Estimates of standard errors were computed using a technique known as jackknife replication. As with any replication method, jackknife replication involves constructing a number of subsamples (replicates) from the full sample and computing the statistic of interest for each replicate. The mean square error of the replicate estimates around the full sample estimate provides an estimate of the variances of the statistics. To construct the replications, 50 stratified subsamples of the full sample were created and then dropped one at a time to define 50 jackknife replicates. A computer program (WesVar) was used to calculate the estimates of standard errors. WesVar is a stand-alone Windows application that computes sampling errors for a wide variety of statistics (totals, percents, ratios, log-odds ratios, general functions of estimates in tables, linear regression parameters, and logistic regression parameters).

The test statistics used in the analysis were calculated using the jackknife variances and thus appropriately reflected the complex nature of the sample design. In addition, Bonferroni adjustments were made to control for multiple comparisons where appropriate. Bonferroni adjustments correct for the fact that a number of comparisons (g) are being made simultaneously. The adjustment is made by dividing the 0.05 significance level by g comparisons, effectively increasing the critical value necessary for a difference to be statistically different. This means that comparisons that would have been significant with an unadjusted critical t value of 1.96 may not be significant with the Bonferroni-adjusted critical t value. For example, the Bonferroni-adjusted critical t value for comparisons between any two of the three categories of institutional size is 2.39, rather than 1.96. This means that there must be a larger difference between the estimates being compared for there to be a statistically significant difference when the Bonferroni adjustment is applied than when it is not used.