Download Supplementary Online Materials A

ONLINE MATERIALS
Online Materials A
Descriptive Statistics for the Observed Data in the Main Experiments 1–7
Table OA1
Number of Objects in Experiments 1–7
Experiment, objects
1, Cities
Unrecognized
objects
97.00
(4.59)
Mean number of objects
(SE)
Tartle objects
Knowledge
objects
45.10
72.35
(3.08)
(3.84)
Nparticipants
49
2, Cities
84.77
(3.51)
44.82
(2.28)
79.56
(3.61)
71
3, Cities
96.95
(3.69)
45.47
(2.84)
71.51
(3.86)
55
4, Countries
11.60
(1.76)
46.25
(5.77)
91.40
(7.80)
20
5, Companies
35.81
(2.71)
6.29
(0.84)
32.33
(1.85)
21
6, Diseases
24.95
(1.92)
7.70
(1.01)
16.30
(1.06)
20
7, Politicians
106.74
12.63
47.74
19
(4.24)
(1.64)
(3.25)
Note. Numbers of objects were computed for each participant individually and then averaged
across participants.
1
ONLINE MATERIALS
Table OA2
Time It Took Participants to Judge an Object as Recognized or Unrecognized in the
Recognition Tasks of Experiments 1–7
Experiment, objects
1, Cities
Means of median time in seconds
(SE)
Unrecognized Tartle objects
Knowledge
objects
objects
.87
.83
.66
(.03)
(.03)
(.01)
2, Cities
.89
(.03)
.81
(.02)
.64
(.01)
3, Cities
.74
(.02)
.72
(.02)
.61
(.01)
4, Countries
1.13
(.08)
.75
(.04)
.60
(.03)
5, Companies
1.19
(.16)
1.17
(.09)
.77
(.03)
6, Diseases
1.39
(.12)
1.27
(.15)
.81
(.03)
7, Politicians
.93
1.10
.78
(.04)
(.04)
(.02)
Note. Times on knowledge and tartle objects are referred to as recognition times in the main
text. Times were computed as medians for each participant individually and then averaged
across participants.
2
ONLINE MATERIALS
Table OA3
Number of Exhaustive Paired Comparisons of Two Objects in Experiments 1–7
Experiment,
objects
Unrecognized
pairs
Mean number of exhaustive comparisons between two objects
(SE)
Tartle–
Knowledge–
Tartle pairs
Tartle–
unrecognized unrecognized
knowledge
pairs
pairs
pairs
565.67
641.57
198.76
421.78
(34.37)
(37.96)
(25.91)
(27.62)
Knowledge
pairs
1, Cities
962.71
(75.01)
2, Cities
765.58
(51.74)
551.99
(31.63)
614.48
(31.16)
182.92
(17.62)
429.96
(18.36)
668.10
(48.58)
3, Cities
935.53
(59.46)
592.44
(35.38)
637.29
(38.12)
195.62
(20.37)
405.24
(27.10)
562.20
(47.80)
4, Countries
91.00
(24.06)
578.80
(119.66)
907.35
(128.09)
1,362.75
(288.87)
3,575.05
(322.47)
4,708.55
(702.67)
5, Companies
696.57
(84.44)
216.57
(32.23)
1,073.10
(65.75)
23.71
(6.58)
197.52
(22.90)
540.71
(65.19)
6, Diseases
333.65
(38.70)
179.70
(21.29)
386.00
(33.43)
35.55
(10.43)
122.00
(17.18)
135.35
(18.49)
7, Politicians
554.14
(45.95)
5,804.47
1,384.63
5,018.21
97.63
551.00
1,210.68
(436.61)
(184.96)
(309.24)
(25.34)
(61.59)
(166.41)
Note. Numbers of pairs were computed for each participant individually and then averaged across participants. Comparisons of cities
are computed within a country.
3
ONLINE MATERIALS
4
Table OA4
Proportion of Correct Inferences Participants Made in Experiments 1–3
Experiment, object,
criterion
Unrecognized
pairs
1, Cities, size
.55
(.02)
2, Cities, fame
.57
(.02)
Mean proportion of correct inferences
(SE)
Tartle–
Knowledge–
Tartle pairs
Tartle–
unrecognized unrecognized
knowledge
pairs
pairs
pairs
.70
.81
.61
.71
(.02)
(.02)
(.05)
(.02)
.84
(.02)
.95
(.01)
.68
(.03)
.79
(.02)
Knowledge
pairs
.73
(.02)
.69
(.02)
3, Cities, size
.51
.60
.76
.57
.62
.61
(.02)
(.02)
(.02)
(.04)
(.02)
(.02)
Note. Proportions of correct inferences were computed for each participant individually and then averaged across participants. City size
corresponds to the number of inhabitants of a city. We operationalized city fame as the proportion of participants who recognized a city
in Experiments 1, 2, and 3.
ONLINE MATERIALS
Table OA5
Inference Times in Experiments 1–3
Experiment,
object,
criterion
1, Cities,
size
2, Cities,
fame
Unrecognized
pairs
2.04
(.10)
1.96
(.09)
Means of median inference times in seconds
(SE)
Tartle–
Knowledge–
Tartle pairs
Tartle–
unrecognized unrecognized
knowledge
pairs
pairs
pairs
1.90
1.67
2.18
1.98
(.09)
(.07)
(.12)
(.08)
1.62
(.06)
1.38
(.03)
1.79
(.06)
1.50
(.04)
Knowledge
pairs
2.14
(.10)
1.62
(.06)
3, Cities,
.93
.92
.89
.94
.88
.91
size
(.01)
(.01)
(.01)
(.02)
(.01)
(.01)
Note. Inference times are the times it took participants to make an inference in the inference tasks. Median inference times were
computed for each participant individually and then averaged across participants.
5
ONLINE MATERIALS
Online Materials B
Stimuli Used in the Experiments
Objects included cities (Experiments 1–3, 10), countries, companies, diseases, and
politicians (Experiments 4–9). Counts of the number of websites in which an object’s name
occurred were produced by the search engine Yahoo on November 3, 2006 (Experiments 1–3),
and on May 15, 2007 (Experiments 4–9).
Experiments 1–3, 10. City names (Table OB1) and statistics on city size were retrieved
from http://www.citypopulation.de. We excluded the capitals from the retrieved lists of cities
because Germans are likely to know for sure that, for instance, Paris and London are the largest
cities in France and Great Britain, respectively. Such conclusive knowledge about the criterion
(i.e., city size) allows people to deduce with certainty (rather than to infer under uncertainty)
that the capital cities are larger than other cities (for a discussion of the differences between
inferences and deductions, see Gigerenzer et al., 1991; Pachur & Hertwig, 2006). We
additionally dropped the smallest of the British, U.S., and Austrian cities as well as the six
smallest Italian cities from the lists of retrieved cities. Dropping these cities allowed us to
divide the tasks in our experiments into even parts that were separated by a reasonable number
of breaks,
Experiments 4–9. Country names (Table OB2) and statistics on countries’ gross
domestic product were retrieved from http://www.destatis.de (German Federal Statistical
Office); company names (Table OB3) and statistics on companies’ market capitalization from
http://deutsche-boerse.com (German Stock Exchange); disease names (Table OB4) from
http://www.rki.de (German Federal Agency for Disease Control and Prevention); and
politicians’ names (Table OB5) from http://de.wikipedia.org.
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ONLINE MATERIALS
Modifications and exclusion of stimuli. The retrieved lists of names were slightly
modified: (a) Where the spelling of names differed from the names in common usage, we used
the more common spelling. (b) We deleted the Democratic Republic of Congo from the
retrieved list of countries. Its name closely resembles that of another country, namely, the
Republic of Congo. Many participants would not know that there are, in fact, two countries
with the name Congo, and we did not want them to mistakenly believe that there was an error
in the set of stimuli. To allow the tasks in our experiments to be divided into even parts
separated by a reasonable number of breaks, we added Monaco, San Marino, Andorra, and
Vatican City as filler stimuli to the list of city names. These four fillers were excluded from all
analyses. Moreover, one name from the country list, Great Britain, was excluded from all
analyses because there was a typographical error in its name. Finally, the countries Myanmar
and Cuba could not be included in all analyses, as we did not find information on these
countries’ gross domestic product. (c) In the history of the Federal Republic of Germany, two
politicians have shared the same name. We used this name only once.
7
ONLINE MATERIALS
Table OB1
City Names (in German) Used in Experiments 1–3, 10
Cities

