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  • Distance & Magnitude EffectsInRhesus Macaques & College StudentsIn collaboration with:Elizabeth Brannon (Duke University)Lisa Son (Barnard College)

  • Which is bigger?a fly or an elephant?

    a jaguar or a cheetah?

    Which city is further from San Francisco?Sacramento or Dallas?Sacramento or Santa Cruz?

    How do we represent such comparisons?

    Propositionally?requires language

    Imagistically?requires pictorial and/or spatial thinking

  • Which letter comes first in the alphabet?N or X?

    K or F?

  • Distance EffectA B C D E F G H I J K L M N O P Q R S T U V W X Y Z Accuracy f(distance)AccuracyCL > AccuracySU

    Reaction Time f(distance) RTC < RTS

  • Magnitude Effect A B C D E F G H I J K L M N O P Q R S T U V W X Y ZAccuracyCF > AccuracyKN > AccuracySV

    RTC < RTK < RTS Accuracy f(magnitude)Reaction Time f(magnitude)

  • Which number is larger? 9 or 4?

    2 or 3?

  • Moyer & Landauer (1967)

  • Distance & Magnitude EffectsDistance and magnitude effects are psychological and not psychophysical processes.

    Differences in RTs cannot be explained by any physical parameter of stimuli.

    They cannot be explained by associative processes which, indeed, predict the opposite of the observed effects.

    They cannot be explained by iterative processes, which predict the opposite of observed effects.

  • How do we make relative judgments of size, distance, weight etc?Prothetic continua intensitive differences (loudness, brightness, etc.)Webers law appliesLogarithmic (Fechner) or power (Stevens) functionsMetathetic continua qualitative differences (hue, pitch, etc.)Webers law does not apply

  • Seven-Item ListsList One List TwoList ThreeList Four

  • A B C D E F G E BSUBSET TEST: WITHIN LISTSSAMPLE SUBSET:(Required order):B E AB AC AD AE AF AG BC BD BE BF BG CD CE CF CG DE DF DG EF EG FGALL SUBSETS:

  • A2 B2 C2 D2 E2 G2 F2 A1 B1 C1 D1 E1 G1 F1 A3 B3 C3 D3 E3 G3 F3A4 B4 C4 D4 E4 G4 F4SUBSET TESTSAMPLE SUBSETS (Required order):E3 G1 B1 F4E3G1D4G3B1F4G3 D4

  • RTs All 7-item subsets-monkey

    REACTION TIMES ON SUBSET TESTS FOLLOWING TRAINING ON 7-ITEM LISTS (MONKEYS)

    INDIVIDUAL SUBSETS

    DISTANCE HELD CONSTANT: EFFECT OF MAGNITUDEMAGNITUDE HELD CONSTANT: EFFECT OF DISTANCE

    pos4 LISTS: INDIVIDUAL SUBSET TESTS4 LISTS: COMBINED SUBSET TEST4 LISTS: RANDOMLY SELECTED PAIRS (WITHIN LISTS)4 LISTS: RANDOMLY SELECTED PAIRS (BETWEEN LISTS)AVERAGEAVERAGE INDIVIDUAL LISTSSUBSET4 LISTS: INDIVIDUAL SUBSET TESTS4 LISTS: COMBINED SUBSET TEST4 LISTS: RANDOMLY SELECTED PAIRS (WITHIN LISTS)4 LISTS: RANDOMLY SELECTED PAIRS (BETWEEN LISTS)AVERAGEAVERAGE INDIVIDUAL LISTSSUBSETAVERAGEAVERAGE INDIVIDUAL LISTS

