risk inclination model ‐ a model for creating an ‘ideal scale’ of measurement
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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. RI. What is Risk Inclination?. - PowerPoint PPT PresentationTRANSCRIPT
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 ModelWhat is Risk Inclination?
feelings of rightness toward knowledge correctness with the possibility of a negative or
positive outcome
Risk inclination is a mental disposition toward an eventuality that has consequences.
Decision making with the possibility of a negative or positive outcome is viewed as “risk taking” (Slovic, 1964)
RI
Risk Inclination ModelConfidence Weighting (CW)
15 points
10 points
5 points
Who was the 1st president of the US?
Washington(2)
Adams(1)
Adams(3)
Van Buren(4) 15points
is used to measure feelings of rightness and risk taking towards the correctness of a test answer selection.
RICW
RICW
RCRisk Inclination Model
10101010101010101010
Center of Mass
a test item test center
RC = Total Point Value (TPV) 100
Measuring students’ confidence towards risk taking on an objective test is done within a restricted context (RC).
Risk Inclination Model
10101010101010101015
Center of Mass
risk
TPV= 100
IF the sum of CWs does NOT equal the TPV, the TPV requirement is violated.
RICW
RC
Risk Inclination Model
5101010101010101015
risk
Center of MassTPV= 100
Accommodation must take place among CWs in order to satisfy the TPV requirement.
RICW
RC
Risk Inclination Model
Center of Mass (COM)
5101010101010101015risk
InclinationTPV= 100
When accommodation takes place, the COM must also shift toward risk in order for balance to be achieved in the system.
Low
RICW
RC
Risk Inclination Model RICW
RC
Using Varignon’s Theorem of 1st factorial moments of probability, inclination can be tracked.
RIS
Risk Inclination Model
.00TPViWWI i
n
i
/*)(1
0
Distributed weighted values: 10, 10, 10, 10, 10, 10, 10, 10, 10, 10
(W0 10 – Wi 10) * 1 = 0(W0 10 – Wi 10) * 2 = 0(W0 10 – Wi 10) * 3 = 0(W0 10 – Wi 10) * 4 = 0(W0 10 – Wi 10) * 5 = 0
(W0 10 – Wi 10) * 6 = 0(W0 10 – Wi 10) * 7 = 0(W0 10 – Wi 10) * 8 = 0(W0 10 – Wi 10) * 9 = 0(W0 10 – Wi 10) *10 = 0
I = 0/100; I = 0
where I is inclination;W0 is middle confidence weight;
Wi is student’s confidence weight;
TPV is total point value of test.
RICW
RC
Tracking inclination toward risk
Risk Inclination Model
.00TPViWWI i
n
i
/*)(1
0
where I is inclination;W0 is middle weight;
Wi is position of value;
TPV is total point value of test.
I = 45/100; I = 0.45
.45
I = 80/100; I = 0.80
.80
I = 105/100; I = 1.05
1.05
I = 120/100; I = 1.201.20
I = 125/100; I = 1.25 1.25
RICW
RC
Tracking inclination toward risk
Risk Inclination (RI) Model
.00
.45
.80
1.05
1.20
1.25
Inclination Scale .00/1.25 =
.45/1.25 =
.80/1.25 =
1.05/1.25 =
1.20/1.25 =
1.25/1.25 =
I /Imax
.00
.36
.64
.84
.96
1.00
RIS
RICW
RC
RISCreating a RI Scale (RIS) from 0 to 1
Risk Inclination (RI) ModelThorndike’s (1920) Requirements for an Ideal Scale of measure• 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.
.00
.36
.64
.84
.96
1.00
RIS
RICW
RC
RIS
Risk Inclination (RI) ModelRisk Inclination Scale (RIS)satisfying Thorndike’s requirements.• 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.
RICW
RC
RIS
.00
.36
.64
.84
.96
1.00
RIS
Risk Inclination (RI) ModelApplications of RIS on objective tests
1. Measure students’ risk taking toward knowledge accuracy between 0 and 1;
2. Measure gender differences in risk taking toward knowledge accuracy between 0 and 1;
3. Risk Inclination Statistic generalizable and can be used with different CWs and TPVs.
RICW
RC
RIS
.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.
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
Thank you.
RICW
RC
RIS