On bias in magnitude scaling and some conjectures of Stevens

Sequential effects in successive ratio estimation

“…Using the mean estimates shown in Table 2, this gives an estimate of of 0.59, which is consistent with values found in other loudness estimation experiments; these tend to be in the range of 0.6-0.7, as shown in Table 1 of DeCarlo (2005). The estimate of the bias b is 0.81, which is also consistent with values obtained in other studies (see Table 1 of DeCarlo, 2005).…”

“…If it is assumed that the corrected exponent obtained via ME and MP (about 0.6) also applies to these other conditions, then one can obtain an estimate of the bias in CMM and successive RE by dividing the obtained exponents (which are estimates of b ) by the corrected exponent of 0.6 (in which case cancels out and one is left with an estimate of the bias, that is, b / b). Note that this approach only assumes that the bias is equal across ME and MP, whereas no assumptions about the bias in CMM are made (see DeCarlo, 2005). For the present loudness experiments, this gives an estimate of bias for the CMM experiment of 1.05, which suggests that there was no bias for CMM.…”

“…This type of generalization has been shown to be quite useful for ME, MP, and CMM (see DeCarlo, 2005). Equation 8 allows for response bias in successive RE-that is, systematic deviations of the ratio estimates from the sensation ratios.…”

“…Note that the inclusion of a bias parameter only affects the parameters of the structural portion of the model; it has no effect on the error process of Equation 7 (and similarly for ME, CMM, and MP). For MP, the exponents of the model are estimates of b/ and b / , respectively (see DeCarlo, 2003DeCarlo, , 2005. Note that if it is assumed that the bias is the same across ME and MP, then taking the geometric mean of the ME exponent, b , and the inverse of the MP exponent, /b, gives an estimate of corrected for bias, as earlier conjectured by Stevens, whereas taking the square root of their ratio gives an estimate of the bias b (see DeCarlo, 2005).…”

Fundamental Measurement of Perceived Length and Perceived Area

“…Complexity of numerical processing affects judgments (Baird, Kreindler, & Jones, 1971;Barth & Paladino, 2011;Booth & Siegler, 2006;DeCarlo, 2005;Duda, 1975;Ekman, Hosman, Lindman, Ljungberg, & Åkesson, 1968;Jones & Marcus, 1961). Mental counting required minimal numerical processing.…”