Calculating nominal group statistics in collaboration studies

In many areas of psychology researchers compare the output of pairs of people with people working individually. This is done by calculating estimates for nominal groups, the output of two individuals if they had worked together. The way this is often done is by creating a single set of pairs either randomly or based on their location in a data file. This paper shows that this approach introduces unnecessary error. Two alternatives are developed and described. The first calculates statistics for all permissible sets of pairs. Unfortunately the number of sets is too large for modern computers for moderate sample sizes. The second alternative calculates statistics on all possible pairs. Several simulations are reported which show that both methods provide good estimates for the mean and trimmed mean. However, the all pairs procedure provides a biased estimate of the variance. Based on simulations, an adjustment is recommended for estimating the variance. Functions in S-Plus/R are provided in an appendix and are available from the author's Web page along with updates and alternatives (www.sussex.ac.uk/users/danw/s-plus/ngstats.htm).