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Arithmétique Mentale dans les Jugements des
Consommateurs : Représentations Mentales, Stratégies de Calcul et les Biais.
Tatiana Sokolova
To cite this version:
Tatiana Sokolova. Arithmétique Mentale dans les Jugements des Consommateurs : Représentations Mentales, Stratégies de Calcul et les Biais.. Gestion et management. HEC, 2015. Français. �NNT : 2015EHEC0006�. �tel-02003455�
ECOLE DES HAUTES ETUDES COMMERCIALES DE PARIS Ecole Doctorale « Sciences du Management/GODI » - ED 533
Gestion Organisation Décision Information
"Mental Arithmetic in Consumer Judgments:
Mental Representations, Computational Strategies and Biases. ”
THESE
présentée et soutenue publiquement le 23 juin 2015 en vue de l’obtention du
DOCTORAT EN SCIENCES DE GESTION
Par
Tatiana SOKOLOVA JURY
Président: Monsieur Gilles LAURENT
Professeur
INSEEC Business School, Paris – France
Directeur de Recherche : Monsieur Marc VANHUELE Professeur
HEC Paris – France
Rapporteurs : Monsieur Manoj THOMAS
Professeur Associé
Samuel Curtis Johnson Graduate School of Management, Cornell University, New York – Etats-Unis
Monsieur Koert VAN ITTERSUM Professeur
Faculty of Economics and Business, University of Groningen – Pays-Bas
Ecole des Hautes Etudes Commerciales
Le Groupe HEC Paris n’entend donner aucune approbation ni improbation aux opinions émises dans les thèses ; ces opinions doivent être considérées
comme propres à leurs auteurs.
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ACKNOWLEDGEMENTS
This has been a long ride and no matter how much fun I have had along the way – I am really glad that I am getting off this train.
I would like to thank several people without whom I would never have made it.
I would like to thank my advisor Marc Vanhuele who has supported me from the first year in the PhD program. A few days ago I was watching the presentation I had given for my specialization exam at the end of my first year. I could watch it because I was a lousy presenter at the time. Marc decided to record my talk so that I could learn from it and get better. There are many things I am grateful to him for. But most of all, I want to thank him for believing in me, which, based on what I see in that first-year video, must have been difficult. I am also extremely grateful to him for helping me grow, for trusting me with choosing the direction of my research and for encouraging me in all my new pursuits.
I am also very grateful to my first-year PhD tutor and a member of my committee, Professor Gilles Laurent. In my first year I would often go and seek his advice on which courses to take or ask for his opinion on my research ideas. I am confident that those first ideas were not really worth his time. Nevertheless, he would always listen to me and give feedback. He has taught me to always think about the “why’s” and “how’s” and the “why not’s” of every research project and I am thankful to him for that.
I want to thank Koert van Ittersum for agreeing to be on dissertation committee and for his thoughtful comments on the previous version of this manuscript. And of course, I have to thank Koert for inspiring the very first paper I wrote which has eventually become a part of my dissertation.
I am extremely fortunate to have had the opportunity to work with two amazing scholars outside HEC: Manoj Thomas at Cornell and Aradhna Krishna at the University of Michigan.
Manoj invited me to Cornell and supported me during my stay in Ithaca. He helped me grow and challenged me to do better. I am always amazed and humbled by his way and speed of thinking, his work ethic and his thirst for new knowledge. I am very thankful for having had the opportunity to work with him and learn from him. I also want to thank Aradhna, who invited me to the University of Michigan. Aradhna is the most energetic and efficient person I know, as is evidenced by the paper we co-authored and finished in a little over five months.
She is known as one of the most productive scholars in marketing, but what amazes me the most is how much she cares about her doctoral students. She will think about our work on weekends, read our manuscripts on vacation and share research ideas with us at 10.00 p.m.
Aradhna inspires me to explore new territories. I am grateful to her for that.
This thesis relied heavily on the knowledge I received through courses from HEC professors.
I would like to especially thank Gilles Laurent and Guilhem Bascle for their courses in the
first year of the PhD program. I am also very grateful to the members of the marketing and
HR departments at HEC who had helped me and supported me at various stages of this
journey. I would especially like to thank Selin Atalay, Tim Heath, Tina Lowery, Mathis
Schulte, LJ Shrum, Amy Sommer and Eric Uhlmann.
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I would like to thank the PhD Program team: Ulrich Hege, Francoise Dauvergne, Caroline Meriaux and Malenie Romil – for their continuous efforts to make this program better. I would also like to thank Lydie Tournaire at the HEC library for her excellent assistance in finding research papers and book chapters. I thank Halina, not just for all the sandwiches and coffee at the bar club, but mostly for making me feel that a little more at home and a little closer to my family.
I would like to thank my friends who made this journey a lot more fun. I want to thank Ali, Moumi, Tim, Martin, Navid, Rita and Shiva for all the nights of “studying” at Expansiel. I also would like to thank Chloe for sharing her wisdom about navigating the rough waters of the PhD and for welcoming me and Panikos in her home in Montrouge. I especially want to thank Yi, my classmate, one of my best friends, my co-author, and my noodle, for being there for me along the way. She is the most giving and kind person I know and I am grateful that she found me worthy of her friendship.
Over the course of these five years I have found my calling and met so many amazing, bright, generous and kind people. But all that being sad, when looking back at all this I will always be most grateful to the program for having met Panikos. He is my love, my best friend, my nasty but friendly reviewer. He has been there for me on my worst and my best days. When nothing seemed to work and my p-values were approaching the rejection rates in A-journals, when I felt that I had no energy, stamina and inspiration to keep on – he would hold me and tell me it would all be fine. And even more importantly, when I had my small victories, gave good talks or got significant results – he would share these happy moments with me. I thank him for making me a better writer, a better researcher and, I hope, a better person.
Finally, I would like to thank my parents and my grandmother. I cannot imagine how hard it had been for my family to let their only child leave for another country and I am always going to be grateful to them for supporting my decision. They have been trusting, patient, generous, understanding, and loving. I do not think I could even repay this debt, but I will keep trying. It is to them that I would like to dedicate this thesis.
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Special thanks also go to Picard, a frozen foods chain, which allowed me work on my
research for an extra hour every day for the last two years of my PhD studies.
5 RESUME
Dans ma thèse, j’étudie les représentations mentales et les processus cognitifs qui sous-tendent le calcul mental sur le marché. Cette thèse contribue à la recherche de
prix psychologiqueen décrivant de nouveaux facteurs qui influencent les jugements de prix des consommateurs. En particulier, je découvre facteurs qui rendent les consommateurs plus ou moins susceptibles d’arrondir les prix vers le bas (Essai 1) et les facteurs qui déterminent leur
tendance à se fixer sur les différences de pourcentage (Essai 3). En outre, cette recherche fournit de nouvelles perspectives à la littérature de budgétisation mentale en identifiant des stratégies de calcul mental qui conduisent à des estimations panier de prix plus précis (Essai 2). Dans l'ensemble, ma recherche va contribuer à notre compréhension des jugements de prix des consommateurs et proposer des contextes et des stratégies conduisant à des évaluations de prix plus précis.
ESSAI 1 : LE BIAS GAUCHE-CHIFFRE: EST-CE UNE BIAIS D’ENCODAGE OU UN BIAIS D’ESTIMATION ?
