Calculating Nominal Group Statistics in Collaboration Studies (Wright, 2007)

Obtaining Representative Nominal Groups (Kelley & Wright, 2010)

What do you do when you want to compare group performance with individuals who are combined into nominal groups? Back in olden days you would just group subjects 1 and 2 together, 3 and 4 together, and so on. Wright (2007) showed this is bad approach and wrote S-Plus and R functions that provided and alternative way to estimate the mean and variance of the nominal groups. A lot of the 2007 paper was spent showing that the olden days approach is bad and covered some mathematical aspects of some alternative approaches. Less concern was spent on how easy the new functions were to work. They produced only the mean and variance estimates, and users had to plug these into other equations. Matthew Kelley and I began discussing alternatives, and produced an algorithm that finds (according to various criteria that the users can decide upon) a set of pairing for the individuals that represents all possible groupings really well. This means that the user can create these groups and run the analyses on these. The solution is also really good compared with those in the 2007 paper. The tables in the new version show how close these representative nominal groupings reproduce the bootstrap estimates of different statistics.

Also, while R is growing in popularity, not everybody uses it. So, Matthew created a C++ version that can be run with some software freely downloaded from the net. The R one is called ngfinder.R. The function ngfinder is part of the newest release of the R package mrt 0.3 (manual) which is on CRAN and the C++ function is here. The R function is a slower than the C++ function, but is more flexible.

The new paper is:

        Kelley, M.R. & Wright, D.B. (2010). Obtaining representative nominal groups. Behavior Research Methods, 42, 36-41.

The original paper is:

    Wright, D. B. (2007). Calculating nominal group statistics in collaboration studies. Behavior Research Methods, 39, 560-570. here.

Here are the functions from the 2007 paper in S-Plus/R. I don't use S-Plus anymore, so if they stop working ... well, I can try to fix.

nomg - this calls ngallpairs by default, or ngallsets

The ngallpairs differs from the S-Plus function in that is change non-matrix data frames into matrices rather than producing an error and ngallsets uses sd rather than stdev.

S-Plus functions for:

ngallsets (tested with S-Plus 6, for R.2.2.0 change stdev to sd)

ngallpairs (tested with S-Plus 6 and R 2.2.0)

These require a matrix of 0s and 1s where 1 means incorrect, and no other variables.  If your coding is the other way around, just do: 

mat<- 1-mat

Unless your sample is small, use ngallpairs.

If you are using these, please email me and tell me how you find them. 

Dan