# Project roadmap

The goal of this roadmap document is to provide a basic skeleton of the components of the project. I will structure the roadmap similarly to an APA research paper. This roadmap may change across the semester.

## Overarching goals for Hao

Hao’s CUNY BA is structured around the topic of quantitative psychology. This independent research course provides an opportunity to acquire skills in experimental methodology, and quantitative methods for analyzing experimental data. Other coursework will cover routine statistical approaches such as ANOVA and related GLM methods. This project further introduces analysis techniques from signal detection theory, information theory, and curve-fitting in the context of psychophysical research. These analysis methods also have wide applicability across psychology, and may not be encountered in other undergraduate level coursework.

## Working Title: The psychophysics of entropy judgments for musical note sequences

## Basic Overview:

This project will present participants with sequences of musical notes that vary in their amount of randomness, from perfectly random to maximally predictable. On each trial, participants will listen to a musical sequence and judge whether it is “more random”, or “more predictable”. Using the method of constant stimuli, or variations of the method, we will establish psychophysical curves showing how people’s judgments correspond to parametric variation of sequence randomness. In general, there appears to be very little work on judgements of entropy, and this project would contribute new empirical data providing insight into basic entropy judgment abilities.

## Introduction (Big picture Questions):

- How do people become sensitive to patterns in their past and present environment?
- Lots of general examples of people showing sensitivity to statistical structure of patterns in their environment
- Frequency sensitivity
- contingency learning
- artificial grammar learning

- Lots of general examples of people showing sensitivity to statistical structure of patterns in their environment

Prior work

- In the musical domain, there is evidence that people can rapidly become sensitive to patterns with specific kinds of statistical structure
- artificial grammar learning for musical stimuli
- plinks (1 second to detect musical style)

- In what ways are people sensitive to variation within patterns?
- information theory
- entropy in a discrete probability distribution
- Prior research on judgments of entropy
- wasserman (variance discrimination)

- Contingency judgment literature
- streamed trials procedure
- psychophysics of contingency judgement

## Specific research questions:

How sensitive are people to entropy within a sequence of musical notes?

- develop a psychophysical procedure to assess basic properties of human ability to judge entropy levels of musical note sequences.
- estimate JNDs (just-noticeable-differences)

- Empirically examine possibly important task parameters, we will not be able to examine them all:
- Specific judgment instructions
- binary choice vs. scrolling value
- Note sequence properties
- number of notes in collection
- semitone distance between notes
- total number of notes per collection
- instrument
- timing

- develop a psychophysical procedure to assess basic properties of human ability to judge entropy levels of musical note sequences.

## Experiment 1:

We will closely follow the general psychophysical approach described by Allan et al. (2008).

## Methods:

A sequence of notes can contain notes of specific pitches that are repeated or not repeated over time. We will examine collections of notes played over time in a regular 16th note rhythm. For example, at 120 BPM, 64 notes can be played in about 8 seconds.

We will construct sequences from collections of 8 different notes. Each note will appear in the sequence with a pre-programmed frequency. A sequence with maximum entropy would have every note played equally often (e.g., each of the 8 notes is played 8 times). We define sequences with the least first-order entropy as being maximally biased, such that one note occurs the most possible times (e.g., 57), while the other notes occur a single time. We construct sequences with intermediate levels of entropy in equal parametric steps, using bits, to cover the full range from most to least random.

Participants will be given a binary judgment task. They will listen to a musical sequence and then decide if it is “more random” or “less random”. Participants will be shown 8 examples from each entropy level.

## Results:

Mean judgments of entropy (e.g., P (“more” random) will be analyzed using signal detection in psychophysical framework. This will allow us to separate sensitivity from bias in the judgement, and estimate parameters such as JNDs.

## Discussion:

What did we learn from doing this?

Return to the general issues.

## References

*Journal of Experimental Psychology: General*137 (2): 226–43. https://doi.org/10.1037/0096-3445.137.2.226.