Human Error in Simple Estimation Tasks

This topic submitted by Emily Garritson and Matt Huelsenbeck ( garritem@muohio.edu huelsemw@muohio ) on 4/28/06. [ Human Nature Team: Emily Garritson and Matt Huelsenbeck-Section: Cummins/Wolfe]

Presented and Prepared by:

Matt Huelsenbeck and Emily Garritson

Project Outline:

I. Introduction
A. Background Information
B. Research Hypotheses & Predictions
C. Disciplines Involved
D. Human Nature Connections

II. Relevance of Research Question
A. Literature Review
B. Larger Question

III. Interdisciplinary Approach

IV. Specific Research Design
A. Experimental Design
B. Research Tasks
C. Experimental Conditions
D. Basic Overview of Trials
E. Social Dimension of Experiment
F. Post Experiment Survey

V. Materials and Methods
A. Materials Utilized
B. Statistics
C. Data Sheet
D. Data Sheet Notation
E. Research Execution Timeline
F. Standards for Team Work

VI. Statistics
A. ANOVAs
B. Independent Samples T-Tests
C. Correlations
D. Rationale behind the Statistics Utilized
E. Qualitative Results

VII. Discussion and Conclusions
VIII. Literature Cited

IX. Appendices
A. Pictorial Demonstrations of the Four Estimation Tasks
B. Methods Information
C. Statistical Information

I. INTRODUCTION

Decision making is a fundamental aspect of human nature. The choices humans make are the legacies of their lives and determine all of their actions. Every decision that a person faces includes an assortment of choices and subsequent outcomes. A rational decision maker evaluates an array of costs and gains pertaining to a situation and chooses what he or she believes to be the most beneficial outcome. Decision makers use any source of information they obtain in order to limit the variables of a situation. The social setting of a decision maker also plays a major role in determining how that person will act. Early and modern human beings have consistently relied on social structure and group decisions for survival (Brewer & Hewstone, 2004). Our project involves the experimentation of individuals and groups in simple decision making tasks of estimation. We will be evaluating the rationality of these decisions based on their congruence with the correct application of mathematical estimations (Allingham, 1999).

For our project, we have constructed two main research hypotheses. To begin, we hypothesize that there will be a significant difference between the data of individual test responses and group test responses. We further predict that the group responses will be more accurate than individual responses for all of our tests because humans are a social species. We think that working groups is more effective than working individually because more opinions and ideas are shared. Therefore, the final answer will be the culmination of the best ideas from the group. Our next prediction entails that responses from subjects who are provided more outside information will be significantly different and more accurate than responses from subjects given no additional information before conducting the tests. In general, all human decisions are affected by some degree of error (Senders & Moray, 1991). We believe that extra information prior to decision making will enhance the answers provided in each task and reduce the amount of human error. Psychologists categorize these types of decision making tasks that provide extra information as Òanchor and adjustmentÓ tasks where people are given some point or figure on which they can base their estimation (Pohl, 2004).

Our project merges facets of several disciplines. The study of decision making derives from cognitive psychology, and our experiments parallel research previously performed in that field. The estimation testing and rational testing we are conducting are critical parts of cognitive psychology. Aside from cognitive psychology, the use of statistics will play a major role in how we will analyze quantitative data to find differences and accuracy levels from test responses. To analyze the data, we will be conducting ANOVA tests to compare our results (Latin square analysis of variance). Lastly, this project will also draw from features of sociology in our study of group behavior in comparison with individual behavior.

Our research has connections to other aspects of human nature involved in this course. Rational decision making is the fundamental basis for the section involving economic human behavior. In addition, Homo economicus is bound by his ability to rationalize through costs and gains and decide which is most beneficial for himself and his kin. In addition, our study of the effectiveness of group decision making relates to the social animal portion of our course. Additionally, the biological segments of our course are linked to our project through the instinctive ability for humans to rationalize and make decisions. Moreover, group decision making also relates to the nature versus nurture argument as to which is more influential in the accuracy of decisions we make, our society or our genes.

II. RELEVANCE OF RESEARCH QUESTION

A. LITERATURE REVIEW

Allingham, M. (1999). Rational choice. Houndmills: MacMillan Press LTD.

Annotation: Chosen for its remarkable relevance to the complex connection between probabilities and rational choices, AllinghamÕs work devotes an entire chapter to questions surrounding problems of uncertainty. In this chapter, Allingham defines rationality as the ability to assign subjective probabilities to given events that ultimately will equal the expected utility of outcome. In other words, a rational choice can be explained through the correct application mathematics. This book also explores the history of logic and the foundations of rational choice theory.

Andrade, Jackie. May, Jon. Cognitive Psychology. New York: Garland. 2004.

Annotation: This book details several topics that pertain to our project. Andrade and May exhibit how linear perspectives are established and estimations on distance are created. This applies to our testing of distance estimation. This book also has a chapter on decision making which illustrates how decisions are made to maximize personal gain. It elaborates upon the extensiveness of decision making and also includes anchor and adjustment demonstrations which we will be included in our project.

