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)

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: Do = Dn or Dn = 0).• UVSD (Green & Swets, 1966): Unequal-variance signal detection assumes continuous memory processes

(problematic restriction: σo = σn).

• 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: Do and Dn ; UVSD: μo and σo)

• accuracy-based payoff manipulation (i.e., receiving different amounts of points in different test blocks) intended to solely affects response parameters (2HTM: gunsure and gold ; UVSD: c1 and c2)

Participants:• 28 undergraduate psychology students (mean age = 22.96 years; SD =

6.14) from the University of FreiburgExperimental 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. 1330-1336). 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), 34-50.

Results 2

• As predicted, study strength manipulation solely affected memory parameters (2HTM: Do and Dn ; UVSD: μo and σo)

• As predicted, payoff manipulation solely affected guessing parameters (2HTM: gunsure

and gold ; UVSD: c1 and c2)

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: Do

and Dn ; UVSD: μo and σo) restricted across payoffs

Model 1 (10 parameters, 2 df):unrestricted model

2HTM: Do1,st, Do

1,ex , Do³,st, Do³,ex,Dn,st, Dn

,ex, gunsure

st, gunsureex, gold

st, goldex

UVSD: : μo1,st , μo

1,ex , μo³,st , μo³,ex, σost,,

σoex, c1

st, c1ex, c2

st, c2ex

Model 3b (5 p, 7 df):Model 2 + response

parameters restricted across

payoffs (2HTM: gunsure and gold ; UVSD: c1 and

c2)

Model 3a (6 p, 6 df):Model 2 + memory

parameters restricted across weak and strong

studied items (2HTM: Do and Dn;

UVSD: μo)

UVSD (Model 1):• G²(56) = 58.73, p = .38

Critical value in a compromise power χ²-test (α = β): : χ²crit = 120.24

• 4% of individuals rejected→ not significant

2HTM (Model 1):• G²(56) = 90.39, p = .002

Critical value in a compromise power χ²-test (α = β): : χ²crit = 120.24

• 11% of individuals rejected

→ not significant

UVSD (Model 2):• ΔG²(84) = 91.86, p = .26; χ²crit =151.72• 11% of individuals

rejected→ not significant

2HTM (Model 2):• Δ G²(84) = 104.43,p = .06 ; χ²crit = 151.72• 11% of individuals rejected→ not significant

UVSD (3a):• Δ G²(28) = 424.17,

p < .001, : χ²crit = 86.70

• 96% of individuals rejected

→ significantUVSD (3b):• Δ G²(56) = 524.21,

p < .001, χ²crit = 120.24

• 93% of individuals rejected

→ significant

2HTM (3a):• Δ G²(28) = 338.70,

p <.001, χ²crit = 86.70

• 93% of individuals rejected

→ significant

2HTM (3b):• Δ G²(56) = 456.16,p <.001, χ²crit = 120.24

• 57 % 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

*quentingronau@web.de