Cet essai se concentre sur l'un des préjugés les plus répandus dans la cognition numérique - l'effet gauche-chiffre (Manning et Sprott 2009; Thomas et Morwitz 2005). Sa robustesse et ses implications ont été démontrées dans une variété de contextes. Toutefois, les mécanismes qui sous-tendent l'effet gauche-chiffre sont encore débattues (Thomas et
Morwitz 2009). On ne sait pas si le biais gauche-chiffre est causé par l'encodage biaisé ou par
mauvais choix de stratégies d'estimation à l'étape de comparaison de prix. Selon le compte
d'encodage biaisé, l'effet se produit parce que les consommateurs ne font pas attention aux
bons chiffres de minimiser leur effort cognitif quand ils codent les prix (par exemple Basu
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2006; Stiving et Winer, 1997); ou parce qu'ils se souviennent des chiffres à gauche plus vivement. Toutefois, les comptes ci-dessus ne sont pas compatibles avec les conclusions dans le domaine de la cognition numérique qui montrent que les gens assistent automatiquement aux chiffres de droite (par exemple, Dehaene et al 1990; Nuerk et al., 2001). Ainsi, le biais gauche-chiffre devrait émerger au stade des calculs mentaux en raison de l'aversion
d’arrondir les prix vers le haut. Cette recherche se développe et teste les prédictions concurrentes du compte d'encodage biaisé et ceux du compte d’estimation biaisée.
Si les prix sont arrondis au plus proches des montants en dollars entiers (par exemple de 2,99 à 3,00), dans la plupart des cas, l'effet gauche-chiffre est éliminé. Si les
consommateurs ronds les prix vers le bas (par exemple, 2,99 à 2,00), ils sont susceptibles de surestimer la différence entre 2.99 et 4.00. Pourquoi les gens sont réticents à arrondir les numéros vers le haut dans les soustractions de nombres à plusieurs chiffres? Contrairement aux partisans du compte d'encodage biaisé qui soutiennent que la polarisation gauche-chiffre est causée par l'avarice cognitive ou par des effets de primauté, nous croyons que l'aversion d’arrondissement est causée par la motivation de préserver l'intégrité des nombres à plusieurs chiffres.
Selon notre compte, lors de l'exécution des comparaisons de magnitude
consommateurs sont intrinsèquement motivés pour préserver la grandeur de prix et de représentations visuelles intactes (Dehaene, 1992). En arrondissant un nombre vers le haut, par rapport à arrondir vers le bas, nous réduisons inévitablement la similitude symbolique perçu entre le nombre initial et le nombre arrondi. Par exemple, 2,75 semble plus
visuellement similaire à 2,00 à 3,00. Le compte d’estimation biaisé suggère que l'effet
gauche-chiffre est plus probable pour les comparaisons «en ligne» que pour les comparaisons de prix basés sur la mémoire. Cela arrive parce que des comparaisons «en ligne» font
similitude visuelle entre les prix réels et arrondis plus accessibles (Zhang et Wang, 2005). En
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revanche, le compte d'encodage biaisé suggère que les comparaisons à base de mémoire, en étant plus exigeants cognitivement (par exemple Lynch et Srull, 1982), devraient renforcer la polarisation gauche-chiffre.
En outre, afin de préserver l'information sur l'ampleur du prix que les consommateurs devraient être plus disposés à arrondir les prix qui sont proches de montants en dollars entiers. Ainsi, le compte de l'estimation biaisé prévoit que la polarisation gauche-chiffre est plus susceptible de se manifester pour 2,75 (moins «arrondible») que pour 2,99 (plus
«arrondible»). Le compte d'encodage biaisé, au contraire, prévoit que la proximité aux nombres ronds n'a aucun effet sur le biais gauche-chiffre. Le compte suggère que les consommateurs, ayant des ressources mémoire limitées, codent prix de plus à gauche ou chiffres sont plus susceptibles de les mémoriser (Bizer et Schindler 2000; Coulter 2001), quels que soient les chiffres à droite de prix. Trois études apportent un soutien aux prédictions du compte de l'estimation biaisé.
Étude 1 a testé l'effet de l’«arrondabilite» de prix sur la polarisation gauche -chiffre.
Les participants ont évalué l'ampleur de la différence entre les prix réguliers et des prix de ventes. Ensuite, ils ont signalé que la stratégie de calcul qu'ils avaient utilisé pour chaque paire de prix. Les prix réguliers et des prix de ventes ont été manipulés sur deux dimensions clés: la différence gauche chiffres entre les prix réguliers et des prix de ventes (grandes vs.
contrôle) et le «arrondabilite» des prix. L'étude a utilisé un design intra-sujets (2 (différence gauche chiffres: grande / contrôle) x 2 (arrondabilite: près de montants en dollars entiers / loin de montants en dollars entiers) x 3 (distance numérique: petit / moyen / grand)).
Conformément avec le compte estimation biaisée, les résultats suggèrent que l'effet gauche- chiffre est réduit à des prix proches de montants en dollars entiers. L'analyse des rapports de stratégie montre que les gens sont plus susceptibles d'arrondir les prix à proximité de
montants en dollars entiers.
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Étude 2 a testé l'effet de l'évaluation basée sur la mémoire sur l'effet gauche-chiffre.
L'étude a utilisé un design factoriel mixte (2 (mode d'évaluation: basée sur la mémoire/ faite sur ligne) x 2 (différence gauche chiffres: grande/ contrôle) x 6 (distance numérique)). Le mode d'évaluation de la différence de prix était le seul facteur inter-sujet. La moitié des participants a fait des évaluations des différences entre les prix régulier et les prix de ventes, en se fondant sur leur mémoire. L'autre moitié des participants a fait les évaluations
« online » - ca veut dire qu'ils avaient des prix présente devant eux quand ils ont fait leurs évaluations. Conformément à nos prévisions, l'effet de la différence gauche chiffres était plus grand pour les évaluations faites «sur ligne».
L'étude 3 reproduit les effets des chiffres de droite et le mode de traitement sur le biais gauche-chiffre. L'étude a utilisé un design factoriel mixte (2 (mode d'évaluation) x 2
(différence gauche-chiffre) x 2 (arrondabilite) x 3 (différence numérique)). L'effet des chiffres de droite et l'effet du mode d'évaluation ont été reproduits.
Trois études fournissent des preuves contre le compte d'encodage biaisé de l'effet gauche-chiffre (Basu 2006; Schindler et Kirby 1997) et trouver un soutien pour le compte d'estimation biaisée. Études 1 et 3 montrent que lorsque les prix approchent montants ronds l'effet gauche-chiffre est réduit. Études 2 et 3 identifie l'évaluation basée sur la mémoire comme un facteur atténuant l'effet gauche-chiffre.
ESSAI 2 : COMMENT MIEUX ESTIMER LE PRIX TOTAL DE LA PANIER : LE RÔLE DE COMMUTATION ENTRE DES STRATEGIES D'ESTIMATION ET LES EFFETS DE SIMPLIFICATION DES PRIX
Cet essai se concentre sur le processus de l'estimation du prix du panier et compare la
précision des différentes stratégies de calcul utilisées par les acheteurs pour suivre leurs
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dépenses totales. Malgré son pertinence pour les consommateurs et les détaillants, le processus de suivi des prix total n'a que récemment commencé à attirer l'attention dans la littérature de comportement des consommateurs (Luna and Kim, 2009; Stilley, Inman, and Wakefield, 2010; van Ittersum, et al. 2010). Des études ont montré que les consommateurs ont une idée sur le prix total des produits dans leur panier pendant qu'ils magasinent (Stilley, et al., 2010) et dans de nombreux cas suivre volontairement leurs dépenses totales (van Ittersum, et al., 2010). Mais comment les consommateurs suivent leurs dépenses totales?
