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Viewed Above The Effect of Using Large versus Small Units in Quantitative Estimates of Length, Weight, and Volume THESIS Presented in Partial Fulfillment of the Requirements for the Degree Master of Arts in the Graduate School of The Ohio State University By Jonghun Sun Graduate Program in Psychology The Ohio State University 2012 Thesis Committee: Michael L. DeKay (Advisor), Ellen Peters, Thomas Nygren Copyrighted by Jonghun Sun 2012 Abstract Previous research has demonstrated that changes in units can affect judgments and decisions. For example, people interpret quantitative information that is expressed as a larger number of small units as being larger than the same quantity expressed as a smaller number of large units. In related work, estimates of length or distance or the monetary value of goods are sometimes larger when participants use large units rather than small units. In all of this research, however, the focus has been on other phenomena (e.g., anchoring, attribute weighting, consumer behavior) rather than on the underlying relationship between numerical estimates and units. In two studies, we anticipated that participants’ estimates of physical quantities (e.g., the weight of a brick) would be larger when participants used larger units (e.g., pounds) than when they used smaller units (e.g., ounces), because their numerical answers would not be adjusted enough to compensate for differences in units. In Study 1, estimates of items’ length, weight, and volume were larger when made in larger units than when made in smaller units. This “unit effect” remained significant when we adjusted for participants’ incorrect knowledge of unit ratios and when we considered only those participants who knew the correct ratios. In addition, the unit effect was larger when participants were less familiar with the units used to make the estimates. In Study 2, participants estimated weight and volume using ii either familiar or unfamiliar (fictional) units. The unit effect was significant for unfamiliar units but not for familiar units. Possible mechanisms for these results are discussed and further research hypotheses are presented. iii Acknowledgments I would like to express my gratitude to my advisor, Dr. Michael L. DeKay, for his patience, support, and guidance. I also would like to thank my committee members, Dr. Ellen Peters and Dr. Thomas Nygren for their helpful advice. My colleagues in the department, Hyebin Rim and Louise Meilleur, have consistently motivated me and provided emotional support. I dedicate this work to my parents, who have always shown endless trust in my potential and talent. iv Vita 2001 ...............................................................Daewon Foreign Language High School, Seoul Korea 2006 ..............................................................B.A. Business Administration, Korea University, Seoul Korea 2010................................................................B.A. Psychology, The Ohio State University Fields of Study Major Field: Psychology v Table of Contents Abstract .............................................................................................................................. ii Acknowledgments.............................................................................................................. iv Vita ...................................................................................................................................... v List of Tables ................................................................................................................... viii List of Figures .................................................................................................................... ix Chapter 1: Introduction ....................................................................................................... 1 Effects of Scale on the Interpretation of Numeric Information ...................................... 1 Reversing the Effect of Unit Size ................................................................................... 5 The Role of Units in Magnitude Estimation ................................................................... 6 The Potential Role of Familiarity in the Unit Effect..................................................... 11 The Goals of the Current Research ............................................................................... 13 Chapter 2: Study 1 ............................................................................................................ 15 Method .......................................................................................................................... 15 Results and Discussion ................................................................................................. 17 Chapter 3: Study 2 ............................................................................................................ 33 vi Method .......................................................................................................................... 33 Results and Discussion ................................................................................................. 35 Chapter 4: General Discussion and Conclusions .............................................................. 48 Inferences from conversational Norms ......................................................................... 51 Conversational Norms in Estimates of Physical Quantities ......................................... 54 Implications of the Unit Effect ..................................................................................... 59 References ......................................................................................................................... 61 Appendix A ....................................................................................................................... 64 vii List of Tables Table 1. The Units Used in Three Conditions (Study1) ................................................... 17 Table 2. Participants’ answers to the conversion ratio and familiarity questions (Study1) ........................................................................................................................................... 24 Table 3. Self Reported Familiarity with Units on a 5-Point Scale (Study 1) .................... 28 Table 4. Units Used in the Six Conditions (2 (Unit Size) x 3 (Familiarity) ) for Each of the Two Items (Study2) .................................................................................................... 35 Table 5. Mean of logged estimates converted to the smallest unit for the target (N=159) (Study2)............................................................................................................................. 37 viii List of Figures Figure 1. Average estimates of length, weight, and volume of six items in the three unit conditions, with ± standard error bars ............................................................................... 18 Figure 2. Objective estimates of length, weight, and volume of six items, plotted as functions of objective units ............................................................................................... 23 Figure 3. Subjective estimates of length, weight, and volume of six objects, plotted as functions of subjective units ............................................................................................. 27 Figure 4. Objective estimates of weight and volume of two items, plotted as functions of objective units by familiarity condition ............................................................................ 40 Figure 5. Subjective estimates of weight and volume of two items, plotted as functions of subjective units by familiarity condition........................................................................... 44 ix Chapter 1: Introduction Quantitative information can be expressed in various units. Depending on the size of the chosen unit, the corresponding numeric value can be easily adjusted to communicate the desired quantity. For instance, we can express one hour of time in minutes or seconds, and adjust the numeric value to 60 or 3600 to make all three expressions equivalent (1 hour = 60 minutes = 3600 seconds). Recent research shows that judgment and decision making is often affected by the way in which quantitative information is expressed, or “framed,” even though there is no difference in the actual magnitude or quantity. Effects of Scale on the Interpretation of Numeric Information Burson and colleagues demonstrated that people’s preference for one option over another can be reversed by manipulating the scales used to describe the attributes of those options (Burson, Larrick, & Lynch, 2009). In their first study, participants evaluated two cell- phone plans. One plan was superior in quality (fewer dropped calls), while the other was superior in price. These two attributes , quality and price, were presented using either an expanded scale (e.g., dropped calls per 1000 calls) or a contracted scale (e.g., dropped calls per 100 calls). Price was presented using an expanded scale (price per year) when the number of dropped calls was presented on the contracted scale, or vice versa, with price on a contracted scale (price per month) when the number of dropped calls was on the expanded scale. If the price was expressed on the 1 expanded scale ($384 per year) so that number was larger than on the contracted scale ($32 per month), and the other attribute was described on the contracted
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