# mazeDiff: Maze Diffculty In Aidenloe/mazeGen: Elithorn Maze Generator

## Description

This function tells us the difficulty level of the rank given a saturation and black node distribution

## Usage

 1 mazeDiff(nodePosition, model = "m1") 

## Arguments

 nodePosition This is the distribution of the colour node positions. model There are three types of model to select from: "m1", "m2" or "m3".

## Details

This function tells us the difficulty level of the rank given a saturation and black node distribution. The calculation of the difficulty level follows the Davies & Davies (1965) paper. In the article, there are three ways to calculate maze difficulty. In Model 1, only two parameters were considered: rank and the number of possible paths through the maximum number of routes.

log(2^{R}/U_{\hat{m}})

where 2^R is the total number of paths and U_{\hat{m}} is the paths through the maximum number of dots. Model 2 includes the saturation parameter. This is calculated based on:

log(2^{R}*s^{a}/U_{\hat{m}})

where s is the saturation and a = 4. The a value is recommended in the paper after using various values. Model 3 extends the second formula to include the minimum number of steps to pass through \hat{m}.

log(2^{R}*s^{a}*l^{b}/U_{\hat{m}})

where l is the minimum steps to pass through \hat{m} and b=4. The b value is recommended in the paper after using various values.

We included all three approaches to calculate maze difficulty. It was to incorporated all the possible parameters of the task features that may potentially influence maze difficulty.

## Author(s)

Aiden Loe and Maria Sanchez

## References

Davies, A. D., & Davies, M. G. (1965). The difficulty and graded scoing of Elithorn's perceptual maze test. British Journal of Psychology, 56(2-3), 295-302.

mazeEst, mazeAbility, np
 1 2 3 4 5 #Black nodes distribution nodePosition <- np(rank=5,satPercent=0.5,seed=1) #calculate difficulty mazeDiff(nodePosition, model="m1")