Quelles sont les stratégies de calcul qu'ils utilisent et quelles sont les stratégies qui conduisent meilleures estimations?
Un article de van Ittersum et ses collègues (2010) fut le premier à répondre
directement aux questions ci-dessus. Les auteurs suggèrent que les consommateurs utilisent de plus la stratégie exacte et des stratégies de simplification afin de suivre leurs dépenses. En se fondant sur des rapports verbaux des participants, van Ittersum et ses collègues concluent que les gens se limitent généralement à une seule stratégie de calcul dominante. Les auteurs proposent également que "la recherche suivante pourrait examiner si, dans quelle mesure et dans quelles conditions les gens utilisent de multiples stratégies". En effet, la commutation entre les stratégies est une caractéristique commune de calcul mental et d'autres tâches cognitives (Lemaire and Lecacheur, 2010; Reder, 1988; Reder and Schunn, 1999). Il est également un déterminant important de la performance. Cela pourrait signifier que les rapports verbaux rétrospectives utilisés par van Ittersum et ses collègues (2010) ont peut-être laissé de côté un facteur potentiellement important de la précision de l'estimation -
commutation entre les stratégies.
Trois études ont porté sur le rôle de la commutation entre les stratégies dans l'estimation du montant total de panier. Les études ont comparé la performance des
différentes stratégies de calcul. Étude 1 a examiné si les gens comptent sur une seule stratégie
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de calcul dominante ou s’ils alternent entre plusieurs stratégies afin de suivre leurs dépenses totales. Les participants ont suivi le prix total d'un panier virtuel et ont rapporté les totaux cumulés intermédiaires pour chaque produit. Les cumuls ont été utilisés pour en déduire des stratégies de calcul appliquées pour chaque produit et pour calculer le nombre de
commutateurs entre les stratégies pour chaque participant. Nous avons ensuite calculé un indice de la variabilité des stratégies. L’indice reflétait la mesure dans laquelle les stratégies dans un panier diffèrent les uns des autres dans le degré de simplification des prix. Les résultats ont indiqué que les participants ont alterne entre plusieurs stratégies au lieu de recourir à une stratégie unique. Ils ont également utilisé des stratégies qui diffèrent les uns des autres dans leurs niveaux de simplification des prix. Les résultats indiquent également que la commutation entre les stratégies qui varient dans leur degré de simplification affecté négativement la précision des participants.
Dans l'étude 2, nous avons capturé le processus d'estimation du montant total du panier plus directement en utilisant l'approche penser à haute voix (Dowker, 1992; Taylor and Dionne, 2000). Les participants ont verbalisé le processus d'estimation des totaux de leurs paniers. Leurs protocoles verbaux ont été utilisés pour calculer les indices de simplification des prix et les indices de la variabilité des stratégies. Les résultats de l'étude 1 ont été
conceptuellement répliqués. Les participants ont commuté entre les stratégies variant en leur degré de la simplification des prix. Leur commutation entre les stratégies eu un impact négatif sur leur exactitude.
Enfin, sachant que la commutation entre stratégies a un impact négatif sur la précision de calcul, nous avons mené une étude de terrain qui a comparé quatre stratégies de calcul les plus utilisés (van Ittersum, et al. 2010). Les clients dans un supermarché devaient suivre leurs dépenses en magasin en utilisant une des quatre stratégies de calcul assigne par le chercheur.
Ils devaient compter sur la même stratégie au long de leur voyage de shopping. L'étude a
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montré que la stratégie d'addition exacte surperformé les stratégies de simplification lorsque le nombre total des produits dans les paniers était petite. Dans le même temps, les résultats ont indiqué que la stratégie d'addition exacte était inférieure aux stratégies de simplification pour les paniers composés de nombreux éléments
Notre article propose des recommandations simples et concrètes sur la façon
d'enseigner aux consommateurs comment suivre leurs dépenses en magasin. Cet article a des implications importantes pour les consommateurs et les organisations qui mettent en œuvre des programmes d'éducation des consommateurs. Notre preuve empirique suggère que les estimateurs stables surpassent les « switchers », et implique que les consommateurs devraient utiliser des stratégies qui sont semblables dans le degré de simplification prix, au lieu de la combinaison de différentes règles de calcul. Ainsi, nous devons souligner l'importance de maintenir stable le degré de simplification des prix tout au long du voyage de shopping.
En ce qui concerne la simplification de niveau de prix, nous dirions qu'il n'y a pas un degré optimal de simplification qui permettrait à tous les acheteurs de suivre avec précision leurs dépenses en magasin. Nous proposons que la précision relative des différentes stratégies dépende des caractéristiques des consommateurs et des types des achats. Dans cet article, nous discutons d'un facteur - le nombre d'articles dans le panier - qui détermine si la stratégie d'addition exacte fonctionne mieux ou pire que les stratégies de simplification. Des
recherches supplémentaires pourraient se pencher sur d'autres facteurs qui modèrent l'effet de
simplification des prix sur la précision.
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ESSAI 3 : EST-CE QUE TOUT EST RELATIVE? L'EFFET DU FORMAT DES
NUMEROS SUR LA PENSEE RELATIVE DANS LES JUGEMENTS NUMÉRIQUES
Cet article utilise la recherche sur la cognition numérique pour identifier un nouveau facteur qui modère la pensée relative dans les décisions des consommateurs. Pensée relative est la tendance à considérer les différences relatives des prix et des niveaux de qualité (par opposition à des différences absolus) dans les décisions individuelles. Cette tendance a été récemment attribué à la pensée intuitive et la psychophysique des évaluations numériques (Azar 2007; Saini et Thota 2010). Parce que la représentation intuitive des nombres n’est pas linéaire, mais logarithmique, les gens perçoivent les différences entre les deux grands
nombres d'être plus petit que les différences entre les petits numéros (Dehaene 1992; Moyer et Landauer 1967). Lorsque les consommateurs se fient plus sur leurs intuitions, l'effet de la pensée relative devient plus forte (Saini et Thota 2010).
Nous proposons que les représentations numériques intuitives qui sous-tendent la pensée relative, soient disponibles pour des nombres entiers entre 1 et 100. Ces
représentations sont sous-développées ou absent pour les grands chiffres et nombres décimaux. Bien que l'information numérique soit omniprésente dans nos vies, notre exposition aux différents formats de numéros est inégale. Nous évaluons rarement de très grands nombres ou des nombres décimaux: les prix des biens les plus fréquemment achetés tombent en dessous de 10 aux États-Unis et en Europe; nous utilisons habituellement numéros entre 1 et 60 pour parler de temps et nous achetons des produits en quantités relativement petits. À la suite de cette exposition insuffisante et le manque d'expérience, les représentations intuitives de grands nombres et des nombres décimaux doivent être sous- développés. Par conséquence, la pensée relative ne doit pas se manifester dans les
comparaisons de ces numéros. Dans cet article, nous proposons que: les gens seront moins
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enclins à penser en termes relatifs quand ils évaluent (a) grands nombres entiers (par rapport à nombres petits) et (b) des nombres décimaux (par rapport à des nombres entiers). Nous proposons que l'expérience dans les évaluations des nombres puisse induire la pensée relative.