Brewer, M.B., & Hewstone, M. (Eds.). (2004). Social cognition. Malden: Blackwell
Publishing Ltd.

Annotation: Because our experiment is testing the differences between group and individual decisions, it seemed relevant to find an excellent source on modern social psychology. This book is a collection of articles and studies all dealing with differing aspects of social thought. The study title ÒShared Cognition in Small GroupsÓ perfectly fit our basic questions about group decision making. After reviewing the history of social psychology theory, the authors investigated what types of behaviors led to the best social decisions. They concluded that groups with members who openly shared all their known information, tended to make the best choices in social settings.

Einhorn, H. & Hogarth, R.M. (1981). Behavioral decision theory: Processes of
judgment and choice. Annual Review of Psychology. 32, 53-88.

Annotation: This study attempts to determine ways of defining rationality and optimal choices in decision making tasks. The authors consider differing variables in decision making tasks and their possible effects on the rationality of the choices. We included this article in our bibliography of sources because of its obvious relevance to our own study. We are also trying to define rationality through decision making tasks and judging which answers are optimal or correct.

Franken, I. & Muris, P. (2005). Individual differences in decision-making. Personality &
Individual Differences. 39(5), 991-998.

Annotation: This article investigates the possible explanations for individual differences in decision making accuracy. The study examined decision making styles through a variety of gambling tasks. The participants first conducted a self-report personality exam, which provided the facilitators with information about the impulsivity, sensitivity, eagerness for reward, and decision making style for each participant. Although this study did actually divide the participants into groups based on their abilities and decision making styles, it is still applicable to our study because it also attempts to determine what makes accurate decisions.

Galotti, K.M. (1999). Cognitive psychology in and out of the laboratory. Belmont:
Wadsworth Publishing Company.

Annotation: Covering almost all areas of cognitive psychology, this text dedicates a single chapter to each of the following topics: problem solving, reasoning, and decision making. These three topics connect to form the basis of our research experiment. In the decision making chapter, Galotti provides the step-by-step procedure for correctly answering probability problems and introduces the topic of expected utility, which is the idea that people shape probabilities on the basis of personal reward. The expected utility theory can explain why a person should be willing to invest everything they have in the St. Petersburg paradox. This book also discusses numerous problems solving heuristics that we can use to identify the types of ways people solve problems (as determined by the answers on the post experiment survey).

Healy, Alice F. Experimental Cognitive Psychology. Washington: American
Psychological Association. 2005.

Annotation: Healy describes the influences of frames of references and anchor points in cognitive testing. Healy also depicts the relationship between perception and action as a goal-directed act. The results from simple tasks, she states, have higher implications into overall behavior of the subjects. This book also demonstrates the importance of control variables when conducting cognitive testing. Our project will use both anchor points and control variables along with connecting simple task responses to greater social issues.

Howell, D.C. (2004). Fundamental statistics for the behavioral sciences. Australia:
Thomson, Brooks/Cole.

Annotation: This textbook is actually the book used by current students enrolled in Psychological Statistics: PSY 293. This book examines various types of statistical analyses like ANOVAs and t-tests and applies them to psychological research studies. Because it thoroughly outlines the criteria and steps needed for ANOVA tests and independent t-tests, we included this textbook into our project. Additionally, the textbook offers guidelines for performing all these tests on computer programs like JMP, so we will utilize it during the statistical phase of the project.

Izawa, Chizuko. Cognitive Psychology Applied. New Jersey: Lawrence Erlbaum
Associates, Inc. 1993.

Annotation: This book outlines the progress in cognitive psychology and how emotions and other settings can influence cognitive decisions. This is relevant to our project because it displays a variety of ways in which studies on cognitive responses can aid in other areas such as mental health and understanding emotions. It shows a broad range of scientific opportunities opened up by study of cognition.

Johnson-Laird, P.N. Shafir Eldar. Reasoning and Decision Making. Oxford: Elsevier
Science Publishers. 1993.

Annotation: This source displays the interaction between reason and decision making. It exhibits the process by which humans make their decisions through a limitation of pros and cons in the situation. Experiments in this book present how individuals can be manipulated in their decision making from slight adjustments to a test. Furthermore, this book assesses rationality and its differentiation from simple logic.

Kahneman, D., Slovic, P., & Tversky, A. (Eds.) (1982). Judgment under uncertainty:
Heuristics and biases. Cambridge: Cambridge University Press.

Annotation: Compiled and edited by three well-known experts in human judgment, this work has provided the foundation for our probability tasks. Our fifth experimental task is actually an example cited in the first chapter of the book. This book explores the different factors affecting human decisions and whether the choices are accurate. The most pertinent information to our topic can be found in the textÕs first chapter where Tversky and Kahneman simply list and explain several categories of errors made in making estimating.

Kahneman, D. & Tversky, A. (1996). On the reality of cognitive illusions. Psychological
Review. 103(3), 582-592.

