Luisa Canal

Inconsistency indices for pairwise comparison matrices: a numerical study

Evaluating the level of inconsistency of pairwise comparisons is often a crucial step in multi criteria decision analysis. Several inconsistency indices have been proposed in the literature to estimate the deviation of expert’s judgments from a situation of full consistency. This paper surveys and analyzes ten indices from the numerical point of view. Specifically, we investigate degrees of agreement between them to check how similar they are. Results show a wide range of behaviors, ranging from very strong to very weak degrees of agreement.

A normal approximation for the chi-square distribution

Abstract An accurate normal approximation for the cumulative distribution function of the chi-square distribution with n degrees of freedom is proposed. This considers a linear combination of appropriate fractional powers of chi-square. Numerical results show that the maximum absolute error associated with the new transformation is substantially lower than that found for other power transformations of a chi-square random variable for all the degrees of freedom considered (1⩽ n ⩽1000).

The Semantics of Biological Forms

This study analyses how certain qualitative perceptual appearances of biological forms are correlated with expressions of natural language. Making use of the Osgood semantic differential, we presented the subjects with 32 drawings of biological forms and a list of 10 pairs of connotative adjectives to be put in correlations with them merely by subjective judgments. The principal components analysis made it possible to group the semantics of forms according to two distinct axes of variability: Harmony and dynamicity. Specifically, the nonspiculed, nonholed, and flat forms were perceived as harmonic and static; the rounded ones were harmonic and dynamic. The elongated forms were somewhat disharmonious and somewhat static. The results suggest the existence in the general population of a correspondence between perceptual and semantic processes, and of a nonsymbolic relation between visual forms and their adjectival expressions in natural language.

Cross-modal associations between materic painting and classical Spanish music

The study analyses the existence of cross-modal associations in the general population between a series of paintings and a series of clips of classical (guitar) music. Because of the complexity of the stimuli, the study differs from previous analyses conducted on the association between visual and auditory stimuli, which predominantly analyzed single tones and colors by means of psychophysical methods and forced choice responses. More recently, the relation between music and shape has been analyzed in terms of music visualization, or relatively to the role played by emotion in the association, and free response paradigms have also been accepted. In our study, in order to investigate what attributes may be responsible for the phenomenon of the association between visual and auditory stimuli, the clip/painting association was tested in two experiments: the first used the semantic differential on a unidimensional rating scale of adjectives; the second employed a specific methodology based on subjective perceptual judgments in first person account. Because of the complexity of the stimuli, it was decided to have the maximum possible uniformity of style, composition and musical color. The results show that multisensory features expressed by adjectives such as “quick,” “agitated,” and “strong,” and their antonyms “slow,” “calm,” and “weak” characterized both the visual and auditory stimuli, and that they may have had a role in the associations. The results also suggest that the main perceptual features responsible for the clip/painting associations were hue, lightness, timbre, and musical tempo. Contrary to what was expected, the musical mode usually related to feelings of happiness (major mode), or to feelings of sadness (minor mode), and spatial orientation (vertical and horizontal) did not play a significant role in the association. The consistency of the associations was shown when evaluated on the whole sample, and after considering the different backgrounds and expertise of the subjects. No substantial difference was found between expert and non-expert subjects. The methods used in the experiment (semantic differential and subjective judgements in first person account) corroborated the interpretation of the results as associations due to patterns of qualitative similarity present in stimuli of different sensory modalities and experienced as such by the subjects. The main result of the study consists in showing the existence of cross-modal associations between highly complex stimuli; furthermore, the second experiment employed a specific methodology based on subjective perceptual judgments.

The Hue of Concepts

The study shows a systematic naturally biased association between percepts and concepts. Specifically, it shows that a series of terms pertaining to an abstract semantic field (related to the frame of ethics in social behaviour) has a nonrandom, highly significant, association with colours (hues). This is the first time that consistent associations between abstract terms and colours have been reported in the general population. The main hypothesis, ie that there appear to be ‘hues of concepts’, was borne out by the results: The abstract terms considered were coloured with blue/green (ie cool) colours as well as their synonyms, while their antonyms were coloured with red/yellow (ie warm) colours. The association provides information about the nature of abstract concepts and their relationship with perception. It also sheds light on the interrelations among words in semantic domains that, to date, have been studied from only a computational viewpoint.

The Tactile Dimensions of Abstract Paintings: A Cross-Modal Study.