Étude 1 a comparé la pensée relative dans les comparaisons des grands nombres par rapport des petits nombres. L'étude a adopté un design inter-sujets (2 (format de prix: cinq chiffres / deux chiffres) x 2 (différence relative: petite (30 contre 50) / grande (5 contre 25))).
Les participants ont choisi entre un billet indirect peu coûteux et un billet direct cher. Les résultats de la régression logistique ont soutenus nos prévisions. Lorsque les prix ont été exprimés dans le format à deux chiffres, les gens étaient plus susceptibles de choisir l'option coûteuse quand la différence relative était petite. Cet effet a été éliminé lorsque les prix ont été exprimés dans le format à cinq chiffres. Ainsi, nous avons trouvé un appui préliminaire à la première prédiction en montrant que la pensée relative a été atténuée dans les jugements des grands nombres.
Étude 2 a examiné la pensée relative dans les comparaisons des grands nombres par rapport des petits nombres. L'étude a adopté un design inter-sujets (2 (format de prix:
nombres décimales / entiers) x 2 (différence relative: petite (30 contre 50) / grande (5 contre 25)). Les participants ont choisi entre un bagel bon marché et un bagel cher avec du fromage.
Les résultats confirment nos prédictions. Les gens étaient beaucoup plus susceptibles de choisir l'option coûteuse lorsque la différence relative de prix était petite dans la condition de nombres entiers, mais pas dans la condition de nombres décimaux.
Étude 3 a exclu la facilité de traitement créée par la répétition des faits arithmétiques
comme une alternative compte des résultats observés. Opérandes (par exemple 5) dans les
problèmes de multiplication communs peuvent rendre leurs produits respectifs cognitivement
plus accessibles (soit 25). Ça peut provoquer des sentiments de facilité cognitive (King et
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Janiszewski 2011). Dans les études 1 et 2, la facilité de traitement de la paire "5 et 25" (paire de grande différence relative) dans la condition des nombres entiers aurait pu faire la
différence entre les prix correspondants paraissent plus grands (Thomas et Morwitz 2009). La condition de nombres décimaux ne bénéficierait pas des sentiments de facilité cognitive depuis les associations de mémoire des simples faits arithmétiques ne sont pas créés pour les décimales. Pour écarter ce compte nous n’avons pas utilisé des numéros liés à des faits de multiplication dans l'étude 3. Sinon, le design était le même que celui de l'étude 2. Les résultats confirment nos prédictions. La pensée relative n’a pas affecté le choix dans la condition des nombres décimaux.
Cette recherche identifie un nouveau facteur affectant la force de la pensée relative, un biais bien établie et pratiquement pertinente dans les décisions individuelles (par exemple Azar 2007; Thaler 1980). Il contribue également à la recherche de la cognition numérique en montrant que les représentations mentales des nombres (intuitive vs. précis), précédemment capturés par des temps de réponse (Cohen 2010; Dehaene, et al 1990), peut également être observée dans les décisions individuelles. Enfin, nos résultats peuvent informer les
gestionnaires sur la façon d'encadrer leurs prix en fonction des produits qu'ils aimeraient
vendre d'abord.
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TABLE OF CONTENTS
OVERVIEW OF THE THESIS ... 16
CHAPTER 1. Essay 1: IGNORING THE CENTS DIGITS: IS IT AN ENCODING BIAS OR A TRANSCODING BIAS?... 18
ABSTRACT ... 18
INTRODUCTION ... 19
CONCEPTUAL FRAMEWORK ... 22
STUDY 1 ... 27
STUDY 2 ... 32
STUDY 3 ... 37
GENERAL DISCUSSION ... 39
REFERENCES ... 44
CHAPTER 2. Essay 2: KEEPING TRACK OF IN-STORE SPENDING: THE ROLE OF COMPUTATIONAL STRATEGY SWITCHING AND PRICE SIMPLIFICATION ... 48
ABSTRACT ... 48
INTRODUCTION ... 49
THEORETICAL BACKGROUND ... 52
STUDY 1 ... 59
STUDY 2 ... 70
STUDY 3 ... 78
GENERAL DISCUSSION ... 86
REFERENCES ... 93
CHAPTER 3. Essay 3: IS IT ALL RELATIVE? THE EFFECT OF NUMBER FORMAT ON RELATIVE THINKING IN NUMERICAL JUDGMENTS ... 98
ABSTRACT ... 98
INTRODUCTION ... 99
CONCEPTUAL FRAMEWORK ... 101
HYPOTHESES ... 105
STUDY 1: LARGE NUMBERS AND RELATIVE THINKING ... 108
STUDY 2: DECIMALS AND RELATIVE THINKING ... 114
STUDY 3: RULING OUT ALTERNATIVE ACCOUNTS ... 120
GENERAL DISCUSSION ... 127
REFERENCES ... 132
16
OVERVIEW OF THE THESIS
Consumers deal with numerical computations every day. People have to judge whether the difference between two multi-digit numbers, such as prices, quality ratings, GPA’s, gas mileage, is small or large. They need to sum up future expenses to estimate annual and monthly budgets (Ulkumen, Thomas, and Morwitz 2008), and to monitor the running totals of their expenses to stay within available budgets (van Ittersum, Pennings, and Wansink 2010). They also have to perform more complex computations when converting multiple discounts into cumulative monetary savings (Chen and Rao 2007).
In my dissertation I look at mental representations and cognitive processes that underlie mental arithmetic in the marketplace. This research contributes to behavioral pricing litera ture by outlining novel factors that influence consumers’ price difference judgments.
Particularly, I uncover factors that make consumers more or less likely to fall prey to the left- digit anchoring bias ( Essay 1 ) and factors that determine their tendency to rely on relative thinking in price difference evaluations ( Essay 3 ). Further, this research provides new insights to the mental budgeting literature by identifying mental computation strategies that lead to more accurate basket price estimates ( Essay 2 ). Overall, I expect my research to contribute to our understanding of consumers’ price judgments and suggest contexts and strategies leading to more accurate price evaluations.
In my first essay I examine the mechanisms underlying the left-digit bias in price comparisons. I develop a set of competing hypotheses emerging from two alternative
accounts of the bias to determine whether the left-digit is caused by inattention to right digits
(e.g., dimes and pennies) during the encoding of multi-digit prices or caused by a propensity
to incorrectly round numbers after the encoding stage. The results from the experiments do
not support the biased encoding account. Two studies show that the left-digit effect can
17
manifest even when consumers encode the right digits in multi-digit prices. Moreover, the studies demonstrate that under memory-based processing allowing people to abstract away from the precise visual encoding of prices, the left-digit effect is reduced. The experiments suggest that the left-digit effect might be caused by rounding-up aversion; after the encoding during the price comparison stage consumers tend to incorrectly round-down prices.
In my second essay I analyze different mental addition strategies used by consumers with limited budgets to monitor total basket prices. I identify possible sources of estimation errors associated with each basket price tracking method. An online and a laboratory study compared exact addition, simplification and a combinations of the above strategies. The results suggest that consumers are better off using a single strategy, rather than combining several methods. A field study with random assignment of computational strategies shows that people arrive at more accurate basket total estimates when they use exact addition for relatively small shopping baskets and when they rely on simplification for relatively large basket sizes.
In the third essay I return to the context of numerical difference evaluations and
develop hypotheses regarding differential activation of relative thinking in price judgments. I
argue that relative thinking will not manifest uniformly across different number formats and
will be weaker for numbers expressed with more (as opposed to fewer) digits and for decimal
numbers (as opposed to integers). The first study using airline ticket purchase scenario finds
support to the first prediction. The remaining two studies provide converging support to the
second prediction in the context of inexpensive product choices.