Aachen

Colombes

Lille

Prato

Aberdeen

Columbus

Limoges

Preston

Albacete

Córdoba

Livorno

Quimper

Alcorcón

Coventry

Logroño

Raleigh

Alicante

Crawley

Lorca

Rankweil

Almería

Créteil

Lorient

Ravenna

Amiens

Dallas

Lübeck

Reading

Anaheim

Denver

Lustenau

Reims

Ancona

Derby

Luton

Rennes

Andria

Detroit

Mailand

Rimini

Angers

Dijon

Mainz

Rostock

Antibes

Dornbirn

Málaga

Roubaix

Arezzo

Dortmund

Mannheim

Rouen

Atlanta

Drancy

Marbella

Sabadell

Augsburg

Dresden

Mataró

Salerno

Aurora

Dudley

Memphis

Salzburg

Austin

Duisburg

Messina

Sassari

Avignon

Dundee

Miami

Schwaz

Avilés

Elche

Modena

Seattle

Badajoz

Erfurt

Mödling

Sevilla

Badalona

Essen

Monza

Siracusa

Baden

Exeter

Móstoles

Slough

Barletta

Ferrara

München

Solingen

Belfast

Florenz

Münster

Spittal

Bergamo

Foggia

Murcia

Steyr

Besançon

Forlì

Nancy

Swansea

Béziers

Fresno

Nanterre

Swindon

Bilbao

Fürth

Nantes

Tampa

Bludenz

Genua

Neapel

Tarent

Bochum

Getafe

Neuss

Tarrasa

Bologna

Gijón

Newark

Telde

Bolton

Glasgow

Newport

Telfs

Bordeaux

Gmunden

Nîmes

Terni

Boston

Granada

Nizza

Ternitz

Bottrop

Grenoble

Norwich

Toledo

Bourges

Guecho

Novara

Toulon

Bozen

Hagen

Nürnberg

Toulouse

Bradford

Hallein

Oakland

Tours

Braunau

Hamburg

Oldham

Traun

Bregenz

Hannover

Omaha

Trient
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ONLINE MATERIALS
Cities

Bremen

Herne

Orense

Triest

Brescia

Hohenems

Orléans

Tucson

Brest

Honolulu

Oviedo

Tulln

Brighton

Houston

Oxford

Tulsa

Brindisi

Huelva

Padua

Turin

Bristol

Ipswich

Palermo

Udine

Buffalo

Kassel

Pamplona

Valence

Burgos

Köflach

Parla

Valencia

Cáceres

Krefeld

Parma

Venedig

Cádiz

Krems

Perugia

Verona

Cagliari

Kufstein

Pesaro

Vicenza

Calais

Latina

Pescara

Villach

Cannes

Lecce

Phoenix

Vitoria

Cardiff

Leeds

Piacenza

Walsall

Casoria

Leganés

Pistoia

Watford

Catania

Leipzig

Plymouth

Wichita

Cesena

Leoben

Poitiers

Wörgl

Chemnitz

Leonding

Poole

Würzburg

Chicago

Lérida

Portland

Zaragoza

Colmar

Lienz

Potsdam

Zwettl
9
ONLINE MATERIALS
Table OB2
Country Names (in German) Used in Experiment 4
Countries

Ägypten

Iran

Pakistan

Albanien

Irland

Panama

Algerien

Island

Papua-Neuguinea

Andorra

Israel

Paraguay

Angola

Italien

Peru

Argentinien

Jamaika

Philippinen

Armenien

Japan

Polen

Aserbaidschan

Jemen

Portugal

Äthiopien

Jordanien

Republik Kongo

Australien

Kambodscha

Ruanda

Bahamas

Kamerun

Rumänien

Bahrain

Kanada

Russland

Bangladesch

Kap Verde

Sambia

Barbados

Kasachstan

San Marino

Belgien

Katar

Saudi-Arabien

Belize

Kenia

Schweden

Benin

Kirgisistan

Schweiz

Bhutan

Kiribati

Senegal

Bolivien

Kolumbien

Serbien und Montenegro

Bosnien und Herzegowina

Komoren

Sierra Leone

Botsuana

Kroatien

Simbabwe

Brasilien

Kuba

Singapur

Brunei Darussalam

Kuwait

Slowakei

Bulgarien

Laos

Slowenien

Burkina Faso

Lesotho

Spanien

Burundi

Lettland

Sri Lanka

Chile

Libanon

Südafrika

China

Libyen

Südkorea

Costa Rica

Litauen

Sudan

Côte d'Ivoire

Luxemburg

Suriname

Dänemark

Madagaskar

Swasiland

Deutschland

Malawi

Syrien

Dominikanische Republik

Malaysia

Tadschikistan

Dschibuti

Malediven

Taiwan

Ecuador

Mali

Tansania

El Salvador

Malta

Thailand

Eritrea

Marokko

Togo

Estland

Mauretanien

Trinidad und Tobago

Finnland

Mauritius

Tschad

Frankreich

Mazedonien

Tschechische Republik
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ONLINE MATERIALS
Countries

Gabun

Mexiko

Tunesien

Gambia

Moldau

Türkei

Georgien

Monaco

Turkmenistan

Ghana

Mongolei

Uganda

Grenada

Mosambik

Ukraine

Griechenland

Myanmar

Ungarn

Großbritannien

Namibia

Uruguay

Guatemala

Nepal

USA

Guinea

Neuseeland

Usbekistan

Guinea-Bissau

Nicaragua

Vatikanstadt

Guyana

Niederlande

Venezuela

Haiti

Niger

Vereinigte Arabische Emirate

Honduras

Nigeria

Vietnam

Indien

Norwegen

Weißrussland

Indonesien

Oman

Zentralafrikanische Republik

Irak

Österreich

Zypern
11
ONLINE MATERIALS
Table OB3
Company Names Used in Experiment 5
Companies

Aareal Bank

Deutsche Postbank

Infineon Technologies

Premiere

adidas

Deutsche Telekom

IVG Immobilien

ProSiebenSat.1 Media

Allianz

Deutz

IWKA

Puma

Altana

Douglas

K+S

Rheinmetall

AMB Generali

E.ON

Karstadt Quelle

RHÖN-KLINIKUM

AWD Holding

EADS

Klöckner

RWE

BASF

Fraport

Krones

Salzgitter

Bayer

Fresenius

LANXESS

SAP

Beiersdorf

Fresenius Medical Care

Leoni

SGL Carbon

Bilfinger Berger

GAGFAH

Linde

Siemens

BMW

GEA Group

MAN

STADA Arzneimittel

Celesio

Hannover

Merck

Südzucker

Commerzbank
Rückversicherung

METRO

Symrise

Continental

HeidelbergCement

MLP

Techem

DaimlerChrysler

Heidelberger

MTU Aero Engines

ThyssenKrupp
Druckmaschinen

DEPFA BANK

Münchener Rück

TUI

Deutsche Bank

Henkel

Norddeutsche Affinerie

Volkswagen

Deutsche Börse

HOCHTIEF

PATRIZIA Immobilien

Vossloh

Deutsche EuroShop

Hugo Boss

Pfleiderer

Wacker Chemie

Deutsche Lufthansa

Hypo Real Estate

Praktiker Bau- und

WINCOR NIXDORF
Deutsche Post

IKB Dt. Industriebank

Heimwerkermärkte
12
ONLINE MATERIALS
Table OB4
Disease Names (in German) Used in Experiments 6 and 8
Diseases

