The handling of multiway tables on computers

Biometrics and Psychometrics: Origins, Commonalities and Differences

“…In other words, data type and data structure should be carefully distinguished. I had a footnote in history here, as Knuth (1968) refers to a paper of mine (Gower 1962) as being one of the first to separate the structure of data (in this case multiway tables) from what operations may be required. Similar choices of scale as those used in psychometrics also occur in biometrics but not with anything like the same frequency.…”

An approach to multidimensional data array processing by computer

“…In this context, see Gower [6] for comments on Algol, Fortran, and PL/I. A few of the explicit procedural requirements can be avoided by the use of Iverson's APL, see Iverson [8].…”

“…Several statisticians have approached the general problem, as it relates to the organization of arrays for experimental designs, by the introduction of special operators (sometimes called data structure operators) as in the papers by Claringbold [3], Gower [7], Nelder [13], and Yates [17]. Earlier undertakings involved operations on individual elements of tables, such as the SCAN operator developed by Gower [6]. However, these special operators require considerable investment in time to understand and to apply, especially to the cases of arrays of time series data.…”

“…For many applications one will want more selective control. A more general capability is specified in expression (6). Even with the break control capabilities specified in expression (2) it is possible to achieve efficiency in storage space and processing as well as in specification.…”

“…If I, J is used, all values within the interval I through J or label I through label J will be used. Other possible ranges could be specified but are excluded for purposes of brevity, since a more general capability is available by use of a table look-up facility in expression (6). This extended break control capability makes it possible not only to determine when a break occurs but also to determine whether this break control value satisfies other subsidiary conditions, such as belonging or not to a specified table of acceptable values or being within a specific range.…”