Annotation: Kahneman and Tversky researched the most common errors made in judgments in this study. They attributed the majority of human errors to base-rate neglect and conjunction errors. Base-rate neglect occurs when a person ignores the actual probability of an event and, instead, uses his own created probability. Conjunction errors result from try to attribute an event to an unrelated event and drawing similar conclusions. This article is helpful to our study because we will be able to see if these causes of errors will be visibly present in our own experiment (through the survey).

Keeney, Ralph L. Sebenius, James K. Zeckhauser, Richard J. Wise Choices:
Decisions, Games, and Negotiations. Boston: President and Fellows of Harvard College.
1996.

Annotation: This book is important to our research because it shows the connections between the study of decision making and the real world. This source expresses decision making as an indispensable factor of the fields of economics, international trade, and health and medicine. There are details of various complex decisions which professionals make everyday and create repercussions for themselves and others.

Kellogg, Ronald T. Cognitive Psychology. London: SAGE Publications, Inc. 1995.

Annotation: Kellogg has two chapters which are foundations of our project entitled, Reasoning and Decision Making, and Sensation and Perception. Kellogg describes different types of reasoning such as conditional reasoning and deductive reasoning. This book also displays how vital reasoning is in the most important and also the most trivial decisions of our lives.

Latin square analysis of variance. (n.d.) Statistics. Retrieved February 15, 2006, from
StatsDirect Limited Web Site:
http://www.statsdirect.com/help/analysis_of_variance/latin.html

Annotation: This website was extremely helpful in designing the Latin Square for our experimental procedure. The website first gave a documented example of a Latin Square experiment and continued to explain why this particular research method is useful and informative. After reading the text of this website, we were able to construct our own Latin Square and understood how it would work in our procedure. The second half of the website was dedicated to the relationship between the Latin Square experimental procedure and the analysis of variance statistic. A thorough step-by-step calculation of an example ANOVA was posted on the website to ensure understanding behind the statistic. We were able to document why we chose to use an ANOVA test in our proposal because of the help provided by this website.

McNamara, Carter. ÒDecision Making.Ó 1999.
http://www.managementhelp.org/prsn_prd/decision.htm

Annotation: This website is designed to be a guideline in good decision making techniques for managers and business owners. This source shows some real world examples of when decisions are important to keep a business running and employees productive.

Over, David E. Evolution and the Psychology of Thinking. New York: Psychology
Press. 2003.

Annotation: This source outlines the evolutionary development of social cooperation. It shows how people work together to make decisions which will benefit the individual and the group. This book also demonstrates the process of probability judgment and how it affects decision making.

Pastor, M.A., & Artieda, J. (Eds.). (1996). Time, internal clocks, and movement.
Amsterdam: Elsevier Science B.V.

Annotation: This collective work compiles several psychological studies all dealing the human perception of time. One particular work focused on the possible cognitive explanations for human time estimation and concluded that selective attention is a key component to prospective time estimation. This book was included in our reference section because it directly discussed the background investigation into the psychological processes involved with time estimation. This background will prove to be useful in examining the results of our own time estimation task in our designed procedure.

Pohl, R.F. (2004). Cognitive illusions: A handbook on fallacies and biases in thinking,
judgment, and memory. Hove: Psychology Press.

Annotation: This book is a collective work of several psychological studies focusing on the field of cognitive illusions or reasons why people make inaccurate choices. One study of particular relevance to our experiment was investigating the strength of the anchoring effect. The anchoring effect, which suggests that people base decisions on ÒanchorsÓ or pieces of seemingly relevant information, was found to be especially powerful in creating inaccurate assessments of subjective probabilities. However, we found this article to be extremely informative, since our conditions are testing for the anchoring effect by allowing some groups/individuals to handle additional information before making estimations.

Senders, J.W., & Moray, N.P. (1991). Human error: Cause, prediction, and reduction.
Hillsdale: Lawrence Erlbaum Associates, Inc.

Annotation: The entirety of this book rests on the notion of human error. The authors begin the text by questioning if error is inherent in human nature? If so, what implications can this have on the everyday life of humans? In the section entitled Predicting Probabilities, Senders and Moray attribute errors in probabilities to circadian rhythms, citing that more errors occur in the morning hours as compared to the errors made in the evening hours. The authors also comment on the incredible range of variability in errors of probabilities. We included this work into our reference section, since it dealt with the same basic topics as our experiment, mainly the accuracy of human decisions.

Simon, Herbert A. ÒDecision Making and Problem Solving.Ó 1986.
http://dieoff.org/page163.htm

Annotation: This website outlines the topics of decision making and rationality. It discusses the breakthroughs in cognitive psychology and theories which go along with it. It also discusses limits to rationality and the variance of rational choices.

