Numerosity and tangibility in investment decisions

Last registered on March 30, 2023


Trial Information

General Information

Numerosity and tangibility in investment decisions
Initial registration date
March 29, 2023

Initial registration date is when the trial was registered.

It corresponds to when the registration was submitted to the Registry to be reviewed for publication.

First published
March 30, 2023, 4:03 PM EDT

First published corresponds to when the trial was first made public on the Registry after being reviewed.


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Primary Investigator

University of Portsmouth

Other Primary Investigator(s)

PI Affiliation
University of Portsmouth
PI Affiliation
Radboud University

Additional Trial Information

In development
Start date
End date
Secondary IDs
Prior work
This trial does not extend or rely on any prior RCTs.
Using experimental finance methodology, we simulate financial decision making under risk in the form of investment tasks. Experimental Currency Units aim to make the situation more realistic. The ECU frame, however, is often arbitrarily chosen. In particular, when tangibility or numerosity - individuals tend to over-infer quantity when it is represented with higher numeric values - has an effect on risk decision making. Do higher ECU frames bias decision making in financial risk-taking tasks? This study aims to test whether the ECU frame - affects financial decision making under risk. Our result will refine experimental finance methodology.
External Link(s)

Registration Citation

Füllbrunn, Sascha, Wolfgang Luhan and Paul-Emile Mangin. 2023. "Numerosity and tangibility in investment decisions." AEA RCT Registry. March 30.
Sponsors & Partners


Experimental Details


We will recruit participants from Prolific. They will participate in an online experiment that collects all independent as well as the dependent measures, i.e. participants’ decisions in 5 experimental conditions (between-subjects design).
Intervention Start Date
Intervention End Date

Primary Outcomes

Primary Outcomes (end points)
1) Research question

How does the ECU framework affect risk taking in financial investment decisions?

With the ECU framework being defined as the exchange rate between Experimental Currency Units used during the experiment and actual currency used for payment.

2) Dependant variables

We first assess the participants' risk perception by presenting them a lottery and asking them to assess how risky they perceive this lottery with a Likert scale.

Then, in two investment tasks, the participants receive and ECU amount to invest.

In task 1, the participants receive an ECU endowment and invest five times in a simple two-outcome lottery (Gneezy and Potters, 1997). The dependent variable is the fraction invested - a measure of risk taking: f = Investment / Endowment. The higher the fraction invested, the higher the risk taken.

In task 2, the participants receive an ECU endowment and invest five times in a three lotteries portfolio decision. The dependent variables form different perspectives on the expected return (r) and the standard deviation (s) of the portfolio. On one hand we consider risk taking as measured by the sharp ratio and the standard deviation. On the other hand, we consider the deviation from the efficiency frontier.

3) Independent variables

Participants appointed to the following treatments receive the corresponding endowment:
o t0: 200 p (1 penny decision level)
o t1: 200 tokens (1 token decision level)
o t2: T1 x 10 = 2,000 tokens (10 token decision level)
o t3: T1 x 10^2 = 20,000 tokens (100 token decision level)
o t4: T1 x 10^3 = 200,000 tokens (1,000 token decision level)

4) Control variables

- Age
- Disposable income
- Gender
- Field of study
- Financial proficiency

5) Testable hypotheses

A) Tangibility: Participants have higher risk aversion with £ than with ECU, so they invest less in to than t1 (for both games).

B) Numerosity : Higher amounts increase numerosity which means that people become more uncertain dealing with higher amounts. Hence, we expect a reduction of participants' precision in all tasks (measured in standard deviation).

C) Non-constant relative risk aversion: Higher amounts induce participants to be more risk averse (Fehr-Duda et al., 2010). Hence, we expect a reduction in risk taking in all tasks when ECU frame increase.

D) Game-board effect: Extreme high amounts reduce understanding and value granted to ECUs by participants (Davis & Holt, 1993), we thus expect less risk aversion and higher standard deviation in the decisions they take.
Primary Outcomes (explanation)
1) Literature

A brief literature review on the topic of ECU effects in experiments can be found in Voslinsky & Azar (2021).

