# Moran’s I Permutation Test

## Contents

## Introduction

This component allows the user to compute the global Moran’s I statistic by using random permutations of x for the given spatial weights matrix, “to establish the rank of the observed statistic in relation to the (number of) simulated values” (Bivand, 2013: 119). In this test the observed values are randomly assigned to areas and the I statistic is simulated for each permutation.

## Inputs

- Dataset – the spatial weight matrix to be used, probably derived from one of the methods above.
- Dataset – the dataset that contains the variable(s) to be tested.
- Moran’s I Permutation Test Input Variable – the variable(s) to be tested.
- Moran’s I Permutation Test Alternative Hypothesis – indicates the alternative hypothesis; can be greater, meaning one sided greater than or less, meaning one sided less than.
- Moran’s I Permutation Test Number of Simulations – the number of simulations performed for the test.

## Outputs

- Moran’s I with its bias and standard error o Moran’s I with rank and pseudo p-value o The alternative hypothesis
- The number of simulations