Adenovirus

Giardiasis

Legionellose

Röteln

Botulismus

Haemophilus influenzae

Lepra

Salmonellose

Brucellose

Hämolytisch-urämisches

Leptospirose

Shigellose
Syndrom

Sonstige virale

Campylobacter-Enteritis

Listeriose

Cholera

Hantavirus-Erkrankung

Malaria

Creutzfeld-Jakob-

Hepatitis A

Masern

Syphilis
Krankheit

Hepatitis B

Meningokokken

Tollwut

Denguefieber

Hepatitis C

Milzbrand

Toxoplasmose

Diphtherie

Hepatitis D

Norovirus-Gastroenteritis

Trichinellose

E.-coli-Enteritis

Hepatitis E

Ornithose

Tuberkulose

Echinokokkose

Hepatitis Non A-E

Paratyphus

Tularämie

EHEC-Erkrankung

HIV-Infektion

Pest

Typhus abdominalis

Fleckfieber

Influenza

Poliomyelitis

Yersiniose

Frühsommer-

Kryptosporidiose

Q-Fieber
Meningoenzephalitiss

Läuserückfallfieber

Rotavirus-Erkrankung
hämorrhagische Fieber
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Table OB5
Politicians’ Names Used in Experiments 7 and 9
Politicians

Konrad Adenauer

Michael Glos

Werner Maihofer

Hans Schuberth

Walter Arendt

Johann Baptist Gradl

Lothar de Maizière

Irmgard Schwaetzer

Egon Bahr

Kurt Gscheidle

Thomas de Maizière

Werner Schwarz

Siegfried Balke

Dieter Haack

Hans Matthöfer

Elisabeth Schwarzhaupt

Martin Bangemann

Kai-Uwe von Hassel

Erich Mende

Christian Schwarz-

Rainer Barzel

Gerda Hasselfeldt

Hans-Joachim von

Gerhart Baum

Volker Hauff
Merkatz

Hans-Christoph Seebohm

Ernst Benda

Helmut Haussmann

Angela Merkel

Horst Seehofer
Wolfgang Mischnick

Rudolf Seiters
Schilling

Christine Bergmann

Gustav Heinemann


Sabine Bergmann-Pohl

Heinrich Hellwege

Jürgen Möllemann

Carl-Dieter Spranger

Theodor Blank

Hermann Höcherl

Alex Möller

Wolfgang Stammberger

Franz Blücher

Bodo Hombach

Werner Müller

Heinz Starke

Norbert Blüm

Antje Huber

Franz Müntefering

Frank Walter Steinmeier

Kurt Bodewig

Richard Jaeger

Fritz Neumayer

Peer Steinbrück

Wolfgang Bötsch

Gerhard Jahn

Alois Niederalt

Manfred Stolpe

Friedrich Bohl

Franz Josef Jung

Wilhelm Niklas

Gerhard Stoltenberg

Jochen Borchert

Jakob Kaiser

Claudia Nolte

Anton Storch

Willy Brandt

Manfred Kanther

Theodor Oberländer

Franz Josef Strauß

Aenne Brauksiepe

Hans Katzer

Rainer Offergeld

Käte Strobel

Heinrich von Brentano di

Ignaz Kiechle

Rainer Ortleb

Peter Struck
Eduard Oswald

Richard Stücklen
Tremezzo

Kurt Georg Kiesinger


Ewald Bucher

Klaus Kinkel

Victor-Emanuel Preusker

Rita Süssmuth

Andreas von Bülow

Hans Klein

Karl Ravens

Wolfgang Tiefensee

Edelgard Bulmahn

Reinhard Klimmt

Günter Rexrodt

Robert Tillmanns

Wolfgang Clement

Helmut Kohl

Heinz Riesenhuber

Klaus Töpfer

Herta Däubler-Gmelin

Waldemar Kraft

Walter Riester

Jürgen Trittin

Rolf Dahlgrün

Günther Krause

Hannelore Rönsch

Hans-Jochen Vogel

Thomas Dehler

Heinrich Krone

Helmut Rohde

Theodor Waigel

Klaus von Dohnanyi

Hans Krüger

Volker Rühe

Walter Wallmann

Werner Dollinger

Paul Krüger

Jürgen Rüttgers

Hansjoachim Walther

Horst Ehmke

Renate Künast

Hermann Schäfer

Jürgen Warnke

Herbert Ehrenberg

Karl-Hans Laermann

Fritz Schäffer

Karl Weber

Hans Eichel

Oskar Lafontaine

Wolfgang Schäuble

Herbert Wehner

Hans A. Engelhard

Manfred Lahnstein

Rudolf Scharping

Heinz Westphal

Björn Engholm

Otto Graf Lambsdorff

Annette Schavan

Ludger Westrick

Erhard Eppler

Lauritz Lauritzen

Walter Scheel

Heidemarie Wieczorek-

Ludwig Erhard

Georg Leber

Karl Schiller
Eberhard Wildermuth
Zeul

Josef Ertl

Robert Lehr

Otto Schily


Franz Etzel

Ursula Lehr

Marie Schlei

Hans Wilhelmi

Andrea Fischer

Ernst Lemmer

Carlo Schmid

Dorothee Wilms
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Politicians

Joschka Fischer

Hans Lenz

Helmut Schmidt

Heinrich Windelen

Katharina Focke

Hans Leussink

Renate Schmidt

Hans-Jürgen Wischnewski

Egon Franke

Sabine Leutheusser-

Ulla Schmidt

Matthias Wissmann

Hans Friderichs
Schnarrenberger

Edzard Schmidt-Jortzig

Manfred Wörner

Anke Fuchs

Ursula von der Leyen

Jürgen Schmude

Franz-Josef Wuermeling

Karl-Heinz Funke

Hermann Lindrath

Kurt Schmücker

Friedrich Zimmermann

Sigmar Gabriel

Heinrich Lübke

Oscar Schneider

Brigitte Zypries

Heiner Geißler

Paul Lücke

Rupert Scholz

Hans-Dietrich Genscher

Hans Lukaschek

Gerhard Schröder
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Online Materials C
Perceptual-Motor Times
In ACT-R, different actions take prescribed amounts of time. We wrote an ACT-R
model that implemented two production rules to model the perceptual-motor times in the trials
in the computerized recognition tasks in our experiments. In each trial, one object was shown at
a time, and participants had to judge whether they recognized the object. Participants
responded by pressing a key. When the first production rule, attend-encode, is fired, a request
is made to attend and encode the object. It takes 50 msec to fire this production rule, and 85
msec to attend and encode the object. When the second production rule, press-key, is fired, a
request is made to press the key. It takes 50 msec to fire this production rule, 250 msec to
prepare the movement, 50 msec to initiate the action, and another 100 msec for the key to be
struck. Thus, the total perceptual-motor time in a trial in the recognition tasks is 585 msec.
Production rule attend-encode
If the goal is to attend and encode an object and the visual location of the object is
known and focused on,
Then attend and encode the object and set the goal to press a key.
Production rule press-key
If the goal is to press a key,
Then prepare the features of the movement, initiate the action, and press the key.
Note that in each trial in the recognition tasks, prior to each presentation of an object, a
small fixation cross was shown in the place where the object would subsequently appear.
Participants were instructed to always fixate on this cross when it appeared. The production
rule attend-encode takes this into account by assuming that a participant would already know
the visual location of an object.
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Online Materials D
Detailed Descriptions of Simulations 1–11 (Main text) and C1–C3 (Appendix C)
The summaries of our simulations are necessarily incomplete, simplified descriptions of
computer code. We invite interested readers to contact us for implementation details.
In Simulations 2, 3, 9, C1, C2, and C3, each run of our memory model can be thought
of as generating one hypothetical person's recognition responses, knowledge responses, and
recognition times for each of the objects considered in the simulation. In those simulations that
additionally involve the timing model, this hypothetical person's predicted data is then fed into
the timing model in the same way as the observed data is fed into it. That is, the simulation
structure imposed by the timing model on the data predicted by the memory model is always
identical to the structure imposed on our observed data.
Using the Ecological Memory Model to Predict Memory Performance From the
Environment: Simulation 1
In Simulation 1, we examined whether environmental data enables our memory model
to account for the probabilities of recognizing objects and retrieving knowledge about them, as
well as for the associated recognition time distributions.
Model Calibration. In ACT-R, a chunk’s activation equals the log odds
(ln[PR/(1−PR)]) that a chunk is needed in the current context. We calibrated the memory model
to log recall odds, which indirectly calibrates log need odds. To calibrate the memory model to
the observed recognition probabilities of Experiment 1, we transformed them and Equation 5
into their log odds forms. In doing so, to avoid division by zero (where PR = 1) and infinity
(where PR = 0), we corrected PR = 1 to PR – 1 / (2N) and PR = 0 to PR + 1 / (2N) (N = number
of participants in Experiment 1). Using the log odds form of the observed recognition
probabilities and of Equation 5, we estimated the constant, cR (-8.52), the total retrieval noise, s
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(.83), and the scaling parameter, bR (.70), in a nonlinear regression analysis. We anchored the
activation scale by setting the expected value of the retrieval criterion distribution, τ, to zero;
an object with an activation of 0 would have a 50% chance of being retrieved. (This parameter
can be arbitrarily set; the memory model’s fit in the regression analysis does not depend on it.)
With these parameters fixed, in a second calibration step we transformed the observed
knowledge probabilities of Experiment 1 and Equation 6 into their log-odds forms and
estimated the constant cK (-9.93) and the scaling parameter bK (.68) in a nonlinear regression
analysis.
In a final calibration step, we calibrated the memory model to the recognition time
distributions of Experiment 1, striking a balance between fitting the distributions’ 25th, 50th,
and 75th percentiles by informally searching the parameter space (i.e., through visual
inspection of Figure 4). Specifically, to calibrate the memory model, we estimated those parts
of each object’s activation distribution that fell above the retrieval criterion, and we computed a
retrieval time distribution from it (i.e., using Equation 7). This is the retrieval time distribution
given that the object is retrieved (cf. Equation 4). We assume there is not just one retrieval
criterion, but rather a probability distribution of retrieval criteria (Appendix B). Therefore, we
split the total retrieval noise estimated previously from the observed recognition probabilities
into criterion noise and activation noise, which determine the shape of the retrieval criterion
and activation distributions, respectively. We then computed retrieval time distributions across
the retrieval criterion distribution. In doing so, we estimated the criterion noise, sτ (.60), and the
