Th e " la w of propagation o[ error" is a tool th a t physical sc ienti s ts have co nve nie ntly and fre qu en tly used in th e ir work for ma n y years, yet an adeq uate refere nce is diffi c u lt to find. In thi s paper an expository rev ie w of thi s topi c is prese nte d , partic ularly in the li ght of c urre nt prac ti ces a nd interpretation s. Examp les on t he acc uracy of th e approximations are give n. The reportin g of th e un ce rtainti es of final res ults is di sc ussed .Key Word s : Approximation, e rror, formula , imprecision, law of e rror, prod uc ts, propaga ti on of e rror, rand om, ratio, syste mati c, s um.

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The problem of interaction in multidime nsional co ntin ge ncy tables is inves ti gated from the viewpoint of information th eory as developed by Kullbac k. The hypothesis of no rth-order interaction is defin ed in the sense of an hypothes is of "generalized " ind ependence of classifications with fix ed rth order marginal restraints. For a three· way table, with given cell probabilities 7Tijk , the minimum discrimination information for a contin ge ncy table with marginals P jj ., P. jk, and P i ... is given by the se t of cell probabilities P 0 k = a jjbj k e ,,·7Ti j k wh ere aij , b j ,., and eik are fun ctions of th e giv e n marginal probabilities, that is, In (p!jJ7T ij") = In a ij + In bj k + In e ,,·, representing no second-order interaction.The minimum di scrimination inl ormation stati sti c, asymptotically distributed as X" with appropriate degrees of freedom is where Xi jk are the observed cell frequencies and Xijk are the " no inte raction" cell frequencies uniquely de termined by a simple co nve rge nt ite rati on process of th e marginals on 7T ijk . For low e r ord e'r marginal restraints the us ual independ ence hypoth eses are ge ne rated when 7Tijk are taken to be the cell probabilities under uniform di stribution. It is shown th at th e set P !j,. satis fi es definitions of no second order interaction in a 2 x 2 x 2 table give n by Bartl ett and no interaction in a r X s X t table by Roy and Kastenbaum, and is also related to that give n by Good. Res ults of application to the analys is of so me "classical " three-dimensional contingency tables are given , together with full details for two four· dimensional examples.