evidenced for the majority of coherence factors, may reflect yet another characteristic of abnormal neurophysiology in ASD. An understanding of this unexpected finding of unusually broad spectral ranges per factor may be gained by drawing analogies to and making possible inferences from the spectral filtering characteristics of complex systems in electrical and/or mechanical engineering . A spectral filter may be defined as a network or circuit that transmits or passes certain frequencies from its input to its output, its pass band, while rejecting other frequencies. On an input/output plot a narrow or sharp filter has a well defined peak response associated with a rapid fall-off on either side, that is, a narrow pass-band. A wide or broad filter, in contrast, possesses a wide pass-band with slow roll-off on either side of a less distinct peak. The "Q" of a filter is a dimensionless number that characterizes a resonant circuit's bandwidth relative to its center frequency. This feature also serves as an indication of how damped a circuit may be. As a physical example of a high Q filter, one might consider a thin, high quality crystal goblet. As an example of a low Q physical filter, one might consider a typical, ceramic coffee mug. High Q circuits are relatively easy to activate, for example, tapping the crystal goblet causes a sustained ringing of moderate amplitude at a single frequency reflecting its narrow pass band and sharp resonance peak, whereas low Q circuits, for example, tapping the ceramic coffee mug produce a brief, low amplitude, broad frequency "thunk" at best. Thus, low Q circuits are more damped than high Q circuits .
Returning to the broad frequency bands identified in the current study, the complex coherence patterns outlined by the factor loadings may serve to identify important 'damped' processing circuit characteristics within the ASD-brain. Factor 15 may reflect reduced connectivity in an important cortical auditory processing circuit. Although it peaks at 24 Hz, there is very little change in Factor 15 loading patterns across a wide pass band from 12-30 Hz - the pattern of a putative low Q, wide bandwidth, heavily damped system. It may be unusually difficult for this circuit to be driven into action by external stimulation, such as speech input. One might speculate that the typical lack of response to verbal input in autism may reflect not the absence of needed cortical circuitry but a poorly responding, low Q circuit response of language cortex that is postulated to be overly damped. The autistic auditory cortex may act more like the coffee mug than the crystal goblet. One might further speculate that there may be intrinsic biological factors in the autistic brain that dampen, inhibit or otherwise limit responsiveness in general, given the overall wide spectral ranges and predominant decrease of connectivity that characterize the coherence factor loading patterns.