scaling parameter F (.49). The activation noise is fixed (sA = .58) once sτ is estimated (Equation
8), and the parameter values for cR and bR were set to the values estimated previously from the
observed recognition probabilities. We assume recognition times are a function of retrieval
times plus perceptual-motor times (Equation 7). We set the standard deviation of the
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perceptual-motor time distribution to .12 sec, which is a value we estimated in conjunction
with the other parameters (F, sτ).
Data Predicted by the Memory Model. To test how well the memory model predicts
behavior, we used Equations 5–8 with the fixed parameters to predict the recognition and
knowledge probabilities (PR and PK respectively) as well as the recognition times in
Experiments 2–9.
Quantifying Cognitive Niches: Simulation 2
In Simulation 2, we quantified the overlap between the niches of the fluency heuristic,
the recognition heuristic, and knowledge-based strategies.
Applying the Timing Model to the Observed data. For each participant of
Experiments 2–7, objects were exhaustively paired and grouped into bins according to the
ranks of each object’s environmental frequency, as measured by its web frequency. There were
50 bins for cities, and 20 bins for countries, companies, diseases, and politicians. (We tried to
allocate the same number of data points to each bin. Where the total number of data points was
not divisible by the number of bins, the size of some bins were increased to accommodate one
extra data point. Which bins’ sizes were increased was determined at random.) For each pair in
each bin, we tested which strategy the participant would have been able to apply to make
inferences about that pair.
Fluency heuristic. To test whether the participant would have been able to apply the
fluency heuristic, we first checked if both objects in a pair were recognized. If so, the
probability of a person being able to apply the fluency heuristic is the probability of detecting a
difference in recognition times. To estimate this detection probability, PD, we fed the
participant’s recognition times into the timing model (Equation 9). In each run of the timing
model, we let it count the number of pulses associated with the person’s recognition time for
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each of the objects in a pair. Across runs of the timing model, for each pair, we counted how
often a difference in pulses was detected and how often it was not detected. For each pair of
recognized objects, we computed the detection probability as the proportion of times a
difference was detected, using Equation 10. If either one or both objects in a pair are
unrecognized, by definition, the probability of a person being able to apply the fluency
heuristic is zero. Across all pairs in a bin, we averaged the probabilities of the participant being
able to apply the fluency heuristic. We averaged the probabilities across participants.
Knowledge-based strategies. Similarly, for each participant, we estimated the
probability that this individual would have been able to apply a knowledge-based strategy,
assuming that knowledge-based strategies, such as those listed in Table 1, are applicable when
knowledge is available about at least one object in a pair. Across the pairs in a bin, we
computed this probability as the proportion of pairs for which knowledge was available. As for
the fluency heuristic, we averaged the probabilities across participants.
Recognition heuristic. Finally, across the pairs in each bin, we computed the
probability that the participant would have been able to apply the recognition heuristic as the
proportion of pairs in which the participant recognized one object but not the other. As for the
fluency heuristic and knowledge-based strategies, we averaged the probabilities across
participants.
Applying the Timing Model to the Data Predicted by the Memory Model. To
generate the predicted data, we ran the memory model 1,500 times, creating 1,500 hypothetical
persons’ predicted recognition and knowledge responses. Specifically, according to the
predicted recognition probability, PR, we determined whether a hypothetical (i.e., simulated)
person would recognize an object and determined the object’s predicted recognition time,
Trecognition, by drawing a sample from the object’s predicted recognition time distribution. If the
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object was recognized, then according to the predicted knowledge probability, PK, we
determined whether that hypothetical person would additionally indicate knowing something
about it. Each hypothetical person’s objects were then exhaustively paired and grouped into
bins according to the ranks of each object’s environmental frequency. The binning procedure
was the same as the one used for the observed data. For each pair in each bin, we tested which
strategy a hypothetical person would have been able to apply to make inferences about that
pair.
Fluency heuristic. To test whether a hypothetical person would have been able to apply
the fluency heuristic, we fed the predicted recognition times into the timing model (Equation
9), using this model to process the hypothetical person’s predicted data in the same way as we
processed our experimental participants’ observed data. Specifically, we used Equation 10 to
compute the predicted detection probability, PD, which is the predicted probability of a
hypothetical person being able to apply the fluency heuristic on predicted pairs of two
recognized objects. If a hypothetical person did not recognize either one or both objects in a
pair, by definition, the predicted probability of the hypothetical person being able to apply the
fluency heuristic is zero on this pair. Across all pairs in a bin, we averaged the predicted
probabilities of a hypothetical person being able to apply the fluency heuristic. We averaged
the predicted probabilities across hypothetical persons.
Knowledge-based strategies. As we did for the observed data, across the pairs in each
bin, we also computed the predicted probability that a hypothetical person would have been
able to apply knowledge-based strategies, processing the hypothetical person’s data in the same
way as we processed the experimental participants’ data. Specifically, we estimated the
probability of a hypothetical person having been able to apply knowledge-based strategies,
assuming that knowledge-based strategies are applicable when knowledge is available about at
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ONLINE MATERIALS
least one object in a pair. Across the pairs in a bin, for each hypothetical person we computed
this probability as the proportion of predicted pairs for which knowledge was available. As for
the fluency heuristic, we averaged this predicted probability across hypothetical persons.
Recognition heuristic. Finally, across the pairs in each bin, we computed the predicted
probability that a hypothetical person would have been able to apply the recognition heuristic
as the proportion of pairs in which the hypothetical person recognized one object but not the
other. As for the fluency heuristic and knowledge-based strategies, we averaged the predicted
probabilities across hypothetical persons.
When Does the Fluency Heuristic Help Make Accurate Inferences? Simulation 3
In Simulation 3, we predicted how the magnitude of the fluency validity changes as a
function of the detection probability, PD. To this end, we applied the timing model to the data
observed in Experiments 2–7 and used both this model and our memory model to generate the
predicted data. In doing so, we predicted validities for inferring cities’ size, countries’ gross
domestic product in 2006, companies’ market capitalization on May 31, 2007, diseases’ fame,
and politicians’ fame. We operationalized fame as the proportion of participants who
recognized a disease in Experiments 6 and 8, and a politician in Experiments 7 and 9,
respectively. (Note that our use of the validity equation excludes objects with equal criterion
values.)
Applying the Timing Model to the Observed Data. The simulation (Equations 9–11)
can be broken into two parts. First, exhaustively pairing the objects, we used the timing model
to estimate for each of each participant’s pairs of two recognized objects the detection
probability, PD, that the participant would have been able to detect a difference in recognition
times between the objects. This is the probability that a person would have been capable of
applying the fluency heuristic. Second, according to the detection probabilities, we grouped
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each participant’s tartle, tartle–knowledge, and knowledge pairs into four bins, running the
timing model a second time to estimate the magnitude of the fluency validity, vfh, in each bin.
(Note that in this and all subsequent analyses involving cities as objects, pairs are made up of
cities from the same country. This is also true for the data analysis shown in Figure 8.)
To estimate the detection probability, PD, in each of a first set of runs of the timing
model, for each of each participant’s pairs of objects, we checked whether a participant would
have detected a difference in the numbers of pulses between two objects. For each of each
participant’s pairs of objects, we computed PD as the proportion of times a difference would
have been detected across this first set of runs of the timing model.
To estimate the fluency validity, vfh, in each of a second set of runs of the timing model,
for each of each participant’s pairs of objects, we let the timing model generate the number of