St. Petersburg paradox. (n.d.). Wikipedia. Retrieved February 17, 2006, from
Answers.com Web site: http://www.answers.com/topic/st-petersburg-paradox

Annotation: This website is solely focused on the St. Petersburg paradox, which was a probability task designed by Daniel Bernoulli in 1738. The paradox questions how much money people would be willing to pay to play a game of chance. Historically, people would not invest enough money to make more than their entry fee; however, the probability work behind the paradox shows that with numerous trials the payoff would compound to infinity. This idea introduces the notion of expected utility, an idea we will be scrutinizing in our experiment.

Student Organization Resources. ÒEffective Group Decision Making.Ó 2003.
http://www.csuchico.edu/sac/leaders/grpdecision.html

Annotation: This website displays different types of group decision making. There are examples of group decisions such as unilateral, majority rule, and otherwise. This website shows the extensiveness of group decision making and how research about it can guide businesses and other aspects of society.

Sunstein, C.R., Kahneman, D., Schkade, D., & Ritov, I. (2002). Predictably incoherent
judgments. Stanford Law Review. 54(6), 1153-1196.

Annotation: This study investigates the decisions made in the legal system and whether they are accurate. The study also investigates the incoherent decisions made in the court system and how they are created. The study used cases of punitive damages and contingent valuation as its foundation for study. This specific article was included in our research because it shows the implications of poor decisions in our legal system.

Please note that all of our previous sources from the project proposal were still utilized in the final write-up. Although we cut the probability tasks from our experiment, all of our sources dealt with human decision making skills, so we wanted to include all of this information into our report.

B. LARGER QUESTION

Our project is structured around discovering the dependency of human beings on sociality. Humans have been the most successful species at establishing a well organized social hierarchy, conducting complex reciprocal altruism and overcoming environmental barriers such as weather and predation (Healy, 2005). All of the previous acts have utilized cooperative decision making for overall benefits to society (Over, 2003). Human success and survival has been driven by the ability to rationalize better in groups whether the decisions are trivial or paramount (Student Organization Resources, 2003). The goal of this project is to display that in application Òtwo heads is better than one.Ó

III. INTERDISCIPLINARY APPROACH

This research project has implications or influences from culture, the social sciences and scientific perspectives. Decision making is dominant in all forms of interactions. Fields which have difficult and profound decisions are economics, international trade, health and medicine, law and politics (Izawa, 1993), (Sunstein et al, 2002). All aspects of culture are influenced by decision making, and sometimes one decision can influence the masses as is such in politics and lawmaking. Furthermore, health and medical professionals must make quick decisions, which can save a life or end in death (Keeney, 1996). In the business field, managers and business owners must make accurate and efficient choices or risk losing money and resources (McNamara, 1999) There are many instances in which humans are faced with extremely important choices, and our study will experiment the accuracy of simple rational decisions to see how some people fare (Kellogg, 1995).

This project will involve the social sciences of cognitive psychology and sociology (Galotti, 1999). We are formatting our experiment around cognitive testing of decision making and rationality. In our project we will utilize the anchor and adjust method and also conduct rational tests which are both methods of cognitive psychological research (Johnson-Laird, 1993). While most cognitive research projects pertain to higher implications of emotions, environment of the subject or other areas, our project deals with the social aspect of decision making. The sociology of our project will be integrated through comparison of group test results and individual test results in order to support our hypothesis that group responses for both decision making and rational tests will be more accurate than individual responses (Franken & Muris, 2005).

IV. SPECIFIC RESEARCH DESIGN

Experimental Design:

Our experimental procedural is twofold: the estimation tasks and the probability tasks. The methodology we will be employing in conducting the four estimation tasks is referred to as the Latin Square method (Latin square analysis of variance). This method provides a within-subject feedback system where each participant will be performing each of the four tasks under a different condition. Likewise, each task will have data scores from all four manipulated subject conditions. Before performing the tasks, each participant will be randomly assigned to one of four arbitrary groups labeled A-D. Each group has a specific designated condition for the four tasks. For example, group A will perform the first task individually with no previous information, the second task in pair with information, the third task in a pair without information, and the final task individually with information. To see the exact condition assignments for each group, please refer to the Latin Square for our experiment, which can be found in Appendix B: Methods Information.

Research Tasks:

Our experiment contains six separate tasks, four using estimation skills and two using probability skills. We believe that utilizing six tasks will be adequate for our experiment because we need four estimation tasks to satisfy our four conditions and two tasks to satisfy our two probability conditions. The specific estimation tasks were chosen based on their relative ease of performance and their familiarity in everyday life, while the probability tasks were chosen from well-known research studies for easy comparison in our discussion. Please refer to Appendix A to view the visual representations of each task.

To ensure complete understanding of our experimental tasks, we will thoroughly explain each task individually making sure to include: an explanation of what the task measures, the correct answer to the task, the process we will utilize to score each performance, and the method by which we will evaluate the accuracy or ÒcorrectnessÓ of the score.

Task 1: Task one is the first of our four estimation tasks. Specifically, this task will be measuring the accuracy of the participantsÕ distance estimations (Andrade, 2004). The task will require the participants to estimate the distance from a marked line on the ground to another tape line. The lines will be placed before experimentation twenty feet away from the line taped on the floor. A participantÕs score on this task will be his/her estimation in feet. From this raw score, we will calculate the individualÕs accuracy score by taking the difference of the expected value (twenty feet in this case) and subtracting his/her score.

