How many laboratories need to participate to make a round robin meaningful?

The more the better. In practice we need a minimum of 15 laboratories for Certification. The same minimum number are required for a worthwhile round robin.

ISO Guide 35:2003 recommended complicated materials need 10-15 laboratories reporting. The concept of the determination of the property values of an RM based on agreement among methods and/or laboratories is based on at least two assumptions; 1) that there exists a population of methods/laboratories that is equally capable in determining the characteristics of the RM to provide results with acceptable accuracy; 2) that the differences between individual results, both within and between methods/laboratories are statistical in nature regardless of the causes (35:10). In practice a large number of labs is needed to overcome the effects of individual lab biases. The more complex the procedure, the larger the between-laboratory variances, the larger the number of participating labs needed to achieve a property value having a "satisfying uncertainty" (35:10.2.2). ISO Guide 35: 2003, Certification of reference materials --General and statistical principles.