The group studies confirm our suggestion that a borderline of X or below will bring in for expert consideration nearly all adults who are feeble-minded from a lack of intellectual ability, while testing IX is a fairly clear indication of such serious deficiency as to justify isolation. That testing X, in the absence of other evidence of conative disturbance, places the case only in an uncertain region so far as isolation is concerned is best indicated by the fact that 1.1% to 1.4% of these 15-year-olds tested this low. We have good evidence that many in special classes, which contain only about the lowest one per cent., afterwards do float in society with or without social assistance. They cannot be presumed to require isolation, as I showed in the previous chapter. It is better to say at present that those testing X require evidence of their deficiency before isolation, except in special classes, is justified. The test diagnosis alone is too uncertain, even when there are no removable handicaps. As to the reliability of these borderlines, too much emphasis can hardly be put upon the fact that they have been determined for only a single group of 653 in a single community. They are undoubtedly not the exact borderlines, although they are the most probable percentage estimates we have at present and were obtained in a group that was as nearly unselected as it is possible to obtain. The method of selection was perfectly objective and excluded no feeble-minded children of this age living in these school districts. The theory of sampling applied to percentages (_228_) enables us to say that the standard deviation of the true lowest 0.5% in samples of this size made under the same conditions would not be more than 0.28%.[12] That is to say, if our result were only affected by the size of our sample the chances are about two out of three that the border of the true lowest 0.5 per cent. would lie between the border of the lowest 0.22% and the lowest 0.78% of a very large sample. Assuming that the distribution in this sample represented that of communities generally, the chances would be two out of three that the true border of the lowest 0.5% for like groups in like communities examined under the same conditions would lie between IX.0 and X.6 or X.4 on the 1908 and 1911 scales respectively. Moreover, the chances that a case in the lowest 0.5% in this sample would be above the doubtful group in a larger sample, _i. e._, get above the lowest 1.5%, would be about 1 in 10,000. On the other hand, the chances that a case above the true lowest 1.5%, _i. e._, above the uncertain group, would get into the lowest 0.5% in a larger sample, _i. e._, be classed as clearly deficient intellectually, would be about 18 in 1,000.