Figure 1B shows the result for a scale with slightly worse discrimination: the variance of the trait is now only 0.767. The items are again nicely scattered, between −2½ SD (−2.05) and 2½ SD (2.05). Thus, we retain the spread of the β values in terms of the SD, so that the expected proportion of individuals scoring a particular number of items remains equal across simulation situation; the resultant distribution of the sum scores will be equal. But now, due to the decreased sensitivity of the scale, the number of items has a more pronounced effect on the attenuation. The sum score correlations are now lower than under the model with variance = 1. However, the attenuation effect is still proportional to the true correlations.