pulses that participant would have counted while recognizing each of the two objects. We let
the timing model then compare these numbers of pulses. In each run of this second set of runs
of the timing model, for the pairs where a participant would have detected a difference in the
numbers of pulses, we checked whether the participant would have made a correct or an
incorrect inference if that person had inferred the object with the smaller number of pulses to
score a higher value on the criterion. The fluency validity, vfh, is the proportion of times the
participant would have made a correct inference, computed across those pairs where the
participant would have detected a difference in the numbers of pulses between two objects.
This yields the fluency validity conditional on the participant having detected a difference in
recognition times.
Specifically for estimating the fluency validity, in each run of this second set of runs of
the timing model, we used each participant’s responses in the recognition and general
knowledge task to classify that participant’s pairs of objects into tartle, tartle–knowledge, and
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ONLINE MATERIALS
knowledge pairs. Within these three types of pairs, for each participant we grouped those pairs
that would have allowed the participant to detect a difference in the numbers of pulses into four
bins, arranged by quartiles of the previously computed (i.e., in the first series of runs of the
timing model) detection probabilities, PD. (In this and all subsequent simulations involving
quartiles of PD, the quartiles were approximated by first ordering the pairs according to PD and
then splitting the pairs into four equal parts; where the total number of data points was not
divisible by the number of bins, we first evenly allocated as many data points as possible to the
four bins and then allocated the remaining data points to the last bin.) In each run of this second
set of runs of the timing model, for each of the 3 × 4 bins (i.e., three types of pairs, four bins),
we computed the average of the previously computed detection probability, PD, as well as the
fluency validity, vfh. We then computed means (including standard errors) across participants.
Finally, we averaged the variables across runs of the second series of runs of the timing model.
Applying the Timing Model to the Data Predicted by the Memory Model. To
generate the combined predictions of the memory model and the timing model, we ran another
simulation using Equations 5–11. The simulation of the memory model was run 1,500 times,
creating 1,500 hypothetical persons’ predicted recognition and knowledge responses. For each
of these 1,500 hypothetical persons, we ran the same two sets of runs of the timing model we
had also run for the observed data.
Specifically, the total simulation comprised three steps. First, we used our memory
model to generate hypothetical persons’ predicted recognition responses, knowledge responses,
and recognition times. Second, we used the timing model to compute for each of each
hypothetical person’s pairs of two recognized objects the predicted detection probability, PD,
that the hypothetical person would have been able to detect a difference in predicted
recognition times between the objects. Third, according to the predicted detection probabilities,
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we grouped each hypothetical person’s predicted tartle, tartle–knowledge, and knowledge pairs
into four bins, arranged by quartiles, running the timing model a second time to compute the
magnitude of the predicted fluency validity, vfh, in each bin.
First, in each run of the memory model, according to the predicted recognition
probability, PR, we determined whether a hypothetical person would recognize an object. If the
object was recognized, then, according to the predicted knowledge probability, PK, we
determined whether that person would additionally know something about it. In each run of the
memory model, that is, for each hypothetical person, we then exhaustively paired objects into
that hypothetical person’s predicted tartle, tartle–knowledge, and knowledge pairs and also
determined each object’s predicted recognition time, Trecognition, by drawing a sample from the
object’s predicted recognition time distribution.
Second, for each hypothetical person, we further used the timing model to compute the
predicted detection probability, PD, that this hypothetical person would have detected a
difference in predicted recognition times between two objects. To compute PD, in each run of a
first set of runs of the timing model for each pair of objects, we checked whether a hypothetical
person would have detected a difference in the predicted numbers of pulses between the two
objects. We computed PD as the proportion of times a difference would have been detected
across this first set of runs of the timing model.
Third, to compute the predicted fluency validity, vfh, in each run of a second set of runs
of the timing model, for each pair of objects, we let the timing model generate the predicted
number of pulses a hypothetical person would have counted while recognizing each of the two
objects in a pair in that run. We let the timing model then compare these predicted numbers of
pulses. As for the observed data, the predicted fluency validity is the proportion of times the
hypothetical person would have made a correct inference, computed across those predicted
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pairs where the person would have detected a difference in the predicted numbers of pulses
between two objects.
Specifically, for computing the predicted fluency validity in each run of this second set
of runs of the timing model, within each hypothetical person’s predicted tartle, tartle–
knowledge, and knowledge pairs we grouped all pairs into four bins by ordering the pairs
according to the previously computed (i.e., in the first series of runs of the timing model)
predicted detection probabilities, PD. Bins were arranged by quartiles in the same way as the
observed data. In each run of this second set of runs of the timing model, for each of the 3 × 4
bins, we averaged the previously computed predicted detection probabilities, PD, as well as the
predicted fluency validity, vfh. In each run of this second set of runs of the timing model, we
then computed means (including standard errors) across hypothetical persons. Finally, we
averaged the variables across the second set of runs of the timing model.
The Fluency Validity and the Knowledge-Based Strategies’ Validities: Simulation 4
In Simulation 4, we examined the magnitude of the fluency validity and the validities of
each of the six knowledge-based strategies on pairs of objects in which one of the knowledgebased strategies and the fluency heuristic were both applicable. We computed the validities in
this situation of overlapping cognitive niches as a function of the detection probability, PD, of a
person being able to apply the fluency heuristic.
Applying the Timing Model to the Observed Data. To examine which strategy would
help a person make the most accurate inferences, we ran a simulation, using Equations 9–11
and 13 on the data observed in Experiments 1 and 3. The simulation can be broken into two
parts. First, exhaustively pairing the objects, we used the timing model to compute for each
participant’s pairs of two recognized objects the detection probability, PD, that the participant
would have detected a difference in recognition times and hence been capable of applying the
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fluency heuristic. Second, we reran the timing model to assess for each of each participant’s
tartle–knowledge and knowledge pairs whether that participant would be able to apply the
fluency heuristic as well as a knowledge-based strategy in that run. For each participant we
grouped the tartle–knowledge and knowledge pairs where one of the knowledge-based
strategies was applicable along with the fluency heuristic into four bins according to the
previously computed detection probabilities, PD. We computed all strategies’ validities (vfh, vt1,
vt2, vttb, vttfc, vttfv1, vttfv2) across the pairs in each bin.
Specifically, to compute the detection probability, PD, in each of a first set of runs of
the timing model, for each of each participant’s pairs of objects, we checked whether that
participant would have detected a difference in the numbers of pulses between two objects. For
each of each participant’s pairs of objects, we computed PD as the proportion of times a
difference would have been detected across this first set of runs of the timing model.
To assess whether a participant would have been able to apply the fluency heuristic, in
each run of a second set of runs of the timing model, for each of each participant’s tartle–
knowledge and knowledge pairs, we let the timing model generate the number of pulses that
participant would have counted while recognizing each of the two objects in a pair. For these
pairs, we also checked whether that person would also have been able to apply a knowledgebased strategy. For take-the-best-cue, take-the-first-value1, and take-the-first-value2, this
entailed letting the timing model generate the numbers of pulses the participant would have
counted when retrieving the cue values. For each comparison between one of the six
knowledge-based strategies and the fluency heuristic, we then selected those tartle–knowledge
and knowledge pairs where the fluency heuristic and the respective knowledge-based strategy
were both applicable.
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Within these tartle–knowledge and knowledge pairs we grouped all pairs into four bins,
