In resolving disputes, the High Court of Australia sometimes has cause to expound upon the relationship between the Australian State and Aboriginal and Torres Strait Islander peoples. This article examines overblown and disingenuous New Right criticism directed towards the High Court in the aftermath of judgments deemed favourable to Indigenous Australians. It finds two themes recur in these attacks: that the High Court’s decision is undemocratic, or that the High Court has acted illegitimately. This article demonstrates that such claims are legally baseless. Drawing on quotes from major players in this debate, the article argues further that beneath this criticism lies a deeper angst over the sovereign foundations of Australia; an anxiety that reappears in arguments against contemporary calls for constitutional reform. As Australia nonetheless inches closer towards constitutional recognition of Aboriginal and Torres Strait Islander peoples, the ferocity of New Right censure suggests that the movement may fear the Australian people do not share their same suspicions.

A method is developed for extending any type of factor solution to new tests. The theoretical basis for this approximating scheme is thoroughly investigated, and then a simplification in the technique is introduced for practical purposes. An example is presented which illustrates the procedure of extending a factor solution to three new tests simultaneously.

A nonparametric test of dispersion with paired replicates data is described which involves jackknifing logarithmic transformations of the ratio of variance estimates for the pre- and post-treatment populations. Results from a Monte Carlo simulation show that the test performs well under Ho and has good power properties. Examples are given of applying the procedure on psychiatric data.

The Doolittle, Wherry-Doolittle, and Summerfield-Lubin methods of multiple correlation are compared theoretically as well as by an application in which a set of predictors is selected. Wherry's method and the Summerfield-Lubin method are shown to be equivalent; the relationship of these methods to the Doolittle method is indicated. The Summerfield-Lubin method, because of its compactness and ease of computation, and because of the meaningfulness of the interim computational values, is recommended as a convenient least squares method of multiple correlation and predictor selection.

A test for multisample sphericity based on the efficient scores criterion is obtained as an alternative to the likelihood ratio test developed by Mendoza.

Two systems of factor analysis—factoring correlations with units in the diagonal cells and factoring correlations with communalities in the diagonal cells—are considered in relation to the commonly used statistical procedure of separating a set of data (scores) into two or more parts. It is shown that both systems of factor analysis imply the separation of the observed data into two orthogonal parts. The matrices used to achieve the separation differ for the two systems of factor analysis.

In the course of developing the minres method of factor analysis the troublesome situation of communalities greater than one arose. This problem—referred to as the generalized Heywood case—is resolved in this paper by means of a process of minimizing the sum of squares of off-diagonal residuals. The resulting solution is superior to the otherwise very efficient original minres method without requiring additional computing time.

This paper describes a method of matrix decomposition which retains the ability of factor analytic techniques to summarize data in terms of a relatively low number of coordinates; but at the same time, does not sacrifice the useful analysis of variance heuristic of partitioning data matrices into independent sources of variation which are relatively simple to interpret. The basic model is essentially a two-way analysis of variance model which requires that the matrix of interaction parameters be decomposed by using factor analytic techniques. Problems of judging statistical significance are discussed; and an illustrative example is presented.

The square root method for the solution of a set of simultaneous linear equations or the reduction of a matrix has been known for some time under a variety of names. Because of its usefulness in statistical work, especially in factor analysis, the square root method is presented in general terms and an example given. Several independently developed “multiple group methods” for factor analysis are compared and synthesized. Their fundamental concepts are set forth and an appropriate system of notation developed. Detailed computational procedures are outlined, and the square root method is emphasized as a computing aid in multiple group analysis.

A simple proof that the squared multiple correlation of a variable with the remaining variables in the set of variables is a lower bound to the communality of that variable is presented.

Maydeu-Olivares and Joe (J. Am. Stat. Assoc. 100:1009–1020, 2005; Psychometrika 71:713–732, 2006) introduced classes of chi-square tests for (sparse) multidimensional multinomial data based on low-order marginal proportions. Our extension provides general conditions under which quadratic forms in linear functions of cell residuals are asymptotically chi-square. The new statistics need not be based on margins, and can be used for one-dimensional multinomials. We also provide theory that explains why limited information statistics have good power, regardless of sparseness. We show how quadratic-form statistics can be constructed that are more powerful than X2 and yet, have approximate chi-square null distribution in finite samples with large models. Examples with models for truncated count data and binary item response data are used to illustrate the theory.

Factor or conditional independence models based on copulas are proposed for multivariate discrete data such as item responses. The factor copula models have interpretations of latent maxima/minima (in comparison with latent means) and can lead to more probability in the joint upper or lower tail compared with factor models based on the discretized multivariate normal distribution (or multidimensional normal ogive model). Details on maximum likelihood estimation of parameters for the factor copula model are given, as well as analysis of the behavior of the log-likelihood. Our general methodology is illustrated with several item response data sets, and it is shown that there is a substantial improvement on existing models both conceptually and in fit to data.