This document summarizes a study examining the relationship between reaction times (RTs) and general cognitive ability (g) using a number comparison task. The study administered the task to two groups of participants with different average g levels. Results confirmed that the higher-g group had faster RTs compared to the moderate-g group. Both groups responded more slowly when numbers were closer together. The diffusion model provided a good fit to the data and supported previous findings of a negative correlation between RTs and g on simple tasks.

1. Relationship between
Reaction Times and General
Cognitive Ability:
——APPLICATION OF THE DIFFUSION MODEL IN NUMBER-COMPARISON TASKS
LEI SHI
UNIVERSITY OF MINNESOTA

2. Outline
 Senior project
 Data analysis
 Discussion

3. Senior project
• BACKGROUND: ABSTRACT,
INTRODUCTION
• EXPERIMENT: CURRENT
STUDY, METHOD, DESIGN
• RESULTS AND CONCLUSION

4. Abstract
 Previous research supports a negative correlation between reaction times (RTs) and the
general cognitive ability (g) on simple laboratory tasks. However, the mechanism of the
correlation remains unclear.
 Ratcliff’s diffusion model and Lee and Chabris’s discovery shed light on understanding
such relationship.
 Current study expands upon previous research on the relationship between g and RTs
by using a larger sample size and administers a number-comparison task to two
groups of participants with different average levels of g .
 The results confirm that the higher-g group achieves faster reaction times compared to
the moderate-g group, and participants in both groups respond more slowly when
stimuli were close to each other.

5. Introduction
 The g-RTs relationship has raised researchers’ interest examining the mechanism
behind this association and creating models to predict the rapid two-choice
decision process.
 However, previous models do not estimate the reaction data accurately and the
mechanism of g-RTs correlation is unclear
 Ratcliff’s diffusion model provides us a comprehensive theoretical explanation of
the mechanism of g-RTs relationship

6. Diffusion model
 The diffusion model assumes that a decision is
made by a random noisy process and
individuals accumulate information from the
starting point (z) to the response boundaries
(a and zero).
 The process of information accumulation
fluctuates before reaching the boundary.
 The decision process is terminated and the
corresponding action is initiated when either
boundary is reached.

7. Components of the diffusion model
 starting point or bias (z): a different amount of information is required before
alternative responses are executed
 threshold separation (a): the distance between the starting point and the point
that the decision is finished
 mean non-decision component (Terr): the combination of the encoding processing
duration and the motor processing duration
 drift rate (v): the rate of accumulation of information, and it depends on the
difficulty of the tasks, the variety of the drift rate and the variety of the starting
point

8. g-RTs Relationship
 Research has shown that relationship between IQ and median RTs is negatively
correlated
 Reaction times increased if stimuli (i.e. two numbers) were close together
 individuals with higher IQ responded faster than individuals with lower IQ in two-
stimulus tasks

9. Current Study Method
 Include standard IQ tests
 Expand sample size
 Control age groups
 Participants
 18-24 years old
 Normal vision
 Native speaker
 High-g group: ACT ≥ 30 or SAT ≥ 1340
 Moderate-g group: ACT ≤25 or SAT ≤ 1140
 Expected sample size: 200

10. Design
 Use Psychopy to conduct the experiment
 Control: room environment, the brightness, the frequency and the position of the
computer monitor
 Experiment content:
 number-comparison test (number from 31-79)
 three psychometric tests (IQ tests)
 Demographic survey

11. Results
• The high-g group achieves higher
IQ scores than the moderate-g
group.
• Mean RTs and the diffusion rate is
faster in the high-g group than in
the moderate-g group.
• The difference of mean RTs
becomes larger when the distance
between the stimulus and the
reference is closer.
Green: high-g group
Blue: moderate-g group
Moderate-g group IQ scores vs. High-g group IQ scores

12. Conclusion
 SAT/ACT score is an excellent measurement for individuals’ IQ
 Individuals with higher g would achieve faster reaction times compared to
individuals with lower g
 The residual time in the high-g group is faster than the residual time in the
moderate-g group
 The diffusion rate of the high-g group is slightly higher than the moderate-g
group
 The diffusion model fits the data very well.

13. Data Analysis
• CHECK NORMALITY
• BUILD MODELS
• TEST MODELS
• FITTING MODELS

14. Data Analysis
 Use R
 Nine groups of data are excluded
 Three parameters are applied in the analysis
 Parameters Estimation (EZ2 package)
 146 subjects in total (94 individuals with high g and 52 individuals with moderate
g)

15. Data Analysis (continued)
 Check normality (Shapiro Wilk normality test)
 p-value < 2.2*10-16
 the distribution approximates to a normal distribution

16. IQ tests
 Two sample t-test
 Total Score = 3* Rapm+1*DAT Space +4*Wordsum
Test p-value
RAPM 2.19*10-6
DAT Space
1.039*10-5
Wordsum
5.973*10-7
Total
1.078*10-9
Table 1. The significance between groups in psychometric
tests.
Moderate-g group IQ scores vs. High-g group IQ scores

17. IQ tests (continued)
 The linear discriminant
 New model:
 LDscore=0.19503*Rapm+0.808*DATSpace+0.
445*Wordsum
 Confirm the previous results
Group means
Rapm DAT space WordSum
Moderate-g
group
8.442 27.923 6.1346
High-g group
10.935 31.720 7.323
Coefficients of linear discriminants
Rapm DAT space WordSum
Linear
discriminants
0.194 0.0845 0.420

18. Reaction Time
 Mixed Linear Regression
 Rt= G+D+ (1|ID)
 G:participants from high-g or moderate-g group
 D: the distance between the number on the screen and the reference number (55).
 Both G and D are fixed effects and ID (i.e. participants’ id code) is the random effect
 correlation between G and D is zero (no interaction)

19. Reaction Time (continued)
 we expect to see that there is a large gap in RTs between 49 and 50, and a large
gap in RTs between 59 and 60. The difference is expected to be similar in the
high-g group and the moderate-g group.
Distance
Numbers
High-g
(millisecond)
Moderate-g
(millisecond)
49 to 50 37.408 40.670
59 to 60 39.801 58.443

20. Fitting the Model
The Comparison between Actual RTs Quantiles and Corresponding Estimated Quantiles
1st Quantile 3rd Quantile 5th Quantile 7th Quantile 9th Quantile
Actual
Quantiles
386.460 421.321 451.601 488.129 560.264
Estimated
Quantiles
400 423 447 479 549
Table 3. The comparison of the moderate-g group between actual quantiles and corresponding estimated
quantiles in the diffusion model from number 31 to 34 and from number 76 to 79.

21. Discussion • EZ MODEL
• LBA

22. LBA & EZ model
EZ model Diffusion Model LBA
Simplified version of the
diffusion model
Simplified version of the
LCA
stochastic stochastic Linear
3 parameters 5 + 2 parameters
Smaller sample size
Simpler
no additional parameters
Comprehensive
Only two-choice tasks
Comprehensive
Simpler
infinite number of
alternative responses
incomplete Inapplicable in some
common paradigms

23. Summary
 Either model might be considered as successful as well established models only if
it
 satisfies the basic features of the decision processing,
 predicts important phenomenon in binary tasks and
 fits a wide range of behavior data under experimental paradigms

24. “
”
All models are wrong, but some are
useful.
--GEORGE BOX (1979)