Confidence ellipses when analyzing simultaneously several contingency tables resulting from free-text descriptions CADORET Marine 1 , BUCHE Marianne 1 , LÊ Sébastien 1 1 Laboratoire de mathématiques appliquées, A GROCAMPUS O UEST , Rennes 1
Outline Confidence ellipses when analyzing simultaneously several contingency tables resulting from free-text descriptions 2
Outline Confidence ellipses when analyzing simultaneously several contingency tables resulting from free-text descriptions 3
Outline Confidence ellipses when analyzing simultaneously several contingency tables resulting from free-text descriptions 4
Outline Confidence ellipses when analyzing simultaneously several contingency tables resulting from free-text descriptions 5
Confidence ellipses when analyzing simultaneously several contingency tables resulting from free-text descriptions 6
Projective tests using Napping, the Rorschach test revisited: are the cultural differences between Asians and Caucasians significant? (M. Buche et al. ) • Psychology test created in the 1920s • Named after the Swiss psychologist Hermann Rorschach, and also known as the Rorschach inkblot test or inkblot test • Psychological test analyzing the perceptions of 10 inkblots 7
Psychology : the Rorschach test, a projective test • Belongs to the projective tests: “Personality test designed to let a person respond to ambiguous stimuli, presumably revealing hidden emotions and internal conflicts” (Wikipedia) • Especially helpful when patients are reluctant to describe their thought • Procedure: the analysis of responses is recorded using a tabulation and scoring grid, counting among other things the occurrence of words (selected on the basis of several studies) Free text description 8
oiseau ange aile pelicans langue coyote vampire antechrist vaisseau 9
bisou joyeuse nature arbre barbichette fleurs peinture masque mer 10
nuit chauve_souris papillon epingle demoniaque animal insecte 11
Confidence ellipses when analyzing simultaneously several contingency tables resulting from free-text descriptions 12
… color rocket hip dress skin skinny love sex … twins circus animal wolf gobelin buffon echo pregnant skull death bat butterfly 13
animal bat couleur danse dissection ecrase etalee noir personne rouge 4 1 0 0 1 0 1 2 0 0 2 0 9 0 1 0 0 0 1 0 2 0 3 0 1 0 0 5 2 5 0 0 3 1 0 0 0 5 4 4 8 4 0 0 2 1 0 4 1 0 7 10 0 0 1 0 0 4 0 0 5 2 0 0 3 2 1 2 1 0 3 0 0 3 1 0 0 1 2 0 3 0 8 0 0 0 0 0 0 0 1 1 8 0 0 1 0 0 0 0 14
Confidence ellipses when analyzing simultaneously several contingency tables resulting from free-text descriptions 15
Why several contingency tables? • Order of presentation and preceding sample can influence the perception (carry-over effect) 16
Why several contingency tables? 17
Why several contingency tables? 18
Why several contingency tables? • Order of presentation and preceding sample can influence the perception (carry-over effect) • Two groups of 20 subjects each • Rorschach’s official order • Randomized order Are the two groups of subjects going to lead us to the same representation? 19
How “simultaneously several contingency tables”? • Becue-Bertaut Monica, Pagès Jérôme (2004) A principal axes method for comparing contingency tables: MFACT. Computational Statistics and Data Analysis . 45 (3). pp. 481-503. • An extension of MFA to contingency tables 20
The global representation 21
The partial representations 22
The partial representations for the usual Rorschach’s order only 23
The partial representations for the randomized order only 24
Intermediate results • Globally the two partial representations reflect a same point of view on the plates as far as free-text description is concerned • In our experiment the order of presentation and preceding sample seem to have influenced the perception of the sets of plates as when the official order is used, plates seem to be well separated, which is not the case when the order is randomized 25
Confidence ellipses when analyzing simultaneously several contingency tables resulting from free-text descriptions CADORET Marine 1 , BUCHE Marianne 1 , LÊ Sébastien 1 1 Laboratoire de mathématiques appliquées, A GROCAMPUS O UEST , Rennes 26
Why confidence ellipses? • Position obtained from a given set of subjects • We can wonder: • What is the role of the subjects in the position of the items? • What might have been the positions of the items if the description had been generated by some other subjects? Construction of confidence ellipses around points of the global and partial representations of MFACT 27
Why confidence ellipses? 28
Why confidence ellipses? CADORET Marine BUCHE Marianne LÊ Sébastien My point of view 29
Why confidence ellipses? CADORET Marine BUCHE Marianne LÊ Sébastien Marianne’s point of view 30
Resampling subjects for each table Subjects Items Words 1 k K 1 1 1 × 0 1 I 1 K 1 1 j 1 × 2 j I I Subjects are resampling with replacement 1 J to obtain a new contingency table (words are considered as fixed) × 1 J I 31
Projection as supplementary elements 1 K 1 1 K 2 1 K P 1 i I 1 i I Each « global »row is projected as a supplementary element using transition formula of MFACT 32
Projection of « global » rows as supplementary element 33
Projection as supplementary elements 1 K 1 1 K 2 1 K P 1 i I 1 i I Each « partial » row (row associated with a contingency table) is projected as a supplementary element 34
Projection as supplementary elements 1 K 1 1 K 2 1 K P 1 i I 1 i I Each « partial » row (row associated with a contingency table) is projected as a supplementary element 35
Projection as supplementary elements 1 K 1 1 K 2 1 K P 1 i I 1 i I Each « partial » row (row associated with a contingency table) is projected as a supplementary element using of MFACT: 36
Projection of « partial » rows as supplementary element 37
Process repeated a large number of times 38
39
Intermediate results • As the ellipses seem to be smaller in the case of the “official order” it reinforces the idea that this order is conditioning the way subjects describe the plates, the global configurations obtained from those subjects 40
Thank you for your attention! 41
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