18
CHAPTER 1. Essay 1: IGNORING THE CENTS DIGITS: IS IT AN ENCODING BIAS OR A TRANSCODING BIAS
2?
ABSTRACT
The left-digit effect is one of the most ubiquitous biases in numerical cognition that has implications for the practice of pricing, yet the psychological mechanism underlying this bias remains unclear. Three experiments were conducted to examine whether the bias is caused by inattention to right digits (e.g., dimes and pennies) during the encoding of multi-digit prices or caused by a propensity to incorrectly round numbers after the encoding stage. The results from the experiments do not support the biased encoding account; they show that the left- digit effect can manifest even when consumers do encode the right digits of a multi-digit price. Our experimental evidence suggest that the left-digit effect might be caused by rounding-up aversion; after the encoding during the price comparison stage consumers tend to incorrectly round-down prices. We identify visual similarity and analog similarity with round numbers as the determinants of rounding-up aversion. The rounding-up aversion account identifies novel moderators of the left-digit effect.
Keywords: behavioral pricing, numerical cognition, mental arithmetic, price magnitude
2
This paper is co-authored with Professor Manoj Thomas. It has been presented at the
Society for Consumer Psychology (SCP) annual conference 2014, the European Marketing
Academy (EMAC) annual conference 2014, and the Association for Consumer Research
(ACR) annual conference 2014. It is currently being revised for resubmission to the Journal
of Consumer Psychology.
19
INTRODUCTION
Judgments of numerical differences are ubiquitous. People often have to judge whether the difference between two multi-digit numbers, such as prices, quality ratings, GPA’s, car mileages, is small or large. Over the past decade behavioral pricing researchers have paid considerable attention to the systematic biases in numerical comparisons to characterize the mental processes that underlie everyday numerical judgments (Chen & Rao 2007; Cheng & Monroe 2013; Coulter 2013; Coulter & Coulter 2007; Manning & Sprott 2009; Monga & Bagchi 2012; Monroe & Lee 1999; Morwitz, Greenleaf, & Johnson 1998;
Thomas & Morwitz 2005). In this paper we focus on a well-documented and one of the most pervasive biases in numerical cognition known as the left-digit effect (Manning & Sprott 2009; Thomas & Morwitz 2005). This effect manifests as individuals’ tendency to anchor their judgments of numerical differences on left-most digits. Falling prey to the left-digit bias, people judge the difference between $2.99 and $4.00 to be significantly larger than that between $3.00 and $4.01 even though the numerical difference is identical (Basu 2006;
Manning & Sprott 2009; Monroe 2003; Schindler & Kirby 1997; Stiving & Winer 1997;
Thomas & Morwitz 2005). The left-digit effect manifests itself not just in laboratory
experiments, but also in real-world settings with non-trivial economic consequences. For
example, shoppers in grocery stores choose the product with lower dime digits without
considering the cents digits (Stiving & Winer 1997). Buyers in the used car market pay
disproportionately higher prices for cars whose mileage falls just below a 10,000-mile
threshold (Lacetera, Pope, & Sydnor 2011) and traders buy stocks priced one penny below
whole dollar amounts (Bhattacharya, Holden, & Jacobsen 2012). Further proving the
importance of the left-digit bias, the Israeli government has recently taken action to make
20
sure consumers are no longer misled by just-below pricing and made retailers only display prices that were multiples of 10 agorot (one hundredth of the new Israeli shekel)
3.
While its robustness and implications have been demonstrated in a variety of contexts, the mechanisms that underlie the left-digit effect continue to be debated (see Thomas &
Morwitz 2009 for a discussion). The issue at the core of the discussion is whether the left- digit bias occurs due to biased encoding (i.e. an encoding bias caused by left-to-right processing) or due to rounding-up aversion (i.e. a transcoding bias caused by the propensity to incorrectly round down numbers that ought to be rounded up). The extant literature largely endorses the former account. Several scholars have attributed this effect to biased encoding of prices’ right digits (Basu 2006; Lacetera, Pope & Sydnor 2011; Stiving & Winer 1997).
According to the biased encoding account the effect emerges during left-to-right price processing as consumers truncate multi-digit prices to their left-most digits and do not pay attention to the right digits to minimize their cognitive effort (e.g. Basu 2006; Stiving &
Winer 1997). A related but slightly different account suggests that because consumers read prices from left to right, they remember left-most digits more vividly (Coulter 2001;
Schindler & Wiman 1989). In support of this view, Stiving and Winer (1997) argue that the left-to-right processing account of multi-digit price comparisons provides the best fitting model to their supermarket sales data and suggest that consumers attend to the cent digits only if the dime digits are identical. In fact, the authors argue that if consumers can compare two prices using the dime digits, then they ignore the cents digits during the encoding stage.
This biased encoding account posits that since the left-digit effect is caused by inattention to right digits, the effect will be (i) independent of the value of the right digits, and (ii) stronger under conditions of memory-based than stimulus-based processing.
3
http://www.consumers.org.il/?catid=%7b82C212BA-66D5-4EAC-9BE9-
AA7A7F525675%7d
21
However, the biased encoding account posited in the marketing and economics
literature is inconsistent with the findings in the numerical cognition domain which show that encoding of multi-digit numbers is inherently holistic in nature. Several cognitive
psychologists have found that people automatically attend to right digits in multi-digit numbers even in tasks that could be successfully completed by only attending to numbers’
left-most digits (Dehaene, Dupoux, & Mehler 1990; Ganor-Stern et al. 2007; Monroe & Lee 1999; Nuerk et al., 2001). Participants’ response latencies in number comparison tasks decrease as target numbers get farther from the comparison standard (e.g. 55) and depend on right digits even outside the standards’ decade (Dehaene et al., 1990; Hinrichs et al., 1981).
For example, it takes people longer to compare 61 to 55 than to compare 67 to 55, even though a decision can be made by only attending to left-most digits. Furthermore, it takes people less time to decide that 42 is smaller than 57 than to decide that 46 is smaller than 62, as in the former case the comparisons of decade and unit digits lead to the same decision – a result which also implies that people automatically attend to right digits in multi-digit numbers (Ganor-Stern et al., 2007; Nuerk et al., 2001).
Thus, the holistic models of multi-digit processing imply that since people
automatically encode all the digits of multi-digit numbers, the left-digit bias cannot be
occurring during the encoding stage; rather, the bias must be occurring at the transcoding
stage due to incorrect rounding in price magnitude comparisons. Disentangling these two
accounts is important because they make different predictions about what factors will
moderate the left-digit effect. The objective of this research is to compare and contrast the
competing predictions that emerge from the biased encoding account and the biased
transcoding account. We test these predictions in three experiments.