Task 2: Task two is our second estimation task. This task judges the accuracy of humans to estimate volume and will entail having the participants pour a designated amount of liquid from one glass into a larger glass. The participants will be instructed to pour a volume of five ounces; therefore, their scores will be the actual volume (in ounces) poured, as measured by the facilitators. Following the procedure in task one, we will define a personÕs accuracy as his/her difference score calculated by subtracting the raw score from the expected score of five ounces.

Task 3: Task three is our third estimation task and tests the participantÕs accuracy in estimating mass. During this task, participants will be directed to lift an object, a baseball bat, and determine its mass in pounds. The participantÕs estimation will be his/her score for the task and will be judged for accuracy by comparing it to the actual mass of one and a half pounds. Using the difference score formula, actual score minus expected score, we will give each participant an accuracy score.

Task 4: Task four concludes the estimation portion of the experiment. This task judges the participantsÕ accuracies in estimating time in seconds (Pastor & Artieda, 1996). The facilitator will instruct the participants to estimate twenty seconds from the designated start command. Using a stopwatch, the facilitator will keep time until the participant says stop. The estimated time by the participant is the raw score for this task and will be judged for accuracy against the expected value of twenty seconds by utilization of the difference formula.

Experimental Conditions:

In our experiment (estimation tasks 1-4), we will be utilizing the application of four general testing conditions. Again, it is important to note that each participant will be completing the four trials under a full rotation of these conditions; therefore, for each participant, we will gather four data points, one under each differing condition. The conditions will be assigned according to the matrix established in the Latin Square by dividing the participants in groups A-D before asking them to perform any estimation tasks. Our first testing condition is referred to as ÒIndividual/No InformationÓ on our Latin Square, so participants will complete the designated task by individually given no previous information. In our second condition, participants will also complete the estimation task individually, but this time they will receive inference information (specific information discussed after all conditions have been stated). The third condition allows participants to answer the questions with a partner given no previous information, while the final task permits the participants to evaluate the estimation task with a partner given a set a previous information before the task.

The second and four estimation conditions utilize the use of outside information and are specified for each task. If the participant is allowed to view information before the completion of task one (distance estimation), he/she will receive a ruler to inspect for twenty seconds before the task. Likewise, if the participant is assigned to see the information before the volume task, he/she will be allowed to hold and inspect a soda can, which holds twelve ounces. The information used before the third task, the mass task, will permit participants to hold a five pound hand weight. Similarly, the participants assigned to view information before the fourth task (time task) will listen to the facilitator read off five seconds from the stopwatch. The information given before each task is constant whether the participant is assigned to perform the task individually or with a partner.

Basic Overview of Trials:

Before beginning with any steps of the procedure, the participants must read and sign an informed consent sheet. Please refer to the Consent Form, which can be viewed in Appendix B: Methods Information. Once the participants have agreed to participate, they will be tested in the following outline of steps.

The first step in our experimental procedure is to assign the participants to an arbitrary group A-D. Because some tasks will require the use of a partner, participants will be assigned initially as pairs. For instance, our first two participants will be assigned to group B. Once individuals have been placed into groups, the data collection process can commence. By referring to the Latin Square design, the two participants will first execute the paired estimation task with a partner given no information. Then, the participants will perform the designated task for partners given information. The participants will split up to individually perform the next two tasks in hopes of keeping their scores independent from one another. One facilitator will test the participant answering the individual task given previous information, while the other participant will complete the individual task given no previous information under the guidance of the second facilitator. When both individuals are finished with their first individual task, they will switch positions to the other facilitator and perform the tasks as mentioned previously. This concludes the estimation task data collection procedure.

Participants will finally be asked a few of the questions from our brief survey, which questions their methods for performing the tasks as well as their comfort and confidence levels between conditions. After the surveys are given orally by the facilitators, the experiment is complete, and the participants are free to leave.

Social Dimension of the Experiment:

Our research conditions for this experiment are testing the significance of socialization in making accurate estimations and probability choices. We are evaluating the choices made in pairs and comparing them to the choices made by the individuals to answer the following question: do humans make better decisions in groups or individually? Ultimately, our project goal is to determine whether social decisions are a natural form of human behavior and if those decisions are ÒbestÓ (Einhorn & Hogarth, 1981). To test the social implications of our experiment, we will be conducting a post experiment survey that allows participants to describe their methods in making decisions (Kanheman & Tversky, 1996), to express their preference in choice situations (partner or individual), and to generate their confidence levels for the decisions they made in both the partner tasks and in the individual tasks. Please refer to our survey below in order to see the full range of questions, which can be found in Appendix B: Methods Information.

