Quentin Frederik Gronau*, Axel Rosenbruch, Paul Bacher, Henrik Singmann, and David Kellen Poster presented at MathPsych, Québec (2014) Validating Recognition Memory Models for a Task with Ternary Response Options Conclusion Results 1 (summed across participants) Results 1 (summed across participants) Method References Theoretical Background Popular recognition memory models are not fully identified for the simplest recognition memory task with two response options (i.e., “OLD” and “NEW”) unless problematic parameter restrictions are introduced: 2HTM (Snodgrass & Corwin, 1988): Two-high threshold model posits discrete latent memory states (problematic restriction: D o = D n or D n = 0). UVSD (Green & Swets, 1966): Unequal-variance signal detection assumes continuous memory processes (problematic restriction: σ o = σ n ). Goal: Validate fully identified versions of 2HTM (Figure 1a) and UVSD (Figure 1b) for a recognition memory task in which we added an “UNSURE” response option (already used by Singmann, Kellen, & Klauer, 2013). „UNSURE“ is a natural extension of the binary case that is easily understood by participants. We conducted a selective influence study in which we tried to experimentally manipulate model parameters: memory strength manipulation (i.e., presenting some items once and others thrice during the study phase) intended to solely affects memory parameters ( 2HTM: D o and D n ; UVSD: μ o and σ o ) accuracy-based payoff manipulation (i.e., receiving different amounts of points in different test blocks) intended to solely affects response parameters (2HTM: g unsure and g old ; UVSD: c 1 and c 2 ) Participants: 28 undergraduate psychology students (mean age = years; SD = 6.14) from the University of Freiburg Experimental Procedure: 4 study-test blocks 2 (study-strength, within-subjects) × 2 (payoff, within-subjects) design: Study Strength: 40 words presented once (i.e., weak items) and 40 words presented thrice (i.e., strong items) -> a total of 160 words, 80 of them being different in each study phase Payoff schemes: two blocks with standard payoff (correct answer: +2 points, “UNSURE”: 0 points, wrong answer: -2 points) and two blocks with extreme payoff (correct answer: +2 points, “UNSURE”: 0 points, wrong answer: -6 points); blocks were pairwise randomized. We successfully validated 2HTM and UVSD for a recognition memory task with three response options, “OLD", “UNSURE", and “NEW": Experimental manipulations, that were expected to selectively influence memory or guessing processes, indeed affected solely the corresponding parameters of the models (i.e., memory and guessing parameters, respectively). Green, D. M. & Swets, J. A. (1966). Signal detection theory and psychophysics. New York: Wiley. Singmann, H., Kellen, D., & Klauer, K. C. (2013). Investigating the Other-Race Effect of Germans towards Turks and Arabs using Multinomial Processing Tree Models. In M. Knauff, M. Pauen, N. Sebanz, & I. Wachsmuth (Eds.), Proceedings of the 35th Annual Conference of the Cognitive Science Society (pp ). Austin, TX: Cognitive Science Society. Snodgrass, J. G., & Corwin, J. (1988). Pragmatics of measuring recognition memory: Applications to Dementia and Amnesia. Journal of Experimental Psychology: General 117(1), Results 2 As predicted, study strength manipulation solely affected memory parameters (2HTM: D o and D n ; UVSD: μ o and σ o ) As predicted, payoff manipulation solely affected guessing parameters (2HTM: g unsure and g old ; UVSD: c 1 and c 2 ) Figure 1: A graphical depiction of 2HTM (a) and UVSD (b) for a recognition memory task with three response options: „OLD", „UNSURE", and „NEW". Model 2 (7 parameters, 5 df) : memory parameters (2HTM: D o and D n ; UVSD: μ o and σ o ) restricted across payoffs Model 1 (10 parameters, 2 df) : unrestricted model 2HTM: D o 1,st, D o 1,ex, D o ³,st, D o ³,ex,D n,st, D n,ex, g unsure st, g unsure ex, g old st, g old ex UVSD: : μ o 1,st, μ o 1,ex, μ o ³,st, μ o ³,ex, σ o st,, σ o ex, c 1 st, c 1 ex, c 2 st, c 2 ex Model 3b (5 p, 7 df) : Model 2 + response parameters restricted across payoffs (2HTM: g unsure and g old ; UVSD: c 1 and c 2 ) Model 3a (6 p, 6 df) : Model 2 + memory parameters restricted across weak and strong studied items (2HTM: D o and D n ; UVSD: μ o ) UVSD (Model 1): G²(56) = 58.73, p =.38 Critical value in a compromise power χ²-test (α = β): : χ² crit = % of individuals rejected → not significant 2HTM (Model 1): G²(56) = 90.39, p =.002 Critical value in a compromise power χ²-test (α = β): : χ² crit = % of individuals rejected → not significant UVSD (Model 2): ΔG²(84) = 91.86, p =.26; χ² crit = % of individuals rejected → not significant 2HTM (Model 2): Δ G²(84) = ,p =.06 ; χ² crit = % of individuals rejected → not significant UVSD (3a): Δ G²(28) = , p <.001, : χ² crit = % of individuals rejected → significant UVSD (3b): Δ G²(56) = , p <.001, χ² crit = % of individuals rejected → significant 2HTM (3a): Δ G²(28) = , p <.001, χ² crit = % of individuals rejected → significant 2HTM (3b): Δ G²(56) = , p <.001, χ² crit = % of individuals rejected → significant Figure 2: Violin plots of the parameter estimates for the unrestricted 2HTM and the unrestricted UVSD, respectively. “1” and “3” represent items presented once and thrice during study phase, respectively, whereas “st” and “ex” are the abbreviations for standard and extreme payoff scheme, respectively. The outer area depicts the density of each variable. The boxplot depicts the first, the second (i.e., the median), and the third quartile and the area 1.5 times the interquartile range outside those values. The mean is depicted as a x. a) b) 2HTM UVSD