22
CONCEPTUAL FRAMEWORK
Rounding-Up Aversion
Given that the biased encoding account is at odds with findings on automatic
encoding of right digits in multi-digit stimuli, we propose that the left-digit bias emerges after
encoding, during mental computations. After a consumer encodes individual prices, to make
purchase decisions she often has to compare two or more prices. Such a price comparison
process requires mental computations. One way to simplify the mental computation is to
round down or round up the multi-digit numbers to the closest round number (Lemaire,
Lecacheur, & Farioli 2000; van Ittersum, Pennings, & Wansink 2010). Correctly rounding
fractional prices to the closest whole dollar amount not only simplifies mental computations,
but in most cases eliminates the left-digit effect. To illustrate with an example, if people
round 2.99 to 3.00, the difference between the rounded numbers - (i.e., 4 and 3) would be
close to the actual difference. However, if, instead of rounding up the number, consumers
incorrectly round the prices down, they are likely to overestimate the difference between 2.99
and 4.00 because the difference between the rounded-down numbers (i.e., 4 and 2) is larger
than the actual difference (1.01). In line with this reasoning some researchers have suggested
that the left-digit effect could be caused by consumers’ aversion to round up fractional prices,
yet, no compelling cognitive account has been offered to explain why people tend to round
prices down, rather than up (see Anderson & Simester, 2003). Thus, in this paper we
formulate and test empirically the rounding-up aversion account of the left-digit anchoring
bias.
23
Why are people reluctant to round-up numbers in multi-digit subtractions
4? According to the biased encoding account the left-digit bias is caused by left-to-right reading. We
believe instead that the effect is caused by rounding-up aversion which is, in turn, caused by the motivation to preserve the integrity of multi-digit numbers while approximating, or transcoding them. According to this account, when approximating numbers, people are intrinsically motivated to keep the mental representation of the approximated number as similar as possible to the original number. The perceived similarity between the
approximated number and the original number plays an important role in rounding decisions.
We theorize about two factors that influence intuitive and spontaneous judgments of numerical similarity – visual similarity and analog similarity between the price and the nearest round number. Rounding-up, compared to rounding- down, inevitably reduces the visual similarity between the original number and the rounded number. For example, 2.75 is more visually similar to 2.00 (they share the left-most digit) than to 3.00. This heuristic assessment of visual similarity makes people more likely to round-down than to round-up. At the same time, assessments of analog (magnitude) similarity between a fractional number and the corresponding upper round number make people more likely to round-up fractional numbers that are closer to whole dollar amounts ($2.99 vs. $2.75). Thus, the rounding-up aversion account uniquely predicts the above factors shaping heuristic assessments of
similarity between the multi-digit number and the corresponding round number will moderate the left-digit effect.
Competing Predictions about Moderators
4
Please note that in our conceptualization we will focus only on fractional prices that need to
be rounded up (e.g., 2.75 and 2.99) because rounding-up aversion and the consequent left-
digit bias is relevant only for these prices.
24
There are two fundamental differences between the biased encoding account and the rounding-up aversion account. First, according to the former, the left-digit bias emerges at the price encoding phase due to inattention to dimes and pennies, whereas per the rounding-up aversion account the bias arises after encoding during the transcoding, or the approximation phase. Second, while the biased encoding account indicates left-to-right processing as the cause of the bias, the rounding-up aversion account implies that there are other factors at play, namely – consumers’ innate tendency to preserve the similarity between the visual representations and the analog magnitudes of the actual and the approximated multi-digit numbers. This leads to competing predictions from the two accounts on when the left-digit effect is more likely.
The Right-Digit Magnitude Sensitivity Hypothesis
The prevalent biased encoding account (see Stiving & Winer 1997) predicts that the magnitude of the dimes and cents should have no effect on the left-digit anchoring bias. It assumes that consumers only encode prices’ left -most digits due to left-to-right processing, irrespective of prices’ right digits. Consequently, the account holds that right digits have no role to play in left-digit anchoring. Formally, the biased encoding account predicts:
H1a: Since consumers do not attend to the dime and cents digits, the left-digit effect will be unaffected by the magnitudes of the right digits.
The rounding-up aversion account makes a different prediction. According to this
account people try to approximate numbers while minimizing the distortion of the visual
representations and analog magnitudes of the numbers. Their reluctance to round depends on
25
two different heuristic cues of similarity between the number and the nearest round number – visual similarity and analog magnitude similarity. When the number is not very close to the upper threshold, the tendency is to round-down numbers because of visual similarity, even if rounding down is incorrect. For example, people are more likely to round down 2.75 to 2 than to round up 2.75 to 3. In this case, the effect of visual similarity dominates the effect of analog similarity. However, when the number is very close to the upper threshold, analog magnitude might become a more salient similarity cue and override the effect of visual similarity of the left-most digits. Consequently, prices close to whole dollar amounts (e.g., 2.99) are more likely to be rounded up because rounding will not change their magnitude noticeably.
In sum, when prices get closer to whole dollar amounts, the relative impact of visual similarity becomes weaker and consumers become more willing to round-up fractional prices.
This, in turn, reduces the left-digit anchoring bias. Formally the rounding-up aversion account predicts that:
H1b: The magnitude of the dimes and cents digits will moderate the left-digit effect such that analog similarity of magnitudes will reduce rounding-up aversion. The left-digit effect is less likely to manifest when the analog magnitudes of the fractional number and the round number are more similar (e.g., $2.99 and $3.00) than when they are less similar (e.g., $2.75 and $3.00).
The Visual Salience Hypothesis
The biased encoding account and the rounding-up aversion account diverge further with regard to the effect of price evaluation mode (memory-based vs. stimulus-based
processing) on the left-digit anchoring bias. Memory-based comparisons are more cognitively
26
demanding. According to the biased encoding account, when memory resources become more limited, people should become more likely to ignore the right digits during encoding to reduce the cognitive effort (Basu 2006; Stiving & Winer 1997). In other words, the left-digit effect should be amplified in memory-based comparisons. Formally, per the biased encoding account:
H2a: Memory-based processing will increase inattention to right digits and thus exacerbate the left-digit effect.
The rounding-up aversion account makes a different prediction. It suggests that consumers are motivated to preserve the integrity of visual representations of prices while approximating them. Visual number representations rely on precise digital encoding of numerical information (Dehaene 1992). For instance, a price of $2.99 is represented as a sequence of digits “2 -9- 9”. The motivation to preserve the precise visual “code” of multi - digit prices makes people inclined to avoid rounding since the number of digits shared by the actual and the rounded price is minimal (e.g. $2.99 vs. $3.00). In line with the above
reasoning, Brainerd and Reyna (1990) postulate that information encoded as a “well- articulated, crystallized structure” is less likely to be subject to transformation.
However, when structured and precise visual price representations are not accessible
during price comparisons, people should become more likely to transform them. Numerical
cognition research supports this idea: people become less likely to rely on structured digital
number representations in memory-based comparisons, and more likely to rely on imprecise
representations of number magnitude (Ganor-Stern, Pinhas, & Tzelgov 2009; Zhang & Wang
2005). Thus, we argue that in contexts of stimulus-based price evaluations where people have
prices visually present in front of them, the difference between actual (e.g. $2.99) and
27
approximated (e.g. $3.00) price representations is highly salient, which should make people reluctant to distort visual representations by rounding. In contrast, in memory-based price evaluations the accuracy of visual representations is more difficult to evaluate as the actual price is not directly accessible in the working memory. Accordingly, people become less sensitive to the visual distortion of prices, and more willing to transform them into nearest round prices that accurately represent price magnitude information, but do not preserve the precise digital encoding. Formally, we expect that:
H2b: Memory-based processing will reduce the effect of visual similarity and thus attenuate the left-digit effect.
STUDY 1
To test the first set of predictions we asked participants in this experiment to evaluate the magnitude of the difference between regular and sale prices. Regular and sale prices were manipulated on two key dimensions: left-digit difference between regular and sale prices (large left-digit difference vs. control) and the magnitude of cents and dime digits. The stimuli are presented in Table 1.