V. MATERIALS AND METHODS

Materials Utilized in Research:

For our experiment, each task requires the use of different materials. To set up the first task, we will use tape to create a line on the ground and will use a tape measure to place another tape line twenty feet away from the original line. If participants are given information before the task, they will receive a yardstick to handle. The second task requires the use of a measuring cup, a large pink cup filled with water, and a smaller glass jar. The participant will use the large glass of water to pour our five ounces into the smaller glass, and the facilitators will measure their poured volume with the measuring cup. If participants are granted permission to view information before this task, they will be given a twelve ounce can of soda. The third task will include the use of the baseball bat and a balance to assign the correct mass of the bat before the trials. If participants are permitted to additional information before the mass estimation task, they will be given a five pound weight to hold. The fourth task relies on the use of a stopwatch to measure the participantsÕ time estimations and can also provide selected participants with the five second count-off. The final step in the procedure states that the participants will reflect on their performances by completing a survey orally. Please note that the actual materials needed for the experiment are bolded within their context of the procedure.

Statistics:

After the data completion phase of our experiment, we will rely on statistical computations to make conclusions regarding our hypotheses. More specifically, we will be utilizing JMP, a statistical computer program, to compute the ANOVA scores for our data (Howell, 2004). The ANOVA test, also referred to as the analysis of variance test, compares the means of two or more variables (Latin square analysis of variance). This statistic will allow us to determine if there exist statistical differences between the accuracy of individual decisions and the accuracy of group decisions. Furthermore, the ANOVA test will allow us to determine which of our four conditions resulted in the most accurate decisions.

For this statistic, we will be utilizing the mean ÒdifferenceÓ score, the expected score minus the actual score, to compare the means (see formula below for further explanation). We must use differences scores in comparing the varying tasks because each task has its own scale. The difference scores provide a level comparison ground among all the tasks.

Formula: Xd = Xe - Xa

Data Sheet:

Please refer to our attached data sheet found in Appendix B.

Data Sheet Notation:
Participant Number: the chronological order of participants (Numbers 1-160)
Group: arbitrary group assignment for experiment (Groups A-D)
Score: raw score for each particular task
Diff: the expected score minus the raw score for each particular task
I/G: whether the participant performed the task as an individual or in a group

Time-Line for Research Execution:

March 20, 2006: begin sampling and collecting data
March 20-March 26, 2006: Week 1 of data collection (sample 24 participants)
March 27-April 2, 2006: Week 2 of data collection (sample 24 participants)
April 3-April 9, 2006: Week 3 of data collection (sample 24 participants)
April 10-April 15, 2006: Week 4 of data collection (sample 24 participants)
April 15, 2006: data collection deadline
April 16-18: organizing data and computing statistics
April 18, 2006: completion of all statistics analyses of the data
April 19-21, 2006: compiling the final report, writing the Results and Discussion
April 21, 2006: final project reports due
April 24, 2006: week of project presentations

Standards for Team Work:
Our research team will work closely together throughout the duration of the experiment and will closely follow the time-table generated in the previous section. The actual data collection procedure requires the help of both facilitators to quickly move the participants from one task to another. The facilitators will each direct the successful completion of three tasks for each pair of participants. The facilitator leading the task will be responsible for giving directions and monitoring the task, while the other facilitator will be responsible for collecting the data scores and preparing the set-up for the next task. After the data collection process, both team members will meet over the course of three weeks to organize the data sheets, compute the statistics, and finalize the final report by co-writing the results and discussion sections. As can easily be seen, both partners will be required to perform an equivalent amount of work for this project.

V. Results

One-Way ANOVAs:

Because this project accumulated such a large amount of data, three types of statistical analyses were used: one-way ANOVAS, independent samples t-tests, and correlations. Before expounding on our quantitative results, it is important to note again that we calculated ÒscoresÓ by taking the estimate and subtracting the correct answer. Thus, we utilized difference scores in all of our calculations. Whether or not the estimate was above or below the correct answer was not a concern in our hypotheses, so we used the absolute values of the difference scores in calculating the statistics.
The ANOVA tests were the first statistical tests performed by the statistical software JMP. We performed one ANOVA test for each of the four estimation tasks: distance, volume, mass, and time. For each test, our null hypothesis was that all the groups (A-D) would perform equally across the task. In contrast, our research hypothesis was that at least one of the subject groups was statistically different from the other groups with an alpha level of rejection set at 0.05. A visual representation of the means for each task can be viewed in Figures 5-8 found in Appendix C. The first ANOVA test determined if the mean distance deviations from the correct answer were significantly different amongst the groups. The ANOVA for distance resulted in an insignificant F-value, F(3,92)=0.4602, p=0.7107. Therefore, we could not reject the null hypothesis for this estimation task. All JMP output windows and graphs for the distance ANOVA can be viewed in Figure 9 found in Appendix C. The volume ANOVA test produced similar results with an insignificant F-value, F(3,92)=0.3612, p=0.7812, which is not greater than the 0.05 alpha level necessary for rejecting the null hypothesis. All JMP output for the volume ANOVA can be viewed in Figure 10 found in Appendix C. In contrast to the distance and volume ANOVAs, the mass ANOVA produced a significant F-value, F(3,92)=14.088, p<.0001. We can reject the null hypothesis for this task. The pairwise comparisons for the mass task indicate that Group C (Individual/No Information) did significantly worse than the other three groups in estimating the mass of the bat. All JMP output for the mass ANOVA can be viewed in Figure 11 found in Appendix C. The final ANOVA test resulted in an overall insignificant F-value, F(3,92)=2.3329, p=0.0792. Thus, we cannot reject the null hypothesis for the time task. However, the pairwise comparisons show that group C (Pair/Information) did significantly better than group B (Individual/No Information), p=0.0148. All JMP output for the time task can be viewed in Figure 12 found in Appendix C. In conclusion, the only significant difference amongst group performance was identified in the mass task with the participants working individually with no outside information performing worse than the participants in other group conditions.

