⁽¹⁾ Originally presented at a seminar at the University of Warwick on 19 March 1991; revised with the benefit of discussion there, and subsequently with my colleagues at the National Institute. It develops ideas previously put forward in a Note in this Review, August 1989. The underlying research forms part of a wider programme of international comparisons of training, education and productivity supported by the Economic and Social Research Council and the Gatsby Foundation, to which bodies my thanks are due. Responsibility for errors remains my own.

⁽²⁾ Strictly speaking NCVQ applies only to England and Wales, and Scotland comes under a separate body (Scotvec); the issues are however much the same, and nothing of substance is sacrificed if, for convenience of exposition, we refer throughout simply to ‘Britain’.

⁽³⁾ Capitals are attached to these words to indicate their technical connotation here.

⁽⁴⁾ For an extreme statement (‘we should just forget reliability altogether’) by NCVQ's Director of Research, see G Jessup, Outcomes: NVQs and the Emerging Model of Education and Training (Falmer, 1991), p.191. Similar views are to be detected in earlier publications from the Training Agency of the Department of Employment in their Guidance Notes for the Development of Assessable Standards for National Certification (Sheffield, 1989); see, for example, the remark on the merits (sic) of oral questioning: ‘it does not require candidates to be able to read or write’ (Guidance Note 5, p.7). Of course someone may be considered a capable carpenter for many purposes without being able to write; the Continental view would be that an employer who wished to employ him as a carpenter is permitted to do so, but he should not be awarded a Vocational Qualification. On the other hand, NCVQ would be prepared to award a Qualification. One of the dangers of the latter approach is that vocational qualifications will acquire a cumulatively lower status in Britain ('suitable for illiterates'), whereas on the Continent great pains have been taken to enhance their esteem.

⁽⁵⁾ HMI, National Vocational Qualifications in Further Education 1989-1990, DES, 1991, pp.6, 8.

⁽⁶⁾ Progress seems to require ever finer grinding. Previously, two Modules were the requirement for a craft qualification in engineering; a Module was then divided into three Segments. On the latest development each Segment is to be divided into an average of four Elements (yielding a total of about a thousand Elements). At the time of writing it seems that extensive negotiations are in progress with NCVQ in several occupational areas. ‘Conditional Accreditation’ has been granted by NCVQ for some existing qualifications, so that government training subsidies may immediately be received by the industry concerned pending agreement on the longer-term re-structuring of their qualification-procedures in accordance with NCVQ's principles.

⁽⁷⁾ E Kirsch, Formation Emploi, Oct-Dec 1990, p.13.

⁽⁸⁾ From a formal point of view the mathematical development that follows in this Appendix is, in essence, no more than an application of the standard theory of stratified and clustered sampling; but I am not aware that it has previously been applied in this context (the algebra here concentrates on the essentials required in the present application and is, I hope, simpler to follow than provided in general texts on sampling theory).

⁽⁹⁾ This corresponds to the intraclass correlation which arises ‘mainly in biological studies’ (G U Yule and M G Kendall, An Introduction to the Theory of Statistics, Griffin, London, 14th edition, 1950, p.272; the charming application to variations in the length of cuckoos' eggs according to nest of foster parent—Robin, Wren or Hedge Sparrow—will bring joy to many a scientific heart: ibid., p.280, based on a a study in Biometrika, 1905). For its application in cluster sampling see, for example, M H Hansen, W N Hurwitz and W G Madow, Sample Survey Methods and Theory (Wiley, 1953), vol. II, ch. 6.

⁽¹⁰⁾ There are 2 n_tn_p covariance terms of the type X_itX_JP which, on taking expected values, reduce to the simple final term in (12).