Method
Ninety nine participants from an online panel (MTurk) took part in this study. The
study employed a 2 (left-digit difference: large vs. control) x 2 (right digits: 99 vs. 75) x 3
(numeric distance: small vs. medium vs. large) within-subjects design.
28
Left-digit difference was manipulated such that for half of the prices the left-digit difference was larger than the actual price difference, while for another half of the prices the left-digit difference was relatively close to the actual price difference. As is clear from Table 1 for half the prices with large left-digit differences, left-to-right processing without rounding would produce a biased judgment. For example, in the pair “$8.00 and $6.99”, if participants anchor their judgments on the left-most digits, the judged difference would be around $2 which is considerably higher than the actual difference of $1.01. For each such pair, we also constructed a control pair wherein the left-digit differences were not misleadingly large. In control pairs left-to-right processing would likely result in an accurate price difference evaluation. For example, in the pair “$8.01 and $7.00” the difference between the left-most digits of the two prices is close to $1 which is close to the actual difference of $1.01.
Table 1. STIMULI USED IN STUDIES 1 AND 3.
Large Left-digit Difference (LDD)
Condition
Control Condition Numeric
distance Right digits
Regular Price
Sale Price
Regular Price
Sale Price
Small 01/99 $8.00 $6.99 $8.00 $7.00
Medium 01/99 $8.00 $4.99 $8.00 $5.00
Large 01/99 $8.00 $2.99 $8.00 $3.00
Small 25/75 $8.00 $6.75 $8.00 $7.00
Medium 25/75 $8.00 $4.75 $8.00 $5.00
Large 25/75 $8.00 $2.75 $8.00 $3.00
Right digit magnitudes were manipulated by changing the prices’ dime and cent
digits, such that the distance to the nearest round number was relatively small for half of the
price pairs, and relatively large for the other half of the pairs. More specifically, half of the
pairs included prices with .99 or .01 endings (e.g. $8.00 and $6.99) wherein the distance
between the fractional prices and the nearest round prices was only .01. For the other half, the
29
prices had .75 or .25 endings and so the distance between the fractional prices and the nearest round prices was .25.
Numeric distance was manipulated, since previous research has shown that the left- digit effect is stronger for small numerical differences (Thomas & Morwitz 2005). The numeric distance was small (1.01, 1.25), medium (3.01, 3.25) or large (5.01, 5.25)
5.
The study was comprised of two tasks. In the first task participants were asked to evaluate 12 pairs of regular and sale prices and to indicate how small or large the discounts were on an 11- point unmarked scale anchored at “Small” on the left and “Large” on the right.
Participants saw pairs of regular and sale prices appear on the screen one pair at a time in random order. Each pair was vertically aligned with the regular price placed above the sale price. The 11-point scale was provided on the same screen below the sale price.
In the second task participants were asked to review the same price pairs in random order and to indicate which strategy they used to compute the discount in each pair.
Participants had to indicate whether they computed the difference between regular and sale prices (a) by first subtracting left-most digits and then adjusting for the right digits or (b) by rounding regular and sale prices to whole dollar amounts. They could also answer that they had not used either of the above subtraction strategies and relied on a different method. It should be noted that we had considered asking the participants to describe the computational strategies they had used in their own words. However several pretests had shown that a
5
While we realized that some of these discount magnitudes could appear unusually large, we did not expect that to affect the cognitive processes underlying price evaluations and bias the results in favor of one of the two competing accounts. Indeed, prior studies (Manning &
Sprott 2009; Thomas & Morwitz 2005) used smaller and, thus, more realistic price
differences to test the moderating role of price difference magnitude in left-digit anchoring.
However, as the three reported studies will show, the pattern of results in our studies closely
replicates prior findings. Thus, it does not appear that price difference magnitude had any
profound effects on the way in which the participants processed the prices in our studies.
30
significant proportion of respondents tends to give uninformative answers to such open-ended questions (e.g. “I looked at the first price, then at the second, and then estimated the
difference”). Thus, we chose to use the multiple-choice response format to get insights into the computational processes underlying price difference estimation.
Results and Discussion
Participants’ magnitude judgments were submitted to a repeated-measures ANOVA.
Means across the 12 price pairs are reported in tables 2. The analysis revealed a main effect of left-digit difference (F(1,98)=40.50, p<.01). The analysis also revealed a main effect of right digits (F(1,98)=9.36, p<.01), and a main effect of numeric distance (F(2,196)=156.29, p<.01). Further, the analysis revealed a significant two-way interaction between left-digit difference and numeric distance. Simple contrasts showed that the effect of left-digit
difference was higher for smaller numeric distance problems ( F (1,98)=37.52, p<.01) than for medium ( F (1,98)=5.25, p<.05) or large numeric distance problems ( F (1,98)=15.37, p<.01), consistent with previous results that the left-digit effect is stronger for small distances (Thomas & Morwitz, 2005). This result suggests that since judgments are made on a logarithmic scale, the effects of left-digit anchoring are stronger for smaller than for larger differences. There was no significant two-way interaction between right digits and numeric distance (F(1,196)=1.76, p>.10), and no significant three-way interaction between left digit difference, right digits and numeric distance (2,186)=2.62, p>.10).
Importantly, in line with the transcoding account predictions, the analysis revealed a
two-way interaction between left-digit difference and right digits ( F (1,97)=4.98, p<.05). The
pattern of means is depicted in Figure 1. Simple contrasts showed that the left-digit effect was
weaker, although statistically significant, when prices were close to whole dollar amounts in
31
magnitude ( M
large LDD=7.06 vs. M
control=6.60; F (1,98)=22.14, p<.01) than when they were far ( M
large LDD=7.38 vs. M
control=6.69; F (1,98)=38.73, p<.01). This result suggests that the left- digit effect was reduced for prices that were close to whole dollar amounts in magnitude (see Figure 1). The analysis of retrospective strategy reports provides additional support to H1b.
Repeated measures logistic regression analysis showed that, in line with the predictions of the transcoding account, “99” endings significantly increased participants’ propensity to round up fractional prices (b=0.67, p=.01). Thus, H1b is supported.
Table 2. STUDY 1: SUMMARY STATISTICS.
Price pairs Large LDD
Condition (SE)
Control Condition (SE) Prices close to whole dollar amounts
$8.01/$7.00 and $8.00/$6.99 4.63 (0.27) 3.96 (0.31)
$8.01/$5.00 and $8.00/$4.99 7.14 (0.17) 6.98 (0.19)
$8.01/$3.00 and $8.00/$2.99 9.39 (0.20) 8.90 (0.18) Prices far from whole dollar amounts
$8.25/$7.00 and $8.00/$6.75 5.28 (0.25) 4.03 (0.29)
$8.25/$5.00 and $8.00/$4.75 7.41 (0.16) 7.06 (0.17)
$8.25/$3.00 and $8.00/$2.75 9.43 (0.23) 8.98 (0.18)
32
Fig. 1. STUDY 1: THE LEFT-DIGIT EFFECT IS WEAKER FOR PRICES CLOSE TO WHOLE DOLLAR AMOUNTS.
STUDY 2
This experiment was designed to test the hypothesis regarding the role of memory- based processing (relative to stimulus-based processing) in left-digit anchoring. Participants assigned to the stimulus-based condition could see the pairs of prices as they judged the difference between the prices. In contrast, participants assigned to the memory-based condition were asked to retain the prices in memory and then judge the difference between the prices. The biased encoding account predicts that memory-based processing, being more cognitively demanding, would increase the left-digit effect. In contrast, the biased
transcoding account suggests that memory-based processing, allowing people to abstract from the precise digital price representations (Zhang & Wang, 2005), would make them more likely to simplify the prices by rounding and, thus, reduce the left-digit effect. Study was designed to test the competing predictions of the two accounts.
