Figure 1C shows an extreme situation where the items have high discriminatory power. The variance is now 100, and the items are evenly scattered between −25 and 25. Note that again, we retain the scatter of the beta values in terms of the SD, and again the sum score distribution will not be different from the earlier simulations. However, with such a sensitive scale, practically everybody that scores less than 1 SD below the mean will show a sum score of 16% of the total number of items. Everybody with a latent score higher than 1 SD below the mean will show a sum score of 84% of the number of items. Moreover, the data will show a scalogram pattern, for example with 3 items with increasing difficulty, the only observed patterns will be 111, 110, 100 and 000. Such a pattern will not be observed when the variance is 1, and even less so with a variance of 0.767: more individuals will then show patterns like 101 and 011, etc. Again, attenuation occurs when the number of items is
