The Mandala Centre

Frequency analysis


Hi! I'm Tim Tyler, and this is a video about frequency analysis - and its significance.

Here we will take the term "frequency analysis" to refer to the analysis of frequencies - or frequency distributions. The frequencies can be either associated with continuous signals, or be associated with categorical data.

It seems to me that frequency analysis is a much neglected field. Part of the problem appears to be one of terminology - until now the field has not really had a proper name.

At the moment, if you search for the term "frequency analysis" on the internet, you will mostly find pages relating to cyphertext frequency analysis - which is a branch of cryptography. The cryptographers are making excellent use of this fine term - however few others are doing so. The point of this video is to try and change that.

Here, I will mostly be discussing frequency analysis of categorical data. This uses statistical frequencies and is a subfield of what is known as Categorical Data Analysis. Categorical data is just data that has already been categorised. It is often represented using histograms and pie charts.

There are a few other existing fields which explicitly use the term "frequency analysis". In particular there is:

However, the umbrella term of "frequency analysis" is conspicuous by its absence. Many other fields use the methods of frequency analysis - however they tend not to refer to it by name.

Those who look at the frequencies of floods, earthquakes and disasters are all using frequency analysis. Much biographic and demographic information is categorical and can be subjected to frequency analysis. For example, gender frequency analysis is very common but also very rarely mentioned.

I favour more use of the "frequency analysis" term - and propose that the term be more widely deployed - starting immediately.

One important area where it could be used is population genetics. Today, this consists largely of frequency analysis of traits - but the term "frequency analysis" is rarely mentioned.

The term "population genetics" is not a terribly good one. Populations are normally defined to be groups of sexually-interbreeding individuals of one species - whereas most of the statistical methods the field actually uses are equally appropriate for any group of organisms - including groups of asexual organisms. Whether the individuals form an interbreeding sexual species or not seems to be not very relevant.

To remedy this, I propose some new field names - in particular:

  • Gene frequency analysis - the study of gene frequencies;
  • Meme frequency analysis - the study of meme frequencies;
  • Trait frequency analysis - the study of trait frequencies;
  • Species frequency analysis - the study of species frequency distributions.
Frequency analysis is equally appropriate for use in univariate analysis, bivariate analysis and multivariate analysis.

The term "frequency analysis" is a fine one. Cryptography shouldn't have a monopoly on its use. I propose we liberate the term and use it more widely.


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