1. Multidimensional scaling Research Methods Fall 2010 Tamás Bőhm

2. Multidimensional scaling (MDS) Earlier methods: measuring the properties of one specific perceptual dimension (e.g. brightness, pitch) – Simple stimuli with one physical dimension varied Spot of light, pure tones etc. MDS: exploring what the perceptual dimensions are – Complex stimuli with multiple dimensions Faces, melodies, etc. Perceptual maps are created from similarity judgments

3. Multidimensional scaling What does the MDS algorithm do? Kruskal & Wish, 1978 From a matrix of distances…

4. Multidimensional scaling What does the MDS algorithm do? …it calculates a map…

5. Multidimensional scaling What does the MDS algorithm do? …but it cannot tell the orientation and the meaning of the axes.

6. Multidimensional scaling Experiment setup 1.Present the stimuli pair-wise and ask the observer how similar they are (e.g. on a 0-100 scale) 2.Create the dissimilarity matrix 3.Run MDS to get a perceptual map of the stimuli 4.Interpret the dimensions of the map

7. Multidimensional scaling Stimuli: 4 different salt concentrations (A: 0.5%, B: 2%, C: 1%, D: 1.5%) 1.Dissimilarity judgments (0: perfect similarity; 100: no similarity) A vs B: 90 A vs C: 10 A vs D: 55 B vs C: 80 B vs D: 35 C vs D: 45 2.Dissimilarity matrix ABCD A901055 B908035 C108045 D553545 Symmetrical (i.e. A vs B = B vs A)

8. Multidimensional scaling 3.Perceptual map: each stimuli represents a point, their distances correspond to dissimilarities ABCD A901055 B908035 C108045 D553545 ACDB 1D solution

9. Multidimensional scaling 4.Interpreting the dimensions: looking for correspondences between physical and perceptual dimensions Dimension 1 (from MDS) Salt concentration A C D B Dimension 1: intensity of salt taste

10. Multidimensional scaling Another example: soft drinks CokeDiet Coke PepsiDiet Pepsi Cherry Coke Diet Cherry Coke Coke Diet Coke20 Pepsi1022 Diet Pepsi221020 Cherry Coke30364045 Diet Cherry Coke3630454020

11. Multidimensional scaling Coke Pepsi Cherry Coke Diet Pepsi Diet Coke Diet Cherry Coke 20 10 30 Cherry taste Diet taste 2D solution

12. Multidimensional scaling Shepard, 1963: Morse-codes presented in pairs to naïve observers (each possible combination) Same/different task Confusion matrix (% same responses): can be interpreted as a dissimilarity matrix

16. Multidimensional scaling Jacobowitz (see Young, 1974): Children and adults judged the similarity of all pairs of 15 parts of the human body Task: rank ordering of similarity to a standard  dissimilarity matrix

17. Multidimensional scaling 7-year-oldsadults

18. Multidimensional scaling Hair (long/short) Jaw (smooth/rugged) Eye (bright/dark)

19. Multidimensional scaling Additional perceptual dimension revealed

20. Multidimensional scaling

21. Directly asking about the perceptual dimensions: –requires prior knowledge –introduces bias MDS: –no prior assumptions about the possible dimensions (exploratory) –no response bias Reveals the hidden structure of the data MDS is about relationships among stimuli (does not tell us about the perception of individual entities)