---
title             : "Pre-registration: memory reconstruction; symmetry"
shorttitle        : "memory reconstruction"

author: 
  - name          : "Matan Mazor"
    affiliation   : "1"
    corresponding : yes    # Define only one corresponding author
    email         : "matan.mazor@all-souls.ox.ac.uk"

  - name          : "Carla Zoe Cremer"
    affiliation   : "1"


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('tidyverse')
library('papaja')
library('pwr')

# 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

Previous research has identified limitations on memory for decisions made before learning a piece of evidence [@wood1978; @gopnik1988; @chew2020; @blank2003; @calvillo2014; @powell1988]. Here we ask whether similar effects can be observed for decisions made minutes ago.

# 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 and their reported first language English. We will collect data until we reach 150 included participants per condition (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.

## Procedure

Participants will play a game and collect bonus points to earn a bonus. In part 1, they will attempt to reveal all black cards in a 5 by 5 grid while touching as few white cards as possible. They will do this four times, in four separate grids. Each grid will start with several black cards revealed, and participants will be told that all black cards are arranged in groups of 2-4 cards each around the revealed cards. 

In part 2, they will attempt to reconstruct their guesses from part 1, grid number 1. Participants who produce the same sequence of guesses will get a 2 USD bonus. 

All participants will start with the same grid in part 1: a symmetric grid with two horizontal islands of size two at the second row from the top and two L-shaped islands of size 3 at the second row from the bottom (see Fig. 1). The remaining grids will be different for two groups of participants: the "symmetric" group will play three left-right symmetric grids, and the "asymmetric" group will play three asymmetric grids. 

```{r board, echo=FALSE, fig.cap="Grid number 1 for the two groups of participants", out.width = '35%'}
knitr::include_graphics("board1.png")
```

## Randomization

The order and of grids 2-4 will be randomised, and so will the assignment of participants to groups. 

# Data analysis

## Rejection criteria

Participants will be excluded if they require more than 2 attempts in one or more of the comprehension questions.

## Hypotheses and analysis plan

This study is designed to test whether participants can accurately recall their actions from several minutes ago, and whether this depends on their knowledge of a hidden rule (symmetry).

Hypothesis 1 (SYMMETRY RULE LEARNING): We will test the null hypothesis that the number of misses (white card guesses) in grids number 2-4 is the same for the symmetric and asymmetric groups. This will be tested using a between-subject t-test on the number of misses in grids number 2-4, separately for each grid.

Hypothesis 2 (RECONSTRUCTED NUMBER OF MISSES BY GROUP): We will test the null hypothesis that the number of white-card guesses in part 2 of the experiment is the same for groups 1 and 2. This will be tested using a between-subject t-test on number of misses in part 2.

Hypothesis 3 (SYMMETRIC ERRORS BY GROUP): Symmetric errors are guesses of white clicks whose symmetric counterpart has been revealed as white. For example, revealing that the top left card is white is a symmetric error if the top right card has already been revealed as white.  We will test if the proportion of symmetric errors out of all errors in part 2 is the same for the two groups. This will be tested using a between-subject t-test on the ratio of symmetric errors out of all errors between participants in the symmetric and asymmetric group.  

Hypothesis 4 (RECONSTRUCTED NUMBER OF MISSES ACCURACY): We will compare the number of misses in grid 1, part 1 and grid 1, part 2. This will be tested using a within-subject t-test, collapsed across both groups of participants.  

Hypothesis 5 (SYMMETRIC ERRORS ACCURACY: SYMMETRIC GROP): We will compare the proportion of symmetric errors in grid 1, part 1 and in grid 1, part 2. This will be tested using a within-subject t-test, on participants from the symmetric group only. 

Hypothesis 6 (SYMMETRIC ERRORS ACCURACY: ASYMMETRIC GROP): We will compare the proportion of symmetric errors in grid 1, part 1 and in grid 1, part 2. This will be tested using a within-subject t-test, on participants from the asymmetric group only. 

## Sample size justification

With 150 participants per group, we will have a statistical power of `r pwr.t.test(n=150,d=0.3, type='paired')$power%>%printnum()` to detect effect sizes of 0.3 standard deviations in a within-subject t-test, and of `r pwr.t.test(n=150,d=0.4, type='two.sample')$power%>%printnum()` to detect an effect of 0.4 standard deviations in a between-subject t-test. 

\newpage

References
