1) Have any data been collected for this study already?

No, no data have been collected for this study yet.

2) What's the main question being asked or hypothesis being tested in this study?

The influence of the probability of an outcome in a risky prospect upon the preference for the prospect (formalised as the decision weighting function in e.g. Prospect Theory) is less linear for decisions involving affect-rich outcomes than it is for decisions that involve affect-poor outcomes. Thus the tendency to overweight low probability outcomes (showing high sensitivity to small deviations from certainty) is larger for affect-rich outcomes than for affect-poor outcomes. Correspondingly, the tendency to be relatively insensitive to differences between two degrees of uncertainty is larger for high-affect than it is for low affect outcomes.

3) Describe the key dependent variable(s) specifying how they will be measured.

Our investigation has 4 experiments, each involving a single affect-rich outcome, and a single affect-poor outcome.

Each experiment has 2 versions, in one version the dependent variable is choice, and in the other version the dependent variable is valuation.

In choice experiments, participants choose between a risky option with the affect-rich outcome, and a risky option with the affect-poor outcome. In valuation, participants price these risky options using a willingness-to-pay procedure.

4) How many and which conditions will participants be assigned to?

For each choice experiment, participants are assigned between-subjects to one of two probability conditions (5% vs. 95%).

Each participant participates in two of the valuation experiments (one of two experiments having positive outcomes; and one of two experiments having negative outcomes).

For each valuation experiment, we manipulate:

The affective content of the outcome (within-subjects, two conditions: affect rich vs affect poor)

The probability level for the outcome (within-subjects, two conditions: 5% vs. 95%)

5) Specify exactly which analyses you will conduct to examine the main question/hypothesis.

Each choice experiment is analysed with a Pearson chi-square test for a 2 x 2 contingency table. If the hypothesis is supported: (a) when the choice options offer positive outcomes, the proportion of participants choosing the affect-rich option decreases with increasing probability, (b) for options with negative outcomes, the proportion of participants choosing the affect-rich option increases with increasing probability.

Each valuation experiment is analysed using a two-way ANOVA with valuation as the dependent variable. The factors are outcome affect (within-subjects, affect rich vs affect poor); probability level (within-subjects, 5% vs. 95%). If the hypotheses is supported, there will be a two-way interaction between probability level and outcome affect such that the increase in valuation with increasing probability is greater for affect-poor options than it is for affect-rich outcomes. If this two-way interaction is statistically significant, simple main effects will be examined to characterise the interaction, and determine whether the data fit the pattern predicted by the hypothesis.

Measures of effect size will be calculated and used in the interpretation of all results, including confidence interval estimates of any differences in means.

6) Describe exactly how outliers will be defined and handled, and your precise rule(s) for excluding observations.

All data will be excluded for any participant who does not explicitly consent to their data being shared (final question of survey) or who completes the entire survey in less than 4 minutes (i.e., < 240 seconds).

Out-of-range values will be excluded from valuation data: zero or negative amounts for willingness-to-pay valuations, or those at or above the stated

£-value of the outcome. One out-of-range response is sufficient to exclude a participant's data for the experiment. The exclusion of these participants will  be done on an experiment-by-experiment basis (i.e., exclusion from one experiment due to an out-of-range valuation will not lead to exclusion from other experiments that do not have out-of-range responses).

7) How many observations will be collected or what will determine sample size? No need to justify decision, but be precise about exactly how the number will be determined.

Sample size will be determined by the number of participants who have completed the online survey by midday on Tuesday 21th November 2023 (London time).

8) Anything else you would like to pre-register? (e.g., secondary analyses, variables collected for exploratory purposes, unusual analyses planned?)

Secondary analyses: To check the robustness of conclusions, the valuation data for the two experiments with negative outcomes (which include an option for which a high'out-of-range' response is not defined) will be re-analysed using trimmed samples. For each experiment, a 5% trim will be applied to the valuation scores for each cell. Participants'data will retained for the experiment only if all four of their valuations remain after trimming.

Possible exploratory analyses: Four participant characteristics are collected to describe the sample; any analyses investigating these characteristics will be exploratory.