Multiple Contingency Research Articles

Piaget's conservation tasks: The logical and development priority of identity conservation

The present research has investigated Elkind's conceptual distinction between identity conservation and equivalence conservation. Although Piaget's description and analysis of conservation acquisition rests primarily on considerations of identity conservation, his assessment format has been exclusively equivalence conservation. The present argument contends that equivalence conservation subsumes identity conservation ability, but also includes a necessary logical deduction sequence for adequate equivalence conservation performance. Accordingly, identity conservation should be an earlier developmental acquisition than equivalence conservation. Appropriate settings were devised for identity and equivalence conservation assessment which equated the two conservation tasks in terms of perceptual cues and memory requirements. The tasks were administered, in a nonrepeated measures design, to equal numbers of males and females at the kindergarten, first, and second grade levels. A nonparametric multiple contingency analysis revealed that the main effects of conservation task type, age levels, and the sex dichotomy were significant. It was concluded that identity conservation definitely precedes equivalence conservation as a developmental achievement. Accordingly, Piaget's view of identity and equivalence conservation as simultaneous or concommitant developments is erroneous. Identity conservation cannot be adequately assessed in the conventional paired-stimulus format, and care should be taken in considering identity processes or explanatory concepts as a complete description of equivalence conservation achievement.

Chi-Square Tests with One Degree of Freedom; Extensions of the Mantel-Haenszel Procedure

Abstract A published method for analyzing multiple 2×2 contingency tables arising in retrospective studies of disease is extended in application and form. Extensions of application include comparisons of age-adjusted death rates, life-table analyses, comparisons of two sets of quantal dosage-response data, and miscellaneous laboratory applications as appropriate. Extensions in form involve considering multiple contingency tables with arbitrarily many rows and/or columns, where rows and columns are orderable, and may even be on a continuous scale. The assignment of some score for each row or column is essential to use of the method. With scores assigned, a deviation of the sum of cross products from expectation, and its variance conditioned on all marginal totals, are computed for each table and a chi square is determined corresponding to the grand total of the deviations. For various specific instances and for various scoring procedures, the procedure extends or is equivalent to the asymptotic form of man...

Errata: Multiple Contingency versus Multiple Correlation; An Old Time-Saving Way of Handling Multiple Contingency

Errata: Multiple Contingency versus Multiple Correlation; An Old Time-Saving Way of Handling Multiple Contingency

Multiple Contingency versus Multiple Correlation; An Old Time-Saving Way of Handling Multiple Contingency

Multiple Contingency versus Multiple Correlation; An Old Time-Saving Way of Handling Multiple Contingency

THE EXACT VALUE OF THE MOMENTS OF THE DISTRIBUTION OF x2 USED AS A TEST OF GOODNESS OF FIT, WHEN EXPECTATIONS ARE SMALL

IN genetical practice we are constantly presented with large numbers of small samples from populations consisting of several well-defined classes. For example in the mouse we can readily obtain hundreds of litters containing anything from one up to about twelve members. Their totals may agree satisfactorily with expectation on a Mendelian basis, for example J coloured, i white, or 9 grey, H black, i white. But we desire to know whether the individual litters can be regarded as random samples from such a population. In addition the problem of homogeneity may arise. That is to say the population as a whole may not conform to any particular expectation. But we may desire to know whether the litters can be regarded as random samples of the population given by the totals. It has long been known that when the numbers expected in any observation are small, the distribution of x2 departs from that given by Pearson (1900). The mean appears sometimes, but not always, to be equal to the number of degrees of freedom. But the variance is no longer exactly equal to twice that number. Exact expressions for it in certain cases have been given by Pearson (1932) and Cochran (1936). These are based on an ingenious application of the theory of multiple contingency by Pearson. It will be shown in this paper that the first few moments can often be calculated by entirely elementary methods involving nothing more advanced than the multinomial theorem. In an accompanying paper (Griineberg and Haldane, 1937) they will be applied to actual data on mice. We first study the distribution of x2 in a n-fold table with n 1 degrees of freedom, then in a (m x n)-fold table with m (n-i) degrees of freedom. For genetical work we are particularly interested in the (n x 2)-fold table with n degrees of freedom. As a limiting case of the 2-fold table with 1 degree of freedom we derive the moments of the variance of samples from a Poisson series, and thence the distribution of x2 in a n-fold table with n degrees of freedom. The important case of the (m x n)-fold table with (m 1) (n 1) degrees of freedom remains to be investigated. Consider a sample of 8 individuals falling into n classes. Let the expected and observed numbers in these classes be:

On the General Theory of Multiple Contingency with Special Reference to Partial Contingency

Journal Article ON THE GENERAL THEORY OF MULTIPLE CONTINGENCY WITH SPECIAL REFERENCE TO PARTIAL CONTINGENCY Get access KARL PEARSON, F.R.S. KARL PEARSON, F.R.S. Search for other works by this author on: Oxford Academic Google Scholar Biometrika, Volume 11, Issue 3, May 1916, Pages 145–158, https://doi.org/10.1093/biomet/11.3.145 Published: 01 May 1916

Testing the equality of risk difference among multiple incomplete two-way contingency tables

Testing the equality of risk difference among multiple incomplete two-way contingency tables