In our research, we tested for the existence of cross-modal visual and tactile associations in the experience of abstract art. Specifically, we measured the association of 60 abstract paintings with four couples of antonyms related to texture, such as warm or cold, smooth or rough, lightweight or heavy, soft or hard, investigating if the different modality of presentation on a computer screen (color versions: natural colors, inverted colors, black and white) gave rise to different associations relative to the four couples of opponent qualities. Second, we tested whether there might be differences between the ratings of the paintings when they were presented as images on a computer screen versus in real life at the museum. The results confirmed that associations between visual and tactile experience with such complex stimuli exist. In the case of the couple warm or cold, a significant inversion of associated qualities occurs when the images are presented in inverted colors as opposed to natural colors; furthermore, when presented in black and white, warm evaluations are “cooled down,” but cold evaluations remain the same. The degree of smoothness could be considered not associated with the color versions. When seen in black and white, both the mean softness and the mean lightweight-ness of the paintings were reduced; however, in the last case, this effect was more evident for the most lightweight pictures. There is only a slight difference between the two presentations of the paintings as images presented on a computer screen and seen in real life, relative to the warm or cold and soft or hard dimensions. Of the four opponent qualities, the three pairs warm or cold, lightweight or heavy, and soft or hard showed the most interesting results in relation to the cross-modal associations.

Pattern of accesses over time in an online asynchronous forum and academic achievements

In this study, the participation of 119 students in an online asynchronous forum as part of an academic course on statistical methods was evaluated. The pattern of accesses during the course was analyzed by means of the cumulative mean function. Taking into account the times (hours) at which accesses occurred, it is possible to achieve more accurate and more sensitive assessment of the role of concomitant variables (gender, final mark of the high school attended, examination outcome). As far as academic achievement was concerned, it emerged that graduating probability within 3.5 years from the end of the course was related only to a regular posting activity and not to the overall number of accesses. [ABSTRACT FROM AUTHOR]

Naturally Biased Associations Between Music and Poetry.

The study analyzes the existence of naturally biased associations in the general population between a series of musical selections and a series of quatrains. Differently from other studies in the field, the association is tested between complex stimuli involving literary texts, which increases the load of the semantic factors. The stimuli were eight quatrains taken from the same poem and eight musical clips taken from a classical musical version of the poem. The experiment was conducted in two phases. First, the participants were asked to rate 10 couples of opposite adjectives on a continuous bipolar scale when reading a quatrain or when listening to a musical clip; then they were asked to associate a given clip directly with the quatrains in decreasing order. The results showed the existence of significant associations between the semantics of the quatrains and the musical selections. They also confirmed the correspondences experienced by the composer when writing the musical version of the poem. Connotative dimensions such as rough or smooth, distressing or serene, turbid or clear, and gloomy or bright, characterizing both the semantic and the auditory stimuli, may have played a role in the associations. The results also shed light on the accomplishment of the two diverse methodologies adopted in the two different phases of the test. Finally, the role of specific musical components and their combinations is likely to have played an important role in the associations, an aspect that shall be addressed in further studies.

Calligraphy and Klee’s Abstract Painting: A Study on Categorical Ambiguity

This study analyses the categorical ambiguity between visual appearances that belong in different categories, such as Oriental Calligraphy and certain Abstract Paintings selected from the works of Klee. In particular, the aim of our research was to identify whether there exist abstract features at the basis of purely visual configurations that determine the way in which they are categorized. Specifically, the intention was to determine whether, and to what extent, two artistic forms that display documented shared graphic and conceptual characteristics differ, or do not differ, visually, and whether certain features exist that identify them as a specific type of graphic work. The assumption that both categories had shared characteristics that made them graphically and conceptually similar and that resulted in categorical ambiguity, was confirmed. Moreover, the presence of some constituent features specific to one or the other was also confirmed. The results show that a Calligraphic Image and an Abstract Painting by Klee can be ‘exchanged’, but the tendency to confuse Calligraphy with an Abstract Painting is greater than that of confusing an Abstract Painting with Calligraphy.

The chi-square controversy: what if Pearson had R?

One of the most famous controversies in the history of Statistics regards the number of the degrees of freedom of a chi-square test. In 1900, Pearson introduced the chi-square test for goodness of fit without recognizing that the degrees of freedom depend on the number of estimated parameters under the null hypothesis. Yule tried an ‘experimental’ approach to check the results by a short series of ‘experiments’. Nowadays, an open-source language such as R gives the opportunity to empirically check the adequateness of Pearsons arguments. Pearson paid crucial attention to the relative error, which he stated ‘will, as a rule, be small’. However, this point is fallacious, as is made evident by the simulations carried out with R. The simulations concentrate on 2×2 tables where the fallacy of the argument is most evident. Moreover, this is one of the most employed cases in the research field.