The first mention of the ECU methodology issue appears in (Davis & Holt, 1993). They present their point of view of the different advantages and drawbacks of using ECU without testing them as follow:

- Expected advantages
• Finer grid that matches better continuous models
• Possibility to vary conversion rates amongst participants
• Intercountry comparability
• Money illusion

- Expected drawbacks
• “Game-board effect”: artificial sense of speculative competitiveness

Because this last drawback, Davis and Holt advise to use experimental currencies only in cases where there are deemed necessary.
There has been only one study that experimentally compares the use ECU and actual currencies in the lab, and they strictly focus on second-price auctions (Drichoutis et al., 2015). No effect has been found in this particular article

2) Theoretical environment and predictions

Our research focuses on participants’ attitude towards risk when confronted to real money or ECU frames. We aim at investigating this phenomenon more in depth in the context of ECUs and aggregating the following existing theories:

- The tangibility effect: the fact that using actual cash versus displaying amounts on computers or forms in the lab changes participants’ behaviour. This effect is first showed by Reinstein & Riener (2012), who found that participants are less generous when using cash than when paid via a computer. In our context, using ECUs brings more distance between the participant and its payoff, causing lower risk aversion.

- The numerosity effect: the fact that face value induces a confusion regarding the perceived actual value of a good. Numerosity perception is the elementary numerical ability in both humans and animals, representing nonverbal information of quantity without counting (Dehaene & Changeux, 1993; Feigenson, Dehaene & Spelke, 2004). This phenomenon has been identified in economics (Fehr & Tyran, 2007; Shafir et al., 1997; Shrivastava et al., 2017) and psychology (Bagchi & Davis, 2016), then extended to consumer behaviour research (Wertenbroch et al., 2007). In the case of ECUs, this theory implies that if participants play with high quantity of ECUs, their perception of actual value may be biased, causing more confusion and thus more variability in the data.

- On high ECU frames, we also follow the findings of Fehr-Duda et al. (2010) where relative risk aversion is not constant but increases with stake size. We thus expect risk aversion to increase with exchange rate.

- The “game-board” effect: proposed by Davis and Holt (1993), they argue that tokens may be less considered by participants than actual money, especially at very high amounts, and thus taken less seriously. Participants’ value perception is thus to be biased downwards, causing decreasing risk aversion and higher variance.

We expect these effects to be true at different stages of the experiments. If using pennies instead of ECUs, the tangibility would prevail and participants would get higher utility from actual money than ECUs, thus taking more serious decisions with actual money rather than ECUs. With ECUs, at intermediate exchange rate, non-constant relative risk aversion is expected to be stronger, as “face value” of the ECUs would bias participants’ perception upwards, bringing them to obtain more utility from tokens at constant actual value. Finally, at very high exchange rates, we expect Davis and Holt (1993) “game-board” theory to be stronger, subjects would then give less value to ECUs, considering them as petty money.

We assume that if participants receiving more utility from a form of currency would pay more attention to the games, play more seriously and thus achieve results closer to the economic optimum. This would also be measured by comparing variances between treatments.

3) Project academic and societal contribution

Academically, the project aims to compensate the current lack of knowledge concerning the use of experimental currency units and how these are perceived by the participants. Such an addition to the literature may provide more tools and better understanding to the experimentalists who use ECUs.
The societal contributions of this work could be first to isolate bias in risk decision-making when individuals take risky decisions with big numbers. We have identified that this contribution can be helpful in the fields of foreign exchange trading and gambling addiction prevention (Palmer et al., 2022).
A better understanding of numerosity could also change the choice architecture in currency trading.

