Risk Inclination Model ‐ A model for creating an ‘Ideal Scale’ of Measurement Brady Michael Jack, Ph.D. Center for General Education  National Sun Yat-sen University

Risk Inclination Model What is Risk Inclination? Risk inclination is a mental disposition toward an eventuality that has consequences. feelings of rightness toward knowledge correctness with the possibility of a negative or positive outcome Decision making with the possibility of a negative or positive outcome is viewed as “risk taking” (Slovic, 1964)

Risk Inclination Model CW Risk Inclination Model Confidence Weighting (CW) is used to measure feelings of rightness and risk taking towards the correctness of a test answer selection. 15 points 10 points 5 points Who was the 1st president of the US? Washington (2) Adams (1) (3) Van Buren (4) 15 points

Risk Inclination Model CW RC Risk Inclination Model Measuring students’ confidence towards risk taking on an objective test is done within a restricted context (RC). 10 Center of Mass RC = Total Point Value (TPV) 100 a test item test center

Risk Inclination Model CW RC Risk Inclination Model IF the sum of CWs does NOT equal the TPV, the TPV requirement is violated. 10 15 Center of Mass risk TPV= 100

Risk Inclination Model CW RC Risk Inclination Model Accommodation must take place among CWs in order to satisfy the TPV requirement. 5 10 15 risk Center of Mass TPV= 100

Risk Inclination Model CW RC Risk Inclination Model When accommodation takes place, the COM must also shift toward risk in order for balance to be achieved in the system. risk Low 5 10 15 Center of Mass (COM) TPV= 100 Inclination

Risk Inclination Model CW RC Risk Inclination Model Using Varignon’s Theorem of 1st factorial moments of probability, inclination can be tracked. RIS

Risk Inclination Model CW RC Risk Inclination Model Tracking inclination toward risk .00 where I is inclination; W0 is middle confidence weight; Wi is student’s confidence weight; TPV is total point value of test. Distributed weighted values: 10, 10, 10, 10, 10, 10, 10, 10, 10, 10 (W0 10 – Wi 10) * 1 = 0 (W0 10 – Wi 10) * 6 = 0 (W0 10 – Wi 10) * 2 = 0 (W0 10 – Wi 10) * 7 = 0 (W0 10 – Wi 10) * 3 = 0 (W0 10 – Wi 10) * 8 = 0 (W0 10 – Wi 10) * 4 = 0 (W0 10 – Wi 10) * 9 = 0 (W0 10 – Wi 10) * 5 = 0 (W0 10 – Wi 10) *10 = 0 I = 0/100; I = 0

Risk Inclination Model CW RC Risk Inclination Model Tracking inclination toward risk .00 where I is inclination; W0 is middle weight; Wi is position of value; TPV is total point value of test. .45 .80 I = 45/100; I = 0.45 1.05 I = 80/100; I = 0.80 I = 105/100; I = 1.05 1.20 I = 120/100; I = 1.20 1.25 I = 125/100; I = 1.25

Risk Inclination (RI) Model CW RC RIS Risk Inclination (RI) Model Creating a RI Scale (RIS) from 0 to 1 I /Imax Inclination Scale RIS .00 .45 .80 1.05 1.20 1.25 .00/1.25 = .00 .45/1.25 = .36 .80/1.25 = .64 1.05/1.25 = .84 1.20/1.25 = .96 1.25/1.25 = 1.00

Risk Inclination (RI) Model CW RC RIS Risk Inclination (RI) Model Thorndike’s (1920) Requirements for an Ideal Scale of measure .00 .36 .64 .84 .96 1.00 RIS Each fact on the scale must be perfectly definable; Each fact must be unique; The distance between each fact must be defined; There must be an absolute point of zero on the scale.

Risk Inclination (RI) Model CW RC RIS Risk Inclination (RI) Model Risk Inclination Scale (RIS)satisfying Thorndike’s requirements. .00 .36 .64 .84 .96 1.00 RIS Each risk inclination score is perfectly definable; Each risk inclination score represents a unique degree of inclination toward risk; The distance between each risk inclination score is mathematically calculated as RIS = I / Imax; Risk inclination scale has an absolute point of zero.

Risk Inclination (RI) Model CW RC RIS Risk Inclination (RI) Model Applications of RIS on objective tests Measure students’ risk taking toward knowledge accuracy between 0 and 1; Measure gender differences in risk taking toward knowledge accuracy between 0 and 1; Risk Inclination Statistic generalizable and can be used with different CWs and TPVs. .00 .36 .64 .84 .96 1.00 RIS Jack, B. M., Liu, C. J., Chiu, H. L., & Tsai, C. W. (2012). Measuring the Confidence of 8th Grade Taiwanese Students' Knowledge of Acids and Bases. International Journal of Science and Mathematics Education, 10, 889-905. Jack, B. M., Hung, K. M., Liu, C. J., & Chiu, H. L. (2009, April 13-17). Utilitarian Model of Confidence Testing for Knowledge-based Societies. Paper presented at the American Education Research Association (AERA), San Diego, CA. Jack, B. M., Liu, C. J., Chiu, H. L., & Shymansky, J. A. (2009, April 13-17). Confidence Testing for Knowledge-based Global Communities. Paper presented at the American Education Research Association (AERA), San Diego, CA.

RI CW RC RIS Risk Inclination Model ‐ A model for creating an ‘Ideal Scale’ of Measurement Thank you. Brady Michael Jack, Ph.D. Center for General Education  National Sun Yat-sen University