---
title             : "Pre-registration: memory for decisions"
shorttitle        : "memory for decisions"

author: 
  - name          : "Keishiro Sawa"
    affiliation   : "1"
    corresponding : no    # Define only one corresponding author
  - name          : "Matan Mazor"
    affiliation   : "1"
    email         : "matan.mazor@all-souls.ox.ac.uk"
    corresponding : yes


affiliation:
  - id            : "1"
    institution   : "University of Oxford"

floatsintext      : no
linenumbers       : yes
draft             : no
mask              : no

figurelist        : no
tablelist         : no
footnotelist      : no

classoption       : "man"
output            : word_document
bibliography: references.bib
---

```{r setup, include = FALSE}
library('groundhog')
groundhog.library(
  c(
    'papaja', #for apa formatting
    'pwr', # for power calculation
    'tidyverse' # for pipe %>%
  ), "2025-06-01"
)

r_refs("r-references.bib")
knitr::opts_chunk$set(echo = FALSE)
```

```{r analysis-preferences}
# Seed for random number generation
set.seed(42)
knitr::opts_chunk$set(cache.extra = knitr::rand_seed)
```

# Motivation

Here we ask whether people can remember decisions they recently made, whether this depends on the accuracy of these decisions, and whether rule learning -- whether explicit or implicit -- biases the reconstruction of previously taken actions. 

# Methods

We report how we determined our sample size, all data exclusions (if any), all manipulations, and all measures in the study. <!-- 21-word solution (Simmons, Nelson & Simonsohn, 2012; retrieved from http://ssrn.com/abstract=2160588) -->

## Participants

The research complies with all relevant ethical regulations, and was approved by the Medical Sciences Interdivisional Research Ethics Committee at the University of Oxford (MSD IDREC 1091017). Participants will be recruited via Prolific, and will give informed consent prior to their participation. To be eligible to take part in this study, their Prolific approval rate will need to be 95% or higher, their reported first language English, and their age between 18 and 60. We will collect data until we reach 100 included participants (after applying our pre-registered exclusion criteria). The entire experiment will take 10 minutes to complete. Participants will be paid £1.5 for their participation, equivalent to an hourly wage of £9. The top-performing 30% of participants will receive an additional bonus of $1 (£0.75).

## Procedure

The experiment will comprise two parts, each consisting of 50 trials. In part 1, participants will make guesses about the location of hidden coins, and in part 2 they will attempt to reconstruct their guess sequence from part 1.

### Part 1

On each trial, participants will be presented with three "boxes", ordered left to right, each labelled with a unique noun (sampled without replacement from a list of 300 common English nouns) and a number (sampled from a uniform distribution over 1-5). Participants will be told that the number indicates the number of items in the box: stones or gems. While stones are worthless, each gem is worth 1 point. Only one of the three boxes has gems in it, and participants' task is to accumulate as many points as possible by collecting gems. After selecting a box with their mouse, the content of the box will be revealed (stones or gems). After 500 ms, the content of the two other boxes will be revealed as well. A counter at the top left corner of the screen will indicate the total number of points accumulated. Participants will need to click on a "continue" button to move to the next trial. 

Before starting part 1, participants will be told that whenever a fruit word appears, it is guaranteed to have gems in it. Three such trials will be included, and will be used as an attention check by us. Participants will also see a leaderboard with the total scores of the top-performing participants, and will complete two comprehension questions. Participants will continue to the main part of the experiment only after correctly answering the two questions, otherwise they will be presented with the instructions again. 

Unbeknownst to participants, gems will only appear in two of the three positions: one position will have red gems and one position will have green gems. The colour of the gems does not make a difference; this colouring scheme is just to make the absence of gems in the third box more salient. 