4) References

Albert, S., & Duffy, J. (2012). Differences in Risk Aversion between Young and Older Adults. Neuroscience and Neuroeconomics, 1, 1–7.
Bagchi, R., & Davis, D. F. (2016). The role of numerosity in judgments and decision-making. Current Opinion in Psychology, 10, 89–93.
Borghans, L., Golsteyn, B. H. H., Heckman, J. J., & Meijers, H. (2009). Gender differences in risk aversion and ambiguity aversion. Journal of the European Economic Association, 7(2–3), 649–658.
Charness, G., Gneezy, U., & Halladay, B. (2016). Experimental methods: Pay one or pay all. Journal of Economic Behavior and Organization, 131, 141–150.
Davis, D., & Holt, C. A. (1993). Experimental economics. In Princeton university press.
Dehaene, S., & Changeux, J. P. (1993). Development of elementary numerical abilities: A neuronal model. Journal of Cognitive Neuroscience, 5(4), 390–407.
Erdfelder, E., FAul, F., Buchner, A., & Lang, A. G. (2009). Statistical power analyses using G*Power 3.1: Tests for correlation and regression analyses. Behavior Research Methods, 41(4), 1149–1160.
Fehr-Duda, H., Bruhin, A., Epper, T., & Schubert, R. (2010). Rationality on the rise : Why relative risk aversion increases with stake size. Journal of Risk and Uncertainty, 40, 147–180.
Fehr, E., & Tyran, J. R. (2007). Money illusion and coordination failure. Games and Economic Behavior, 58(2), 246–268.
Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8(7), 307–314.
Füllbrunn, S., & Luhan, W. (2020). Responsibility and limited liability in decision making for others – An experimental consideration. Journal of Economic Psychology, 77.
Gneezy, U., & Potters, J. (1997). An experiment on risk taking and evaluation periods. Quarterly Journal of Economics, 112(2), 631–645.
Hartog, J., Ferrer-i-Carbonell, A., & Jonker, N. (2002). Linking measured risk aversion to individual characteristics. Kyklos, 55(1), 3–26.
Kroll, Y., Levy, H., & Rapoport, A. (1988). Experimental tests of the mean-variance model for portfolio selection. Organizational Behavior and Human Decision Processes, 42(3), 388–410.
Palmer, L., Cringle, N., & Clark, L. (2022). A scoping review of experimental manipulations examining the impact of monetary format on gambling behaviour. International Gambling Studies, 1–23.
Reinstein, D., & Riener, G. (2012). Decomposing desert and tangibility effects in a charitable giving experiment. Experimental Economics, 229–240.
Rieger, M. O., Wang, M., & Hens, T. (2015). Risk preferences around the world. Management Science, 61(3), 637–648.
Shafir, E., Diamond, P., & Tversky, A. (1997). Money illusion. Quarterly Journal of Economics, CXII(2), 341–374.
Shrivastava, S., Jain, G., Nayakankuppam, D., Gaeth, G. J., & Levin, I. P. (2017). Numerosity and allocation behavior: Insights using the dictator game. Judgment and Decision Making, 12(6), 527–536.
Voslinsky, A., & Azar, O. H. (2021). Incentives in experimental economics. Journal of Behavioral and Experimental Economics , 93(March), 101706.
Wertenbroch, K., Soman, D., & Chattopadhyay, A. (2007). On the perceived value of money: The reference dependence of currency numerosity effects. Journal of Consumer Research, 34(1), 1–10.

Secondary Outcomes

Secondary Outcomes (end points)
Following the literature, we expect:
- Risk aversion to be higher for female participants (Borghans et al., 2009),
- Risk aversion to increase with participants’ age (Albert & Duffy, 2012),
- Risk aversion to increase with disposable income (Hartog et al., 2002),
- Country of birth: we expect subjects from countries with more individualistic cultures to be more risk averse (Rieger et al., 2015),
- Variance to increase for non-native English speakers (as understanding of the instructions may decrease),
- Variance to increase for people studying non-economic topics.
Secondary Outcomes (explanation)

Experimental Design

Experimental Design
Design description

Participants will be recruited via Prolific. We may also recruit participants from Portsmouth University and Radboud University subject pools (except for members of the Faculty of Business and Law), or MTurk to verify the validity of our findings for different types of crowds. We will use the software Qualtrics to code the experiment.

Step 1: Presentation of consent form. Participants refusing to sign will stop the experiment at this stage, and be paid the show-up fee.

Step 2: Randomization into treatments (see treatments detail below) when sending the session link to participants. Each session corresponds to a treatment, following a between subject approach.

Step 3: General instructions and payment information. Details are given on experiments duration, payment procedures and anonymity.

Step 4: Control task to determine participants' risk perception.

Step 5: Treatment instructions. Participants are presented the instructions for the respective treatment that they were randomly allocated into.
- Game 1: simple Investment game
- Game 2: portfolio building game

Step 6: Demographic questionnaire
Experimental Design Details
Not available
Randomization Method
All participants take part in the same Qualtrics survey. The survey randomly allocates treatments to the participants keeping the observations per treatment at the same size.
Randomization Unit
Was the treatment clustered?

Experiment Characteristics

Sample size: planned number of clusters
Sample size: planned number of observations
500 participants in total.
Sample size (or number of clusters) by treatment arms
100 participants per treatment.
Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
Stat test: Mann-Whitney Number of tails: 2 α: 0.05 1-β: 0.80 d: 0.5 Participants per treatment: 67 Total required number of participants: 335 Following the hypothesis of an inverted u-shape utility curve for tokens, two-tails analysis is necessary. We picked d=0.5 for detection of medium effects, following existing experiments on investment games (Füllbrunn & Luhan, 2020). This power calculation has been computed with the software G*Power (Erdfelder et al., 2009). According to this figure, we will need 67 participants per treatment, with one baseline and 4 treatments, that makes a total of 335 participants. We decided to plan for a margin in order to still have enough observations in the case participants fail attention check. So, we increased our total number of observations to 500.

Institutional Review Boards (IRBs)

IRB Name
IRB Approval Date
IRB Approval Number
Analysis Plan

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