    AB223016002011230920371947AB223016002011230920371947AB19921992

    BC282519792289229423472364AC206814742197235820241913AC19681968

    CD263822311989319425132286AD153117921774282819811699AD18401840

    DE340323422182311727612642AE187426452300199422032273AE22382238

    EF333424572361311328162717AF206022511902237821482071AF21092109

    FG301123373307343730232885AG196622661992245321692074AG21222122

    AC206814742197235820241913BC282519792289229423472364BC23552355

    BD230537811918260626532668BD230537811918260626532668BD26602660

    CE269724972611238725482601BE292223132909270727132715BE27142714

    DF263429892177241325532600BF197218281937330422601912BF20862086

    EG296922162472279526132552BG222817092073219520512003BG20272027

    AD153117921774282819811699CD263822311989319425132286CD23992399

    BE292223132909270727132715CE269724972611238725482601CE25752575

    CF250818832161232522192184CF250818832161232522192184CF22012201

    DG257021722651327426672464CG256918711968252522332136CG21852185

    AE187426452300199422032273DE340323422182311727612642DE27012701

    BF197218281937330422601912DF263429892177241325532600DF25762576

    CG256918711968252522332136DG257021722651327426672464DG25662566

    AF206022511902237821482071EF333424572361311328162717EF27672767

    BG222817092073219520512003EG296922162472279526132552EG25822582

    AG196623371992245321872098FG301123373307343730232885FG29542954

    AVERAGED ACROSS SUBSETS OF SAME DISTANCE OR MAGNITUDE

    DISTANCE HELD CONSTANT: EFFECT OF MAGNITUDEMAGNITUDE HELD CONSTANT: EFFECT OF DISTANCE

    DISTANCE4 LISTS: INDIVIDUAL SUBSET TESTS4 LISTS: COMBINED SUBSET TEST4 LISTS: RANDOMLY SELECTED PAIRS (WITHIN LISTS)4 LISTS: RANDOMLY SELECTED PAIRS (BETWEEN LISTS)AVERAGEAVERAGE INDIVIDUAL LISTSSUBSET4 LISTS: INDIVIDUAL SUBSET TESTS4 LISTS: COMBINED SUBSET TEST4 LISTS: RANDOMLY SELECTED PAIRS (WITHIN LISTS)4 LISTS: RANDOMLY SELECTED PAIRS (BETWEEN LISTS)AVERAGEAVERAGE INDIVIDUAL LISTSSUBSET

    1290721582356291125832474195520052029238620941996

    2253425912275251224782467245023222225262124052333

    3238320402374278323952266260321212182260823782302

    4213821152068260822322107286925012336293426602569

    5214419801988228621002037315123362417295427152635

    6196623371992245321872098301123373307343730232885

    SUBSETAVERAGEAVERAGE INDIVIDUAL LISTS

    AB20371947

    AC23472364

    AD25132286

    AE27612642

    AF28162717

    AG30232885

    BC20241913

    BD26532668

    BE25482601

    BF25532600

    BG26132552

    CD19811699

    CE27132715

    CF22192184

    CG26672464

    DE22032273

    DF22601912

    DG22332136

    EF21482071

    EG20512003

    FG21872098

    ACCURACY-ALL WITHIN LISTS

    86.284722222284.450644841386.2585.6617890212

    9595.6812594.595.0604166667

    96.0937595.825520833310097.3064236111

    10096.31696428579697.4389880952

    94.866071428697.26562510097.3772321429

    96.87597.6562510098.1770833333

    Monkeys (n=4)Four 7-Item Arbitrary Lists

    4 LISTS: COMBINED SUBSET TEST

    4 LISTS: INDIVIDUAL SUBSET TESTS

    4 LISTS: RANDOMLY SELECTED PAIRS (WITHIN LISTS)

    AVERAGE INDIVIDUAL LISTS

    DISTANCE

    PER CENT CORRECT

    ACCURACY TO 1ST ITEM OF SUBSET

  • RTs All 7-item subsets-monkey

    REACTION TIMES ON SUBSET TESTS FOLLOWING TRAINING ON 7-ITEM LISTS (MONKEYS)

