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DIN
DIN (Difference index) is a so called effect-size metric, i.e. a measure designed1) for the purpose of quantifying the relevance of a difference between values. DIN is implemented for extracting prominent units from a text (keywords) in the KWords tool.
Significance and relevance
When comparing values (e.g. frequencies of words) we should be aware not only of the statistical significance but also whether the difference under consideration is actually relevant for the description. Statistical significance can be obtained by several tests (e.g. chi2 test, Fisher's test or log-likelihood test).2) Significance is usually expressed as a p-value, i.e. the probability that the difference is caused by chance or variation within the data.
Even if the difference is significant it does not necessarily entails that it is also relevant for the description. Even a small difference can be significant when there is a lot of measurements available. That is why the statistical significance information is often combined with the effect-size estimation.
How it works
In the model example of extracting prominent words (keywords) from a text we proceed in the following way. For units which display a statistically significant difference, the DIN value is subsequently calculated:
$$DIN = 100 \times \frac{RelFq(Ttxt) - RelFq(RefC)}{RelFq(Ttxt) + RelFq(RefC)}$$
where $RelFq(Ttxt)$ is the relative frequency of the phenomenon in the analyzed text (target text) and $RelFq(RefC)$ is the relative frequency of the same phenomenon in the reference corpus.
The formula takes into account the difference between relative frequencies (numerator) in relation to the frequency level of the items under comparison (denominator). This reference frequency level can be represented by their average value, as can be seen in following formula which is equivalent with the above (the coefficient changed from 100 to 50 in order to keep the DIN values within the desired range):
DIN Values
The DIN values are designed to reach values from -100 to 100, it being understood that:
- a value of -100 means that the given phenomenon does not occur in the analyzed text and is only in the reference corpus (therefore the word is not prominent in the analyzed text)
- a value of 0 means that the given phenomenon has approximately the same relative frequency in the analyzed text and in the reference corpus (therefore the word is not prominent in the analyzed text)
- a value of 100 means that the word occurs only in the analyzed text (it can therefore be a very prominent word 3))
In texts of up to 20 thousand words in length and for analysis of word forms, DIN values in the 75-100 range can be considered to be of interest and they indicate that the unit is probably prominent and can be used as a basis for the interpretation of the entire text.
Furthermore, the KWords application offers a whole range of additional information for work with keywords. Apart from the list of keywords and their values it is the data dispersion graph (showing the status of the individual keywords in the text), a graph of so-called keyword links, i.e. relations between keywords in the text and also a concordance of keywords for an analysis of their immediate context.
The KWords application was also designed for creating analyses of temporal (or other) data series. If the user inputs more texts into the application (the maximum amount is 20), the so-called multi-analysis regime is activated. This regime analyzes all the inserted texts and the results of the individual analyses are compared based on the DIN.
