This section contains technical notes referred to in the text.

Technical Note 1

To compute the average correlation between background knowledge and academic achievement, I first analyzed the correlations from the studies reported in Chapter 1 to determine outliers, using techniques reported by Tukey (1977). An outlier is a correlation that does not “fit” within a given set. It is either much larger or much smaller than the other correlations. I then transformed the remaining correlations using the Fisher Z transformation and computed the average of these transformed correlations. This step is necessary because differences between correlations do not constitute an equal interval scale. That is, differences between large correlations are not mathematically equal to differences between small correlations. The average Z transformed correlation was then transformed back to the original metric.

Technical Note 2