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