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Jun 17, 2023 188 likes •608 views

Confidence ellipses when analyzing simultaneously several contingency tables resulting from free-text descriptions CADORET Marine 1 , BUCHE Marianne 1 , L Sbastien 1 1 Laboratoire de mathmatiques appliques, A GROCAMPUS O UEST , Rennes 1

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Confidence ellipses when analyzing simultaneously several contingency tables resulting from free-text descriptions

CADORET Marine1 , BUCHE Marianne1, LÊ Sébastien1

1 Laboratoire de mathématiques appliquées, AGROCAMPUS OUEST, Rennes

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Confidence ellipses when analyzing simultaneously several contingency tables resulting from free-text descriptions

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Outline

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Confidence ellipses when analyzing simultaneously several contingency tables resulting from free-text descriptions

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Outline

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Confidence ellipses when analyzing simultaneously several contingency tables resulting from free-text descriptions

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Outline

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Confidence ellipses when analyzing simultaneously several contingency tables resulting from free-text descriptions

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Outline

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Confidence ellipses when analyzing simultaneously several contingency tables resulting from free-text descriptions

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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
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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

  • ccurrence of words (selected on the basis of several studies)

 Free text description

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vampire coyote ange aile

  • iseau

pelicans langue vaisseau antechrist

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nature arbre mer masque barbichette fleurs peinture bisou joyeuse

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chauve_souris papillon animal insecte epingle demoniaque nuit

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Confidence ellipses when analyzing simultaneously several contingency tables resulting from free-text descriptions

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color rocket twins animal hip skin bat skull love gobelin echo dress skinny sex circus wolf buffon pregnant death butterfly

… …

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animal bat couleur danse dissection ecrase etalee noir personne rouge 4 1 1 1 2 2 9 1 1 2 3 1 5 2 5 3 1 5 4 4 8 4 2 1 4 1 7 10 1 4 5 2 3 2 1 2 1 3 3 1 1 2 3 8 1 1 8 1

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Confidence ellipses when analyzing simultaneously several contingency tables resulting from free-text descriptions

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Why several contingency tables?

  • Order of presentation and preceding sample can influence the

perception (carry-over effect)

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Why several contingency tables?

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Why several contingency tables?

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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?

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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
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The global representation

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The partial representations

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The partial representations for the usual Rorschach’s order only

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The partial representations for the randomized order only

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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

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Confidence ellipses when analyzing simultaneously several contingency tables resulting from free-text descriptions

CADORET Marine1 , BUCHE Marianne1, LÊ Sébastien1

1 Laboratoire de mathématiques appliquées, AGROCAMPUS OUEST, Rennes

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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

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Why confidence ellipses?

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Why confidence ellipses?

CADORET Marine BUCHE Marianne LÊ Sébastien

My point of view

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Why confidence ellipses?

CADORET Marine BUCHE Marianne LÊ Sébastien

Marianne’s point of view

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1 K1 k Words Items Subjects 1 I 1 I 1 I 1 1 j j J J

× 0 × 2 × 1

1 K1 1 I Subjects are resampling with replacement to obtain a new contingency table (words are considered as fixed)

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Resampling subjects for each table

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1 K1 1 I i 1 K2 1 KP 1 I i Each « global »row is projected as a supplementary element using transition formula of MFACT

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Projection as supplementary elements

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Projection of « global » rows as supplementary element

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1 K1 1 I i 1 K2 1 KP 1 I i Each « partial » row (row associated with a contingency table) is projected as a supplementary element

Projection as supplementary elements

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1 K1 1 I i 1 K2 1 KP 1 I i Each « partial » row (row associated with a contingency table) is projected as a supplementary element

Projection as supplementary elements

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1 K1 1 I i 1 K2 1 KP 1 I i Each « partial » row (row associated with a contingency table) is projected as a supplementary element using of MFACT:

Projection as supplementary elements

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Projection of « partial » rows as supplementary element

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Process repeated a large number of times

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Intermediate results

  • As the ellipses seem to be smaller in the case of the “official
  • rder” it reinforces the idea that this order is conditioning the

way subjects describe the plates, the global configurations

  • btained from those subjects
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Thank you for your attention!