Independent Samples T-Tests:

The next set of statistical analyses we performed on our data was a series of independent samples t-tests. The first four t-tests examined the relationship between group size and performance on each task, disregarding whether the participants received the additional information. For these t-tests, our null hypothesis stated that the two group sizesÕ means for each task would be equal; while our research hypothesis stated that the means would be statistically different (indicating that group type does affect the accuracy of the estimations). Both the distance task and volume task produced insignificant results, p=0.8733 and p=0.4526. Moreover, we had to retain the null hypothesis for these tests, which stated that the participants would perform with the same accuracy regardless of whether they were in a pair or participated individually. The other estimation tasks, mass and time, produced significant t-values, which allowed us to reject the null hypothesis for both tasks. In the mass estimation, participants placed with a partner scored significantly higher than participants who worked alone, t(94)=-3.50909, p=0.0009. Likewise, the participants working as a pair for the time task were significantly better at estimating twenty seconds than the individual participants, t(94)=-2.36327, p=0.0202. All JMP output for these four t-tests (including graphs and each pair studentÕs t graph) can be viewed as Figures 13-16 in Appendix C. In short, the independent samples t-tests revealed significant differences between group size and accuracy for the mass and time tests.

Following a similar rationale as the previous tests, our next set of statistical tests used independent samples t-tests to determine the effects of additional information on accuracy in the tasks, disregarding whether the participant was in a pair or working alone. For these four t-tests, our null hypothesis was simply that the means between the two information conditions would be equal for each task; while the research hypothesis was that the two means would be significantly different (indicating that information has an effect on accuracy). The t-test performed on the results of the distance task produced a significant t-value, t(94)=-2.89381, p=0.0047. The participants given the yard stick to help guide their estimations actually performed worse than the participants given no information before estimating. On the other hand, the volume task resulted in insignificant t-value, t(94)=-0.61641, p=0.5392. In this case, receiving the twelve ounce can of pop did not affect the accuracy of the volume estimation. The mass task produced a very significant t-value, t(94)=4.081346, p=0.0001. Those participants given the opportunity to use a five pound hand weight estimated the mass significantly better than the participants who were required to make an estimate without any information. The final t-test for time ended with an insignificant t-value, t(94)=1.134734, p=0.2594. Therefore, whether or not a participant hears the five second count-off previous to estimating had no significant affect on the outcome. All JMP output (including graphs and each pair studentÕs t graphs) can be viewed in Figures 17-20 in Appendix C. In summary, performance on the distance and mass tasks was significantly affected by the use of additional information.

Correlations:

As a final analysis of our results, we decided to see if correlations existed between any pairs of the estimation tasks. More specifically, we wanted to see if doing well on one type of task would be indicative of doing well on another task or if doing well on one type of task was statistically related to doing poorly on a different task. To visualize these relationships, we utilized JMP to produce a Scatterplot Matrix, which compared all the tasks to one another. Unfortunately, only one of the six correlations was significant at an alpha level of 0.05. This significant correlation was between mass and distance, p=0.0042. The negative correlation coefficient of -0.2895 for this relationship implies that performing well on the mass task is correlated to doing poorly on the distance task. All JMP output for the correlation tests can be viewed as Figure 21 in Appendix C. In brief, only one correlation, mass and distance, was found to have significant linear relationship.

Rationalization Behind the Statistics Utilized:

The set-up of our experiment formed an interesting web of data that was relatively difficult to analyze statistically because each data point was under the manipulation of two variables. Therefore, we settled on our three tests: ANOVA, t-tests, and correlations. The ANOVAs were used for each task type in order to see if one condition type was superior to the others in performing the task accurately. The t-tests were used to see if our two variables, group type and access to information, had a significant affect on the accuracy of the resulting estimations for each task type. Finally, we used correlations as a last measure to find relationships between the tasks themselves. We acknowledge that more thorough statistics could have probably been called upon for a greater picture of our data. However, our combined lack of advanced statistical knowledge limited our scope to basic tests we conducted. Overall, we were satisfied with the information we were able to pull from our data and believe it is enough to formulate our conclusions.