### Part 2

Immediately after completing part 1, participants will be instructed about part 2. Here, they will be presented with the exact same sequence of 50 box arrangements as before, but their task will be different. Instead of guessing the location of the gems, they will attempt to reconstruct the exact same sequence of guesses as in part 1. For every trial in which they guess the same box they had guessed in part 1, they will receive 3 points. In part 2, feedback about the number of accummualted points thus far will be delivered once in every 10 trials instead of after each individual trial. Participants will continue to part 2 only after correctly answering the two comprehension questions, otherwise they will be presented with the instructions again. 

At the end of the experiment participants will be asked whether they noticed a regularity in the location of the gems, and whether they had any comments. 

```{r design, echo=FALSE, fig.cap="Experimental design. Elements are not drawn to scale. In part 1 (upper panel), participants will make 60 decisions between three boxes. Each box will be labelled with a unique noun and a number in the range of 1 and 5, indicating the number of stones or gems in the box. On each trial, only one box will contain gems, and the other two boxes will contain stones. A gem is worth a point, but a stone is valueless. Participants will not be told that one position (left, middle, or right) will always contain stones. In part 2 (lower panel), participants will attempt to produce the same series of guesses as in part 1. Accurately reproducing a decision will reward them with three points. They will receive feedback once in every 10 trials.   ", out.width = '75%'}
knitr::include_graphics("figures/design.png")
```

## Randomization

The box labels and their associated numbers will be determined pseudo-randomly by the Mersenne Twister pseudorandom number generator, initialized in a way that ensures registration time-locking [@mazor2019].

# Data analysis

## Rejection criteria

Participants will be excluded if they fail to choose the fruit-labelled box in two or more catch trials. We will also exclude participants for having extremely fast reaction times in one or more of the tasks (below 100 milliseconds in more than 25% of the trials), or for requiring three or more rounds of instructions in part 1 or in round 2.

## Hypotheses and analysis plan

This study is designed to test participants' ability to reconstruct their past decisions or guesses.

Hypothesis 1 (RULE LEARNING: AVOIDANCE): We will test the null hypothesis that the likelihood of selecting the stones-only box in part 1 is equal to chance (1/3). This will be tested using a one-sample t-test against $\mu=1/3$. A proportion lower than 1/3 will be taken as evidence for learning. 

Hypothesis 2 (RULE LEARNING: SLOPES): We will test the null hypothesis that the probability of selecting the stones-only box in part 1 does not change with time. This will be tested using a one-sample t-test on subject-specific slopes (in log-odds units) from a logistic regression fitted to the data of individual participants $choose\_stones\_only \sim trial\_number$. 

Hypothesis 3 (RECONSTRUCTION ACCURACY): We will test the null hypothesis that participants' accuracy in reconstructing their choices from part 1 is at chance (1/3). This will be tested using a one-sample t-test against $\mu=1/3$.

Hypothesis 4 (RECONSTRUCTION ACCURACY BY GUESS ACCURACY): We will test the null hypothesis that participants' accuracy in reconstructing their choices from part 1 is the same for decisions in which they revealed gems or stones. This will be tested using a paired t-test.

Hypothesis 5 (REMEMBERED ACCURACY VERSUS TRUE ACCURACY): We will test the null hypothesis that participants' remembered decisions coincide similarly with the true location of gems as their actual decisions in part 1.  This will be tested using a paired t-test.

Hypothesis 5 (POSITION BIAS IN RECONSTRUCTION ERRORS): We will test the null hypothesis that participants' remembered decisions are not biased for or against the stones-only location. For this, we will focus on trials in which the original decision revealed gems, but they made an error in reconstruction. We will compare the probability of choosing the stones-only position against 50%. Since different participatns will have different number of trials for this analysis, this will be tested using a mixed-effects logistic regression ($chose\_stones\_only \sim 1+(1|subj\_id)$, run with lme4's glmer, assuming a binomial variable and using a bobyqa optimizer). 


## Sample size justification

With 100 participants, we will have a statistical power of `r pwr.t.test(n=100,d=0.4, type='paired')$power%>%printnum()` to detect effect sizes of 0.4 standard deviations in a within-subject t-test.

\newpage

References
