Permutation Test

In Linguistics, permutation test is important to analyze the abundant and very divergent linguistics data for which normalization of a population set is impossible. The data are acquired by comparing two languages in contact and the purpose of this test is usually to find syntactic differences between those languages. The factors influencing the degree of differences are the mother tongue of the speakers, other languages they know, the length and time of experience in the second language, the role of formal instruction. This test would make the data of such studies amenable or easy to control. After doing the test, not only numerical value to the difference between two syntactic varieties but also confidence in the measure of examining the source of the difference and answers to linguistic questions about relative or volatility of syntactic structures can be gained. As complement to permutation test, Monte Carlo Sampling method is introduced to complete enumeration of the data. It can well approximate the distribution using random samples and make testing on large data, like in linguistic testing, possible. Below is an example of testing on linguistic using permutation test:

1. Determine differences between 2 vectors of trigrams of two tested languages, which will be the test statistic

2. Permute a pair of sentences from two sub-corpus, compare the differences of resulting two vectors of trigrams (compute test statistics for this permutation)

3. Repeat step (2) e.g. 10,000 times, each time, pairs of sentences are picked randomly (Monte Carlo technique).

4. Estimate the statistic significance and the probability that the original samples were due to chance (p-value).



Permutation Tests for Complex Data: Theory, Applications and Software (Wiley Series in Probability and Statistics)

Permutation Tests: A Practical Guide to Resampling Methods for Testing Hypotheses (Springer Series in Statistics)

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