Qualitative Results:

As stated in our methods section, we included time during each experimentation round to ask a few of our survey questions to each participant. These questions provided qualitative results that aided in our interdisciplinary approach. We did not seriously analyze these responses because we felt as if we already had enough data and statistics to determine the validity of our hypotheses. We did, however, note some of the participantsÕ responses that could be included in our discussion. For instance, a few participants, who were students from foreign countries, were extremely bewildered by the tasks where they had to estimate in the Standard English measurement system without outside information. Additionally, students, upon learning the answer to the distance task, informed us that they changed their initial estimate because twenty feet was too common of a number. Besides providing feedback on the estimations tasks, the participants also commented on working within a pair. Some of them preferred to work with a partner to check their answer, while other people preferred to work alone if they felt like they were a relatively good estimator. In short, the qualitative results of our experiment were useful in writing the discussion of the report.

V. Discussion and Conclusions

The goals of this research project were to discover if simple estimations made by test subjects were more accurate within groups, and after given additional. We hypothesized that there would be a significant difference between group and individuals responses and furthermore group responses would be more accurate. We also hypothesized that responses that followed additional information being given would be significantly different and more accurate than responses with no additional information. Both hypotheses were not fully supported through analysis of our data, but some of the individual Latin square groups and estimation tasks showed results that supported our hypotheses.

We analyzed additional information versus no information, and group versus individual responses separate from one another. In the analysis of the effects of additional information being given to the subjects we found that there was not a significant difference between the categories of additional information and no information in the results of the volume and time tasks. In the distance task a significant difference was noted between the categories, but no information was more accurate than additional information, which does not support our hypothesis. In mass though, these was a significant difference and the subjects given additional information were more accurate than those without information, supporting our hypothesis. Overall our hypothesis that additional information would improve the accuracy of the results was not supported by three of the four tasks, with the exception of mass which is the only task which supported this hypothesis.

When we analyzed the data for group versus individual responses we found that the distance, volume, and mass tasks produced results which were not significantly different between the two categories. Time, on the other hand, did show a significant difference between group and individual responses and the group responses were more accurate. Therefore, data from three of the four tasks did not support this hypothesis, while the results from the time task did support our hypothesis. ItÕs also notable that the only task which displayed any significant difference between the categories also showed results in which group responses were more accurate than individual responses.

After analyzing the individual hypothesis for differences between groups and individuals, and additional information and no information we compared the accuracies of the Latin square groups (A, B, C, D) within each task. For the distance and volume tasks, across all four groups there was not a significant difference. These results express that for distance and volume, it was not important whether the subjects received additional information or were in a group. The time task did not show a significant difference between all groups also. However, there was a significant difference between the groups B and C. Moreover, group C was more accurate than group B. The B group was testing of individuals with no information, while the C group was paired with information. The C group was also the most accurate between all four groups these results partially supports both of our hypotheses. Lastly, there was a significant difference across the groups of the mass task. Group C did the worst, while the other three groups did significantly better. Group C involved individuals with no additional information. The other three groups had either additional information or group settings in them. As a result, the statistical findings from the mass task best support both of our hypotheses.

A possible reason we could not find significantly different statistics for most of our tasks is due to the complicated nature of our statistics. Each task had different numerical results and their accuracy could not be statistically compared. We could only conduct t-tests and ANOVAÕs to compare the individual tasks against themselves because of the diversity of our statistics. Therefore, the total difference and accuracy between all four of the tasks could not be conducted for either of our hypotheses. We would have had to attain much more data for each task, and possibly involve multiple assignments within each task, as other psychological studies have done. Brewer and Hewstone in their research on social cognition utilize massive amounts of data from group subjects (Brewer, M.B., & Hewstone, M., 2004). Although we found some differences in our data which supported our hypotheses, they were not all encompassing and did not affect the total data from each task enough to be significantly supportive. If we had a larger sample size, these differences would have either been subdued or notably significant and our results would have been more conclusive.

Our research utilized many techniques which have been applied in other studies on cognitive psychology and decision making. The additional information we gave to subjects paralleled the usage of frames of references and anchor and adjust methods included in studies done by Alice Healy (Healy, Alice F., 2005). Healy also applies her studies to higher social issues which we have done in our study with the predictions of group dependency in decision making. Additionally, the social cognition aspects of our study have been examined by various psychologists such as Herbert Simon (Simon, Herbert 1986).

There are several alterations which may improve the quality of this research. Being able to convert metric distances into the English measurement system would have been quite helpful. If we attained more subjects, we could have broadened the size of the groups. We considered a ÒgroupÓ as two people, and if we had more people it would be significantly more representative of actual group decisions. A better study would also involve multiple tasks for each estimation type. Finally, additional research could utilize misleading information in an anchor and adjust setting instead of frames of references.

VIII. Literature Cited

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Brewer, M.B., & Hewstone, M. (Eds.). (2004). Social cognition. Malden: Blackwell
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Franken, I. & Muris, P. (2005). Individual differences in decision-making. Personality & Individual Differences. 39(5), 991-998.