Decomposing the problem-size effect: A comparison of response time distributions across cultures

Abstract

Is the locus of the problem-size effect in mental arithmetic different across cultures? In a novel approach to this question, the ex-Gaussian distributional model was applied to response times for large (e.g., 8 3 9) and small (e.g., 2 3 3) problems obtained from Chinese and Canadian graduate students in a multiplication production task (LeFevre & Liu, 1997). The problem-size effect for the Chinese group occurred in m (the mean of the normal component), whereas the problem-size effect for the Canadian group occurred in both m and t (the mean of the exponential component). The results support the position that the problem-size effect for the Chinese group is purely a memory-retrieval effect, whereas for the Canadian group, it is an effect of both retrieval and the use of nonretrieval solution procedures.

Interoperation transfer in Chinese–English bilinguals’ arithmetic

“…Campbell and Thompson concluded that their NACs' memory for large additions was too weak to attract inhibition and RIF. In contrast, previous research with Asian-Chinese university students has indicated almost exclusive use of retrieval for large additions, albeit slower retrieval than for small additions (e.g., Campbell & Xue, 2001;Penner-Wilger et al, 2002). Near exclusive reliance on memory retrieval for large additions would make our AsianChinese participants more susceptible to RIF for these problems than Campbell and Thompson's NAC participants.…”

Calculation latency: The μ of memory and the τ of transformation

“…Campbell & Austin, 2002;Campbell & Fugelsang, 2001;Campbell et al, 2004;Campbell & Timm, 2000;Campbell & Xue, 2001). Following on the findings of Penner-Wilger et al (2002), the experiment had two main theoretical purposes. The first was to provide converging evidence for the conclusion that procedure use is reflected more in τ than in μ. Penner-Wilger et al inferred this based on expected differences in the frequencies and RT characteristics of procedures, when compared with retrieval.…”

“…Penner-Wilger, Leth-Steensen, & LeFevre (2002) used the ex-Gaussian model to examine differences in RT distributions across cultures, focusing on the PSE. Young adults educated in Canada or China solved single-digit multiplication problems.…”

Psychological interpretation of the ex-Gaussian and shifted Wald parameters: A diffusion model analysis

“…51-57), go/no-go tasks (Heathcote, 2004;Schwarz, 2001), or tasks that involve saccadic eye movements that result in very few errors (Carpenter & Williams, 1995). It is not clear whether the cognitive inter- Balota and Spieler (1999) stimulus driven automatic (nonanalytic) processes central attention demanding (analytic) processes Blough (1988Blough ( , 1989 component of RT unrelated to stimulus variables (e.g., neural transmission and motor response) momentary probability of target detection/ search component of RT Epstein et al (2006), Leth-Steensen et al (2000) attentional lapses Hohle (1968a, 1968b) response choice latency/response competition Gordon and Carson (1990), Hohle (1965), Madden et al (1999), Possamaï (1991), Rotello and Zeng (2008) duration of residual processes (e.g., sensory and motor processes) durations of the decisional phase of RT Kieffaber et al (2006) attentional cognitive processes intentional cognitive processes Penner-Wilger, Leth-Steensen, and Lefevre (2002) retrieval processes nonretrieval/procedure use Rohrer (1996Rohrer ( , 2002, Rohrer and Wixted (1994), Wixted, Ghadisha, and Vera (1997), Wixted and Rohrer (1993) initial pause preceding the retrieval of the first response mean recall latency/ongoing memory search Schmiedek, Oberauer, Wilhelm, Süß, and Wittmann (2007) higher cognitive functioning (e.g., working memory and reasoning) Spieler, Balota, and Faust (1996) more central processing component…”