This section contains technical notes referred to in the text.
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.
Throughout the book, I report a number of correlations between sets of variables. Most often one of these variables is academic achievement. The first example in Chapter 1 uses academic background knowledge as the other variable and reports a correlation of .66 between the two. One way to interpret a correlation is in a “predictive sense”—the extent to which performance on one variable predicts performance on the other variable. In the examples in this book, academic achievement is typically the variable that is being predicted. The correlation between the “predicted” variable (e.g., academic achievement) and the “predictor” variable can