# How can I calculate if the difference between two word frequencies in one corpus is significant?

I want to study orthographical variants, for example:

Can firefighter, fire-fighter and fire fighter be considered orthographical variants (the difference in frequency in a corpus is not statistically/practically significant), or should one or more of these orthographical forms be considered "wrong"/"irregular" (the difference in frequency is statistically/practically significant)?

In a corpus of 926,766,504 words, I get the following frequency counts (on lemmas):

• firefighter = 3,349
• fire-fighter = 336
• fire fighter = 1,338

What statistical measure(s) can I use to say, for example, that there is not a large enough difference between firefighter and fire fighter to consider the latter "irregular", but that the difference between firefighter and fire-fighter is significant?

One specific sub-question:

If I work with probabilities (e.g. firefighter = 0,667; fire-fighter = 0,067; fire fighter = 0,266), is there a way to measure if the difference is significant? (Beyond just stating the obvious that the one occurs with a higher probability than the other.)

• A corpus cannot tell you if an orthographic variant is correct or not. Typically a panel of native speakers is used to rate correctness. – Anonymous Physicist Nov 28 '16 at 8:23
• I used "wrong" specifically between inverted commas, because that is not the real issue here. It is more about whether a certain form occurs so frequently that it could be considered a viable spelling alternative. Such statistical information would typically inform a panel of experts, as you mentioned. – Gerhard Van Huyssteen Nov 28 '16 at 14:27
• What is the difference between "correct" and "viable spelling alternative?" I do not think there is one. I disagree with you about the "real issue." The real issue is that a corpus does not contain correctness information. – Anonymous Physicist Nov 28 '16 at 23:21