Can we disregard the whole model? Omnibus non-inferiority testing for R2 in multi-variable linear regression and in ANOVA

Determining a lack of association between an outcome variable and a number of different explanatory variables is frequently necessary in order to disregard a proposed model (i.e., to confirm the lack of a meaningful association between an outcome and predictors). Despite this, the literature rarely offers information about, or technical recommendations concerning, the appropriate statistical methodology to be used to accomplish this task. This paper introduces non-inferiority tests for ANOVA and linear regression analyses, which correspond to the standard widely used F test for and R², respectively. A simulation study is conducted to examine the Type I error rates and statistical power of the tests, and a comparison is made with an alternative Bayesian testing approach. The results indicate that the proposed non-inferiority test is a potentially useful tool for ‘testing the null’.     

More evidence for a relational shift in the development of analogy: Children's performance on a causal-mapping task

Gentner (1988) has proposed a relational shift whereby children interpret analogy and metaphor first in terms of object similarity and then in terms of relational similarity. Goswami (1996) argues against the relational shift hypothesis, citing as evidence a study performed by Goswami and Brown (1989) in which 3-, 4-, and 6-year-old children were able to correctly complete pictorial A:B::C:? analogies based on familiar causal relations, and, contrary to the predictions of the relational shift hypothesis, made very few object-similarity errors despite the presence of an object-similarity choice. In the present experiment we obtained similarity ratings of Goswami and Brown's stimuli and found that the materials did not contain a true object similarity choice and therefore that study was not an adequate test of the relational shift hypothesis. After appropriate modifications to their methodology, we found that 4- and 5-year-old children's performance was consistent with the relational shift hypothesis: First, object-similarity errors were highly frequent initially and decreased with age; second, the rate of relational (correct) responding increased with age; and third, performance on the analogues was positively related to children's knowledge about the participating causal relations. We conclude by proposing an explanation for the relational shift based on an alignment view of similarity comparison and, further, suggest a new role for object similarity in children's analogical development.     

“God as Friend”: Metaphoric Theology in Pastoral Care

Because of postmodernity's claim of deconstruction, the naming of God has become a crucial issue for a hermeneutics of pastoral care. Inadequate and inappropriate perceptions of God, because of specific experiences of faith, create unhelpful images of God which eventually lead to a pathology of faith. Taking into consideration the figurative means of symbolic language and its rootedness in culture, this article explores the possibility of the metaphor, God as Friend, in order to move beyond the paradigm of the suffering God (theopaschitic theology) to the paradigm of the faithful God—God as our Soul Friend.     

LE DÉVELOPPEMENT DE LA CONSERVATION DES LONGUEURS DE DEUX HORIZONTALES DÉCALÉES

Trois groupes d'enfants (102 Canadiens français urbains, 110 Rwandais ruraux scolarisés, 74 Rwandais ruraux non scolarisés) subissent une épreuve de conservation des longueurs de deux tiges dont l'égalité est d'abord constatée par coïncidence des extrémités et dont l'une (la plus rapprochée de S, ou la plus rapprochée de E) ou les deux sont ensuite déplacées. L'analyse des résultats montre que: a) les plus jeunes enfants de chacun des groupes sont fortement inclinés à estimer plus longue la tige réellement déplacée (ou jugée déplacée) et/ou la tige la plus rapprochée de S; b) la conservation est acquise par les enfants de chacun des groupes, mais dans l'ordre chronologique suivant: Canadiens français, Rwandais scolarisés, Rwandais non scolarisés; c) dans chacun des groupes, les jugements de conservation s'appuient principalement sur l'identité et les jugements de non-conservation sur le déplacement et/ou le dépassement de l'une des tiges. Ces résultats suggèrent que la thèse de Piaget voulant que l'enfant passe d'une conception topologique ordinale à une conception euclidienne dans l'acquisition de la conservation des longueurs peut s'appliquer à des milieux différents malgré de larges différences d'urbanisation et de scolarisation.     

APPRENTISSAGE DE LA CONSERVATION DES QUANTITÉS LIQUIDES CHEZ DES ENFANTS RWANDAIS ET CANADIENS-FRANCAIS1

Three groups of 16 subjects (rural school Rwandese, rural unschooled Rwandese and urban school French-Canadian children), classified as preoperational on a pretest including eight tests of conservation, were trained on the conservation of liquid quantities by a method based on anticipation of levels and compensation of dimensions. It was found that a) the performance of all three groups, when compared with controls, was significantly higher on two successive post-tests (two months interval); b) the three groups did not differ from one another either in global scores on both post-tests or in number of training sessions required for learning; c) the types of justification were based predominantly on perceptual features and on identity in non-conservation and conservation judgments, respectively. Results are discussed mainly in terms of the kind of justifications given by the three groups, the relative effectiveness of the two types of training given, and the genuineness of the conservation induced.