Multidimensional Scaling Methods for Absolute Identification Data

Multidimensional Scaling Methods for Absolute Identification Data Pennie Dodds (Pennie.Dodds@newcastle.edu.au) School of Psychology, University Drive Callaghan, NSW, Australia Chris Donkin (cdonkin@indiana.edu) Department of Psychological and Brain Sciences, 1101 E. 10th S. Bloomington, Indiana Scott Brown (Scott.Brown@newcastle.edu.au) School of Psychology, University Drive Callaghan, NSW, Australia Andrew Heathcote (Andrew.Heathcote@newcastle.edu.au) School of Psychology, University Drive Callaghan, NSW, Australia Abstract Absolute identification exposes a fundamental limit in human information processing. Recent studies have shown that this limit might be extended if participants are given sufficient opportunity to practice. An alternative explanation is that the stimuli used – which vary on only one physical dimension – may elicit psychological representations that vary on two (or more) dimensions. Participants may learn to take advantage of this characteristic during practice, thus improving performance. We use multi-dimensional scaling to examine this question, and conclude that despite some evidence towards the existence of two dimensions, a one dimensional account cannot be excluded. Keywords: absolute identification; unidimensional stimuli; multidimensional scaling; MDS; learning A typical Absolute Identification (AI) task uses stimuli that vary on only one physical dimension, such as loudness, brightness, or length. These stimuli are first presented to the participant one at a time, each uniquely labeled (e.g. #1 through to n). The participant is then presented with random stimuli from the set, without the label, and asked to try and remember the label given to it previously. This seemingly simple task exhibits many interesting benchmark phenomena. The one of most concern for the current paper is the apparent limitation in performance. The maximum number of stimuli that people were previously thought to be able to perfectly identify was only 7±2 (Miller, 1956). Performance was thought to improve slightly with practice and then reach a low asymptote (Pollack, 1952; Garner 1953). This finding was particularly surprising given that this limit appeared to be resistant to practice (Garner, 1953; Weber, Green & Luce, 1977), and was generally consistent across a range of modalities (e.g. line length: Lacouture, Li & Marley, 1998; tone frequency: Pollack, 1952; Hartman, 1954; tone loudness: Garner, 1953; Weber, Green & Luce, 1977). In addition, this limitation appears to be unique to unidimensional stimuli. For example, people are able to remember hundreds of faces and names, and dozens of alphabet shapes. It is generally accepted that this is because objects such as faces, names, and letters vary on multiple dimensions. Performance generally increases as the number of dimensions increase (Eriksen & Hake, 1955). This makes intuitive sense when one considers the individual dimensions on a multidimensional object. For example, if people are able to learn to perfectly identify 7 lengths, and 7 widths, they could potentially learn to identify 49 rectangles formed by a combination of lengths and widths. Despite decades of research confirming this limit in performance for unidimensional stimuli, more recent research has suggested that we may be able to significantly increase this limit through practice (Rouder, Morey, Cowan and Pfaltz, 2004; Dodds, Donkin, Brown & Heathcote, submitted). For example, given approximately 10 hours of practice over 10 days, Dodds et al.’s participants learned to perfectly identify a maximum of 17.5 stimuli (out of a possible 36), a level significantly beyond the 7±2 limit suggested by Miller (1956). From 58 participants that took part in a series of AI tasks, 22 exceeded the upper end of Miller’s limit range (nine stimuli). Other Stimulus Dimensions The results from Dodds et al. (submitted) were not limited to the identification of lines varying in length. Dodds et al. also used a wide range of other stimuli, and found similar learning effects. For example, dots varying in separation, lines varying in angle and tones varying in pitch all demonstrated similar results. Participants learned to perfectly identify a maximum of 12.6 stimuli using dots varying in separation, 10.4 using lines varying in angle and 17.5 using tones varying in frequency, all exceeding Miller’s (1956) upper limit of 9 stimuli. The learning effects from Rouder et al. (2004) and Dodds et al. (submitted) may be attributed to the type of stimuli employed. The existence of severe limitations in