7.06
7.38
6.60 6.69
5.00 5.50 6.00 6.50 7.00 7.50 8.00
$0.01 to whole dollar amount $0.25 to whole dollar amount
Judged discount magnitude
Large left-digit difference Control
33 Method
One hundred and twenty Mechanical Turk panelists took part in this study in
exchange for a small monetary reward. The study employed a 2 (price difference evaluations mode: stimulus-based vs. memory-based) x 2 (left-digit difference: large vs. control) x 6 (numeric distance: 6 levels) mixed factorial design, with price difference evaluation mode as a between-subjects factor and left-digit difference and numeric distance as within-subjects factors.
As in Study 1 we manipulated the left-digit differences between regular and sale prices, such that for half of the prices the left-digit difference was relatively close to the actual price difference, while for another half of the prices the left-digit difference was larger than the actual price difference. In addition we manipulated the numeric distance between the prices and used six level of price difference (from 1.01 to 6.01). Table 3 presents the stimuli used in Study 2.
Table 3. STIMULI USED IN STUDY 2.
Large LDD Condition
Control Condition Numeric Distance
Regular Price
Sale Price
Regular Price
Sale Price
1.01 $8.00 $6.99 $8.01 $7.00
2.01 $8.00 $5.99 $8.01 $6.00
3.01 $8.00 $4.99 $8.01 $5.00
4.01 $8.00 $3.99 $8.01 $4.00
5.01 $8.00 $2.99 $8.01 $3.00
6.01 $8.00 $1.99 $8.01 $2.00
As in Study 1, participants were asked to estimate the difference between regular and sale prices and to evaluate how large or small this difference was. Participants in the
stimulus-based evaluation condition saw the regular and the sale prices simultaneously, the
34
regular price above the sale price, with the 11-point price difference evaluation scale placed at the bottom of the screen. Thus, the regular price, the sale price, and the response scale were presented on the same screen. In contrast, participants in the memory-based evaluation
condition saw the stimuli and the response scale on separate sequential screens, each screen separated by an asterisk. They saw prices appear on the screen one by one, the regular price shown before the sale price, with each price followed by an asterisk. The asterisks were used to further reduce the accessibility of the visual code and, consequently, of symbolic number representations by “clearing” the visuospatial sketchpad (Baddeley & Hitch 1974). The 11- point evaluation scale appeared at the end of each price difference evaluation trial in the memory-based evaluation condition.
Results and Discussion
Price Difference Evaluations. Participants’ magnitude judgments were submitted to a repeated-measures ANOVA with left-digit difference (large vs. control) and numeric distance (6 levels) as within-subjects factors, and evaluation mode (stimulus-based vs. memory-based) as a between-subjects factor. Means across the two between-subject conditions and across the 12 price pairs are reported in table 4. The main effect of the left-digit difference was
significant ( F (1, 118) = 33.57, p <.001), as was the main effect of numeric distance
(F(2.77/336.27) = 353.62, p<.001). The two-way interaction between left-digit difference and numeric distance was not significant (F(4.78/564.32) = 1.35, p=.24
6. A series of planned
6
The interaction was not significant because several participants mistakenly evaluated the sale prices (e.g. 7.00), instead of the differences between regular and sale prices (e.g. 8.01 vs.
7.00), as small or large. For those participants the data followed the reversed pattern: small price differences (8.01 – 7.00 = 1.01) produced large evaluations and vice versa. More importantly, the left-digit effect pattern and its interaction with the numeric distance was also reversed: control pairs (8.01 vs. 7.00) produced larger evaluations than large left-digit
difference pairs (8.00 vs. 6.99), and this effect was weaker for small numeric distances (i.e.
35
contrasts showed that, as in the previous study, the left-digit effect was more likely to manifest for the smallest numeric distance ( M
large LDD= 3.33 vs. M
control= 2.61, F (1, 118) = 16.49, p < .001, η
2= 0.12) than for the largest numeric distance ( M
large LDD= 9.66 vs. M
control= 9.40, F (1, 118) = 1.68, p = .20, η
2= 0.01). The interaction between evaluation mode and numeric distance was not significant (F<1), and neither was the three-way interaction between left-digit difference, numeric-distance, and evaluation mode (F<1).
Most importantly, the interaction between type of left digits and evaluation mode was significant ( F (1, 118) = 3.86, p = .05). We further analyzed the effect of the left-digit
difference across the two evaluation mode conditions. Consistent with our predictions, the effect of left-digit difference was larger under stimulus-based processing ( M
large LDD= 6.71 vs. M
control= 6.19, F (1, 118) = 31.14, p < .001, η
2= 0.21), than under memory-based
processing ( M
large LDD= 6.48 vs. M
control= 6.22, F (1, 118) = 7.09, p < .01, η
2= 0.06). Figure 2 summarizes the means for the interaction between left-digit difference and evaluation mode.
In sum, when the accessibility of the visual price representations in the working
memory was reduced, participants were more likely to round the multi-digit prices and the
left-digit effect was reduced. These results support the biased transcoding account which
suggests that reducing the relative saliency of precise visual price representations can change
the cognitive strategies that people use for mental subtractions. More specifically, these
results support H2 which posits that memory-based processing can facilitate rounding of
fractional numbers. The results would also suggest that the left-digit effect is more likely to
for high sale prices). We could identify such cases by excluding price evaluations that were
more than 3SD away from their respective price pair means. When participants with such
biased evaluations were excluded (n=17), the results for the main hypothesized interaction
(LDD*Evaluation mode) became stronger (F=6.3, p=.013), and the interaction between LDD
and Numeric Distance became significant (F=3.3, p=.008). The pattern of means for the
interaction suggests that the LDE gets smaller as the numerical distance between prices
increases.
36
manifest when shoppers make stimulus-based in store price comparisons and less likely to manifest when they make memory-based across store price comparisons.
Table 4. STUDY 2: SUMMARY OF MEANS.
Stimulus-based evaluation (SE)
Memory-based evaluation (SE)
Numeric distance Large LDD*
Condition Control LDD
Condition* Large LDD*
Condition Control LDD Condition*
$1.01 3.61 (0.27) 2.60 (0.28) 3.05 (0.27) 2.62 (0.29)
$2.01 4.87 (0.22) 4.24 (0.24) 4.47 (0.23) 4.19 (0.24)
$3.01 6.03 (0.22) 5.60 (0.23) 5.79 (0.23) 5.76 (0.24)
$4.01 7.13 (0.23) 6.94 (0.21) 7.33 (0.24) 7.09 (0.22)
$5.01 8.77 (0.22) 8.21 (0.21) 8.79 (0.23) 8.43 (0.22)
$6.01 9.85 (0.26) 9.55 (0.25) 9.47 (0.26) 9.26 (0.26) Fig. 2. STUDY 2: THE LEFT-DIGIT EFFECTS IS WEAKER UNDER MEMORY-BASED PROCESSING.
6.71
6.48
6.19 6.22
5.00 5.50 6.00 6.50 7.00 7.50 8.00
Stimulus-based evaluation Memory-based evaluation
Judged discount magnitude
Large left-digit difference Control