    INDIVIDUAL SUBSETS

    DISTANCE HELD CONSTANT: EFFECT OF MAGNITUDEMAGNITUDE HELD CONSTANT: EFFECT OF DISTANCE

    pos4 LISTS: INDIVIDUAL SUBSET TESTS4 LISTS: COMBINED SUBSET TEST4 LISTS: RANDOMLY SELECTED PAIRS (WITHIN LISTS)4 LISTS: RANDOMLY SELECTED PAIRS (BETWEEN LISTS)AVERAGEAVERAGE INDIVIDUAL LISTSSUBSET4 LISTS: INDIVIDUAL SUBSET TESTS4 LISTS: COMBINED SUBSET TEST4 LISTS: RANDOMLY SELECTED PAIRS (WITHIN LISTS)4 LISTS: RANDOMLY SELECTED PAIRS (BETWEEN LISTS)AVERAGEAVERAGE INDIVIDUAL LISTSSUBSETAVERAGEAVERAGE INDIVIDUAL LISTS

    AB223016002011230920371947AB223016002011230920371947AB19921992

    BC282519792289229423472364AC206814742197235820241913AC19681968

    CD263822311989319425132286AD153117921774282819811699AD18401840

    DE340323422182311727612642AE187426452300199422032273AE22382238

    EF333424572361311328162717AF206022511902237821482071AF21092109

    FG301123373307343730232885AG196622661992245321692074AG21222122

    AC206814742197235820241913BC282519792289229423472364BC23552355

    BD230537811918260626532668BD230537811918260626532668BD26602660

    CE269724972611238725482601BE292223132909270727132715BE27142714

    DF263429892177241325532600BF197218281937330422601912BF20862086

    EG296922162472279526132552BG222817092073219520512003BG20272027

    AD153117921774282819811699CD263822311989319425132286CD23992399

    BE292223132909270727132715CE269724972611238725482601CE25752575

    CF250818832161232522192184CF250818832161232522192184CF22012201

    DG257021722651327426672464CG256918711968252522332136CG21852185

    AE187426452300199422032273DE340323422182311727612642DE27012701

    BF197218281937330422601912DF263429892177241325532600DF25762576

    CG256918711968252522332136DG257021722651327426672464DG25662566

    AF206022511902237821482071EF333424572361311328162717EF27672767

    BG222817092073219520512003EG296922162472279526132552EG25822582

    AG196623371992245321872098FG301123373307343730232885FG29542954

    AVERAGED ACROSS SUBSETS OF SAME DISTANCE OR MAGNITUDE

    DISTANCE HELD CONSTANT: EFFECT OF MAGNITUDEMAGNITUDE HELD CONSTANT: EFFECT OF DISTANCE

    DISTANCE4 LISTS: INDIVIDUAL SUBSET TESTS4 LISTS: COMBINED SUBSET TEST4 LISTS: RANDOMLY SELECTED PAIRS (WITHIN LISTS)4 LISTS: RANDOMLY SELECTED PAIRS (BETWEEN LISTS)AVERAGEAVERAGE INDIVIDUAL LISTSSUBSET4 LISTS: INDIVIDUAL SUBSET TESTS4 LISTS: COMBINED SUBSET TEST4 LISTS: RANDOMLY SELECTED PAIRS (WITHIN LISTS)4 LISTS: RANDOMLY SELECTED PAIRS (BETWEEN LISTS)AVERAGEAVERAGE INDIVIDUAL LISTSSUBSET

    1290721582356291125832474195520052029238620941996

    2253425912275251224782467245023222225262124052333

    3238320402374278323952266260321212182260823782302

    4213821152068260822322107286925012336293426602569

    5214419801988228621002037315123362417295427152635

    6196623371992245321872098301123373307343730232885

    SUBSETAVERAGEAVERAGE INDIVIDUAL LISTS

    AB20371947

    AC23472364

    AD25132286

    AE27612642

    AF28162717

    AG30232885

    BC20241913

    BD26532668

    BE25482601

    BF25532600

    BG26132552

    CD19811699

    CE27132715

    CF22192184

    CG26672464

    DE22032273

    DF22601912

    DG22332136

    EF21482071

    EG20512003

    FG21872098

    ACCURACY-ALL WITHIN LISTS

    86.284722222284.450644841386.2585.6617890212

    9595.6812594.595.0604166667

    96.0937595.825520833310097.3064236111

    10096.31696428579697.