# Combining Data from Multiple Participants for Statistical Analysis in a Facial Expression Memory Task

I am working on a project involving a memory task for facial expressions, consisting of two phases:

1. Encoding Phase: There are 8 trials in which participants view 8 different virtual characters, each displaying one of four facial expressions (pain, anger, sadness, neutral).

2. Recall Phase: This phase consists of 24 trials (in a random order), divided into three categories:

• 8 "Old identity, old expression" Trials: Participants must recognize characters with the same facial expressions as those shown during the Encoding Phase. The task is to confirm if they have seen the exact character-expression combination previously.
• 8 "Old identity, new expression" Trials: Here, the characters are the same as those seen in the Encoding Phase, but they display different facial expressions. Participants need to identify that they have seen the character before, albeit with a different expression.
• 8 "New identity" Trials: These trials feature entirely new characters that were not presented in the Encoding Phase. Participants must identify that they have not seen these characters before.
• In all cases (of the recall phase), participants are required to specify whether they have seen the exact character-expression combination, only the character (with a different expression), or if they haven’t seen the character at all.

One challenge I'm facing with the data from this task is the limited number of trials per participant for each condition, which restricts the utility of standard statistical methods typically used for such tasks (e.g. signal detection theory). For instance, calculating the hit rate for the expression of pain involves only 2 trials, as there are only 2 "old" trials featuring a pain expression among the 8 "old" trials. This results in a hit rate that can only assume a few values (0%, 50%, 100%), which undermines its meaningfulness.

My question is: Are there any statistical techniques that allow for the combination of data across multiple participants to form "macro-participants" for the calculation of statistics such as hit rate or accuracy? The idea would be to randomly group data from 3 or 4 participants to compute these statistics and then perform hypothesis testing on them.

I appreciate any guidance or references to methods that could help address this issue.