1. 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

2. 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)

3. Risk Inclination ModelCW
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

4. Risk Inclination ModelCW 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

5. Risk Inclination ModelCW 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

6. Risk Inclination ModelCW 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

7. Risk Inclination ModelCW 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

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

9. Risk Inclination ModelCW 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

10. Risk Inclination ModelCW 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

11. Risk Inclination (RI) ModelCW 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

12. Risk Inclination (RI) ModelCW 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.

13. Risk Inclination (RI) ModelCW 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.

14. Risk Inclination (RI) ModelCW 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 th Grade Taiwanese Students' Knowledge of Acids and Bases. International
Journal of Science and Mathematics Education, 10,
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.

15. 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