arranged by quartiles of the previously (i.e., in the first series of runs of the timing model)
computed detection probabilities, PD. Quartiles were approximated as described in Simulation
3. For each of the 2 × 4 bins (i.e., two types of pairs, four bins), we calculated the mean
detection probability, PD, as well as the validities (vfh, vt1, vt2, vttb, vttfc, vttfv1, vttfv2) for the
fluency heuristic and the knowledge-based strategies and computed means (including standard
errors) across participants. Finally, we averaged the variables across the second set of runs of
the timing model.
The Fluency Heuristic Accordance Rate and the Knowledge-based Strategies’
Accordance Rates: Simulation 5
In Simulation 5, we examined how well the fluency heuristic and each of six
knowledge-based strategies predicted people’s inferences on the pairs of objects for which one
of the knowledge-based strategies and the fluency heuristic were both applicable. We
computed the strategies’ accordance rates in this situation of overlapping cognitive niches as a
function of the detection probability, PD, of a person being able to apply the fluency heuristic.
(Note that in this and all other simulations involving accordance rates or other measures that
depend on participants’ actual behavior—i.e., inference times, proportion of correct
inferences—we focused only on those pairs of objects the participant had actually seen in the
inference task. In contrast, simulations involving measures—i.e., validities—that do not depend
on participant’s actual behavior were run by exhaustively pairing objects with each other.)
Applying the Timing Model to the Observed Data. To examine how well the
strategies account for people’s inferences, we ran a simulation with Equations 9, 10, 12, and 13
on the data observed in Experiment 1. The simulation can be broken into two parts. First, as in
Simulation 4, in a first series of runs of the timing model, we computed for each participant’s
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pairs of two recognized objects the detection probability, PD, that the participant would be able
to apply the fluency heuristic. Second, as in Simulation 4, we ran a second series of runs of the
timing model to assess for each of each participant’s tartle–knowledge and knowledge pairs
whether that participant would be able to apply the fluency heuristic as well as each of the six
knowledge-based strategies. Then, diverging from Simulation 4, in each of this second series of
runs of the timing model, we computed the competing strategies’ accordance rates, kfh, kt1, kt2,
kttb, kttfc, kttfv1, kttfv2 (rather than their validities), on those tartle–knowledge and knowledge pairs
where each of the six knowledge-based strategies, respectively, was applicable simultaneously
with the fluency heuristic. To this end, we grouped these pairs into four bins, arranged by
quartiles of the previously (i.e., in the first series of runs of the timing model) computed
detection probabilities, PD. Quartiles were approximated as described in Simulation 3. For each
of the 2 × 4 bins (i.e., two types of pairs, four bins), we calculated the mean detection
probability, PD, as well as each of the competing strategies’ accordance rate and computed
means (including standard errors) across participants. As in Simulation 4, we averaged the
variables across the second series of runs of the timing model.
Do People Adopt the Fluency Heuristic When They Cannot Use Knowledge? Simulation 6
In Simulation 6, we examined the magnitude of the fluency heuristic accordance rate on
tartle pairs in Experiment 2, in which participants (i.e., in the instruct group) were instructed to
always use the fluency heuristic when inferring which of two cities is recognized by more
students. In addition, we examined the magnitude of the fluency heuristic accordance rate on
tartle pairs in Experiment 1.
Applying the Timing Model to the Observed Data. To model people’s inferences
with the fluency heuristic, we modified the design of Simulation 5 (Equations 9, 10, and 12).
First, in a first series of runs of the timing model, we computed for each participant’s pairs of
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tartle objects the detection probability, PD, that the participant would be able to apply the
fluency heuristic. Second, in each run of a second series of runs of the timing model, we
assessed for each participant’s tartle pairs (rather than tartle–knowledge and knowledge pairs
as in Simulation 5) which city the participant would infer to score a larger value on the
criterion. In doing so, we computed the fluency heuristic accordance rate (kfh) on the tartle pairs
conditional on the fluency heuristic being applicable (rather than conditional on this heuristic
being applicable simultaneously with the other strategies, as in Simulation 5). We grouped each
participant’s tartle pairs in which the participant would have been able to apply the fluency
heuristic into four bins according to the previously computed (i.e., in the first series of runs of
the timing model) detection probabilities, PD. Bins were arranged by quartiles of the previously
computed detection probabilities, PD. Quartiles were approximated as described in Simulation
3. As in Simulation 5, for each of the four bins, we computed the mean detection probability,
PD, as well as the accordance rate (kfh) for the fluency heuristic and computed means (including
standard errors) across participants. Finally, we averaged the variables across the second set of
runs of the timing model.
When Is the Fluency Heuristic Easy to Use? Simulation 7
In Simulation 7, we considered participants in the instruct group of Experiment 2. In the
instruct group, participants were instructed to always apply the fluency heuristic when inferring
which of two cities was recognized by more students. We examined (a) how well the fluency
heuristic predicted participants’ inferences, (b) the proportion of correct inferences they made,
and (c) the time it took them to make an inference. We computed these behavioral data as a
function of the detection probability, PD, of a person being able to apply the fluency heuristic.
Applying the Timing Model to the Observed Data. To model people’s inferences
with the fluency heuristic, we modified the design of Simulation 5 (Equations 9, 10, 12). As in
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Simulation 5, in a first set of runs of the timing model, we computed for each participant’s
pairs of two recognized cities the detection probability, PD, that the participant would have
been able to detect a difference in recognition times and apply the fluency heuristic. Deviating
from Simulation 5, in a second set of runs of the timing model, we then computed three kinds
of behavioral data conditional on a participant having been able to apply the fluency heuristic.
First, for each pair of recognized cities, we used the timing model to assess which city
the participant would infer was recognized by more students, assuming the participant had used
the fluency heuristic. Second, on those pairs where the participant had made an inference
consistent with the fluency heuristic, we also examined how many correct inferences the
participant had made, taking the proportion of participants from Experiments 1, 2, and 3 who
had recognized each city as a criterion for which city was recognized by more students. Third,
on those pairs where the participant had made an inference consistent with the fluency
heuristic, we furthermore assessed the time it took the participant to make an inference; we
refer to this time as inference time.
As in Simulation 5, in each run of this second set of runs of the timing model we then
grouped the pairs into four bins, arranged by quartiles of the previously computed detection
probabilities, PD. Quartiles were approximated as described in Simulation 3. For each of the
four bins, we computed (a) the fluency heuristic accordance rate, (b) the proportion of correct
inferences, and (c) the median inference time across the pairs in a bin. As in Simulation 5, for
each of the bins, we also computed the mean detection probability, PD. In each run of this
second set of runs of the timing model, we then computed means (including standard errors)
across participants. Finally, we averaged the variables across runs of the second series of runs
of the timing model.
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When Is the Fluency Heuristic Fast to Use? Simulation 8
Simulation 8 is identical to Simulation 5, except that we ran the former on the data
observed in Experiment 3, and the latter on the data observed in Experiment 1. In both
simulations, we calculated the fluency heuristic’s and each of the six knowledge-based
strategies’ accordance rates conditional on the fluency heuristic and a knowledge-based
strategy both being applicable, plotting each strategy’s accordance rate as a function of the
probability, PD, that a person would have been able to detect a difference in recognition times
and apply the fluency heuristic.
Recognition Validity as a Function of Perceived Recognition Times: Simulation 9
In Simulation 9, we predicted the recognition validity for inferring cities’ size,
countries’ gross domestic product in 2006, companies’ market capitalization on May 31, 2007,
diseases’ fame, and politicians’ fame in Experiments 2–7. To this end, we used our memory
model in conjunction with the timing model.
Applying the Timing Model to the Observed Data. To compute the observed
recognition validity, vrh, we ran a simulation using Equations 9 and 11. Using participants’
responses in the recognition and general knowledge tasks in Experiments 2–7, we exhaustively
paired each participant’s objects into tartle–unrecognized and knowledge–unrecognized pairs.
Then, for each participant’s recognized objects, we let the timing model generate the number of
pulses that participant would have counted while recognizing each object. We grouped each
participant’s tartle–unrecognized and knowledge–unrecognized pairs into four bins according
to the numbers of pulses accumulated for the recognized objects. Bins were arranged by
quartiles of the numbers of pulses. Quartiles were approximated as described in Simulation 3.
In each of the 2 × 4 bins (two types of pairs, four bins), we calculated the mean number of
pulses as well as the recognition validity (vrh) for each participant. We computed means
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(including standard errors) across participants. Finally, we averaged the variables across runs
of the timing model.
Applying the Timing Model to the Data Predicted by the Memory Model. To
generate the combined predictions of our memory model and the timing model, we ran another
simulation using Equations 5–9 and 11. The simulation of the memory model was run 1,500
times, generating 1,500 hypothetical person’s predicted recognition and knowledge responses.
For each of these 1,500 hypothetical persons, we ran the same set of runs of the timing model
we had also run for the observed data.
That is, first, in each run of the memory model, according to the predicted recognition
probability, PR, we determined whether a hypothetical person would recognize an object. If the
object was recognized, then, according to the predicted knowledge probability, PK, we
determined whether that hypothetical person would additionally know something about it. In
each run, that is, for each hypothetical person, we also determined each object’s predicted
recognition time, Trecognition, by drawing a sample from the object’s predicted recognition time
distribution. In each run, we then exhaustively paired these objects into predicted tartle–
unrecognized and knowledge–unrecognized pairs.
Second, for each hypothetical person’s predicted recognized objects, we let the timing
model generate the predicted number of pulses that participant would have counted while
recognizing each object. We grouped each hypothetical person’s predicted tartle–unrecognized
and knowledge–unrecognized pairs into four bins according to the predicted numbers of pulses
accumulated for the recognized objects. Bins were arranged by quartiles of the predicted
numbers of pulses. Quartiles were approximated as described in Simulation 3. For each of the 2
× 4 bins (two types of pairs, four bins), we calculated the mean predicted number of pulses, as
well as the predicted recognition validity. We computed means (including standard errors)
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across runs of the memory model, that is, across hypothetical persons. Finally, we averaged the
variables across runs of the timing model.
When Is the Recognition Heuristic Easy and Fast to Use? Simulation 10
In Simulation 10, in Experiment 1 and in the no-instruct group of Experiment 2, we
examined (a) the magnitude of the recognition heuristic accordance rate, (b) the proportion of
correct inferences participants made, and (c) the time it took them to make an inference. We
computed these behavioral data as a function of a person’s perceived recognition times.
Applying the Timing Model to the Observed Data. The simulation (Equations 9, 12)
is similar to the way we processed the observed data in Simulation 9. Using participants’
responses in the recognition and general knowledge tasks in Experiment 1 and the no-instruct
group of Experiment 2, we grouped each participant’s objects into tartle–unrecognized and
knowledge–unrecognized pairs. For each participant, we let the timing model generate for each
of the recognized objects the number of pulses the participant would have perceived when
recognizing this object. We grouped each participant’s tartle–unrecognized and knowledge–
unrecognized pairs into four bins according to the numbers of pulses accumulated for the
recognized objects. Bins were arranged by quartiles of the numbers of pulses. Quartiles were
approximated as described in Simulation 3. For each participant, in each of the 2 × 4 bins (two
types of pairs, four bins), we calculated the mean number of pulses and the recognition
heuristic accordance rate (krh). On those pairs where a participant had made an inference
consistent with the recognition heuristic, we also computed the proportion of correct inferences
the participant made as well as the median inference time it took the participant to make an
inference. (In the no-instruct group of Experiment 2, we took the proportion of participants
from Experiments 1, 2, and 3 who had recognized each city as a criterion for which city was
recognized by more students.) For all of these variables, we computed means (including
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standard errors) across participants. Finally, we averaged the variables across runs of the timing
model.
When Are Knowledge-Based Strategies Easy to Use? Simulation 11
In Simulation 11, we explored how the magnitude of the knowledge-based strategies’
validities increases as a function of how easy it is for a person to apply the knowledge-based
strategies. In doing so, we computed validities for inferring cities’ size.
Applying the Timing Model to the Observed Data. The simulation (Equations 9, 11,
13) can be broken into two parts. First, using participants’ responses in the recognition and
general knowledge tasks in Experiments 1 and 3, we exhaustively paired each participant’s
objects into tartle–knowledge and knowledge pairs. We assessed how effortful it would have
been for a participant to use a strategy. For the integration strategies tally1 and tally2, we
computed differences between sums of cue values as a measure of effort (the more the sums of
cue values differ, the less effortful it is to use an integration strategy), and for the lexicographic
and sequential sampling strategies take-the-best, take-the-first-cue, take-the-first-value1, and
take-the-first-value2, the number of comparisons of cue values that need to be considered prior
to making an inference (the more comparisons that need to be considered, the more effortful it
is to make an inference). For take-the-first-cue, take-the-first-value1, and take-the-first-value2,
this required running the timing model, using each participant’s reaction times observed for
each cue value in the cue-knowledge tasks as input for the timing model, and computing the
effort as average over runs of the timing model.
Second, for each participant and each strategy, we selected those tartle–knowledge and
knowledge pairs where a strategy was applicable. For take-the-first-cue, take-the-first-value1,
and take-the-first-value2, this required a second series of runs of the timing model. In each run
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of this second series of runs, we used the timing model to determine for each pair of objects
whether take-the-first-cue, take-the-first-value1, and take-the-first-value2 were applicable.
We grouped those pairs where a strategy was applicable into four bins according to the
previously calculated effort involved in using the strategy. Bins were arranged by quartiles of
each strategy’s respective currency of effort. In each of the 2 × 4 bins (two types of pairs, four
bins), for each participant, we calculated each strategy’s validity (vt1, vt2, vttb, vttfc, vttfv1, vttfv2) as
well as averages of each strategy’s currency of effort. We computed means (including standard
errors) across participants. In the case of take-the-first-cue, take-the-first-value1, and take-thefirst-value2, we additionally averaged these data across the second series of runs of the timing
model. For each strategy, this simulation procedure yields its validity and the effort involved in
using it conditional on the strategy being applicable.
Robustness of Model Predictions Across Proxies for Effort: Simulation C1
In Simulation C1, we predicted how the magnitude of the fluency validity changes as a
function of the raw differences in recognition times between two objects, irrespective of the
pulses associated with the objects’ recognition times and irrespective of whether a person
would have detected a difference in pulses. To this end, we modified the design of Simulation
3, using our memory model alone, that is, without the timing model, generating the predicted
data from web frequency to predict the fluency validity in Experiments 2–7. As in Simulation
3, we predicted validities for inferring cities’ size, countries’ gross domestic product in 2006,
companies’ market capitalization on May 31, 2007, diseases’ fame, and politicians’ fame.
Observed data. To compute the observed fluency validity, vfh, we used each
participant’s responses in the recognition and general knowledge tasks in Experiments 2–7 to
exhaustively pair the objects that the participant recognized into tartle, tartle–knowledge, and
knowledge pairs. For each participant we grouped these pairs into four bins by ordering the
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pairs according to the observed differences in raw recognition times between the objects. Bins
were arranged by quartiles of the recognition times. Quartiles were approximated as described
in Simulation 3. For each of the 3 × 4 bins (three types of pairs, four bins), we computed for
each participant the fluency validity for the paired comparisons of the objects in the bin,
assuming that a person using the fluency heuristic would infer an object with a shorter
recognition time to score a larger value on the criterion than an object with a longer recognition
time. For each participant we also computed the median of the observed recognition time
differences between two objects in a bin. We computed means (including standard errors)
across participants.
Data Predicted by the Memory Model. To generate the predictions of our memory
model, we ran a simulation using Equations 5–8 and 11. This simulation of the memory model
was run 1,500 times, creating 1,500 hypothetical persons’ predicted recognition and knowledge
responses. Specifically, in each run of the memory model, according to the predicted
recognition probability, PR, we determined whether a hypothetical person would recognize an
object. If the object was recognized, then, according to the predicted knowledge probability,
PK, we determined whether that hypothetical person would additionally know something about
it. In each run, that is, for each hypothetical person, we also determined each object’s predicted
recognition time, Trecognition, by drawing a sample from the object’s predicted recognition time
distribution. For each hypothetical person, we exhaustively paired these objects into predicted
tartle, tartle–knowledge and knowledge pairs. Within these pairs we computed the difference in
predicted recognition times between two objects.
For each hypothetical person, we then used the predicted recognition time differences to
divide the three types of pairs further into four bins. Bins were arranged by quartiles of the
predicted recognition time differences. Quartiles were approximated as described in Simulation
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3. Finally, for each hypothetical person, we computed the predicted fluency validity, vfh, in
each of the 3 × 4 bins (three types of pairs, four bins), assuming that a hypothetical person
using the fluency heuristic would infer an object with a shorter predicted recognition time to
score a larger value on the criterion than an object with a longer predicted recognition time. In
addition, we computed the median of the predicted recognition time differences between two
objects in a bin. We computed means (including standard errors) across hypothetical persons.
Robustness of Model Predictions Across Proxies for Effort: Simulation C2
In Simulation C2, we predicted how the magnitude of the fluency validity changes as a
function of the difference in pulses between two objects. To this end, we applied the timing
model to the data observed in Experiments 2–7 and used both this model and our memory
model to generate the predicted data from web frequency. The simulation procedure is similar
to that of Simulation 3. However, pairs of objects are binned by the difference in pulses
between two objects and not by the probability of a person detecting a difference in pulses. As
in Simulation 3, we predicted validities for inferring cities’ size, countries’ gross domestic
product in 2006, companies’ market capitalization on May 31, 2007, diseases’ fame, and
politicians’ fame.
Applying the Timing Model to the Observed Data. Exhaustively pairing the objects,
we used the timing model (Equations 9, 11) to generate for each of each participant’s
recognized objects the number of pulses that the participant would have counted while
recognizing each object. According to the difference in the numbers of pulses between two
objects, we grouped each participant’s tartle, tartle–knowledge, and knowledge pairs into four
bins, calculating the magnitude of the fluency validity in each bin.
To estimate the fluency validity, vfh, in each run of the timing model, for each of each
participant’s pairs of objects, we let the timing model generate the number of pulses that
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participant would have counted while recognizing each of the two objects in a pair. We let the
timing model then compare these numbers of pulses. In each run of the timing model, for the
pairs where a participant would have detected a difference in the numbers of pulses, we
checked whether the participant would have made a correct or an incorrect inference if that
person had inferred the object with the smaller number of pulses to score a higher value on the
criterion. The fluency validity, vfh, is the proportion of times the participant would have made a
correct inference, computed across those pairs where the participant would have detected a
difference in the numbers of pulses between two objects. This yields the fluency validity
conditional on the participant having detected a difference in recognition times.
Specifically for estimating the fluency validity, in each run of the timing model, we
used each participant’s responses in the recognition and general knowledge task to classify that
participant’s pairs of objects into tartle, tartle–knowledge, and knowledge pairs. Within these
three types of pairs, for each participant we grouped those pairs that would have allowed the
participant to detect a difference in the numbers of pulses into four bins by ordering the pairs
according to the differences in pulses between two objects. Bins were arranged by quartiles of
the differences in pulses. Quartiles were approximated as described in Simulation 3. In each
run of the timing model, for each of the 3 × 4 bins (i.e., three types of pairs, four bins), we
computed the average of the differences in pulses between two objects, as well as the fluency
validity, vfh. We then computed means (including standard errors) across participants. Finally,
we averaged the variables across runs of the timing model.
Applying the Timing Model to the Data Predicted by the Memory Model. To
generate the combined predictions of our memory model and the timing model, we ran a
simulation using Equations 5–9 and 11. The simulation of the memory model was run 1,500
times, creating 1,500 hypothetical persons’ predicted recognition and knowledge responses.
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For each of these hypothetical persons, we ran the same runs of the timing model we had also
run for the observed data. The total simulation comprises two steps.
First, in each run of our memory model, according to the predicted recognition
probability, PR, we determined whether a hypothetical person would recognize an object. If the
object was recognized, then, according to the predicted knowledge probability, PK, we
determined whether that hypothetical person would additionally know something about it. In
each run, that is, for each hypothetical person, we then exhaustively paired objects into
predicted tartle, tartle–knowledge, and knowledge pairs. In each run, we also determined each
object’s predicted recognition time, Trecognition, by drawing a sample from the object’s predicted
recognition time distribution.
Second, to compute the predicted fluency validity, vfh, for each hypothetical person, for
each pair of objects, we ran a series of runs of the timing model, letting this model generate the
predicted number of pulses the hypothetical person would have counted while recognizing each
of the two objects in a pair. In each run of the timing model, we let the timing model compare
the predicted numbers of pulses the person would have counted. As for the observed data, the
predicted fluency validity is the proportion of times the hypothetical person would have made a
correct inference, computed across those pairs where the person would have detected a
difference in the predicted numbers of pulses between two objects.
Specifically, for computing the predicted fluency validity in each of the runs of the
timing model, within each hypothetical person’s predicted tartle, tartle–knowledge, and
knowledge pairs we grouped all pairs into four bins by ordering the pairs according to the
differences in predicted numbers of pulses. The bins were arranged by quartiles of the
differences in predicted numbers of pulses in the same way as we binned the observed data. In
each of the runs of the timing model, for each of the 3 × 4 bins, we computed the averages of
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the previously computed differences in predicted numbers of pulses, as well as the predicted
fluency validity. In each run of the timing model, we then computed means (including standard
errors) across hypothetical persons. Finally, we averaged the variables across runs of the timing
model.
Recognition Times as a Function of Knowledge: Simulation C3
In Simulation C3, we used our memory model to predict recognition times for tartle and
knowledge objects.
Observed data. We used participants’ responses in the recognition and general
knowledge tasks of Experiments 2–7 to identify tartle and knowledge objects. For each
participant, we calculated the median recognition times for these objects, averaging the
medians across participants. We also computed standard errors.
Data Predicted by the Memory Model. In a simulation, we used Equations 5–8. The
simulation was run 1,500 times, creating hypothetical persons’ predicted recognition and
knowledge responses. Specifically, in each run of the memory model, according to the
predicted recognition probability, PR, we determined whether a hypothetical person would
recognize an object. If the object was recognized, then, according to the predicted knowledge
probability, PK, we determined whether that person would additionally know something about
it. In each run, that is, for each hypothetical person, we also determined each object’s predicted
recognition time, Trecognition, by drawing a sample from the object’s predicted recognition time
distribution. For each hypothetical person, we computed the medians of these predicted
recognition times separately for predicted tartle and knowledge objects. For each of these types
of objects, we then averaged the medians across hypothetical persons. We also computed
standard errors.
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