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I have seen statistical acronyms (e.g. sd, iid, GLM, DV) written in lower case and capitals. The examples I just gave are how I recall seeing them most of the time.

But I am wondering if there is some standard for these or if different authors just do what seems right to them.

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    $\begingroup$ I would imagine that an academic journal specialized in statistics would have a style guide proscribing which acronyms are capitalized, and that this guide may vary between statistics journals. $\endgroup$ – Sycorax Jul 21 at 15:39
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If you need to include a statistical acronym in a report or manuscript, the best thing you can do in my view is to define its meaning in that write-up the first time you use the acronym and then reference the acronym in the remainder of the write-up. This way, your readers will be clear on how YOU want them to interpret the meaning of the acronym. This is particularly important for acronyms like GLM which can be interpreted as "Generalized Linear Model(s)" or "General Linear Model".

For example, you would first declare in your Methods section that "We will use a generalized linear model (GLM) to analyze our data." and then state in your Results section that "Our GLM model produced the results stated in Table 2."

You can't possibly control consistency of use/meaning of acronyms by other people but you can control how YOU want your readers to relate to the acronyms you use and how consistent YOU are in your use of these acronyms.

If I had a choice, I would stick with upper case letters for acronyms, but that is a matter of personal preference.

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    $\begingroup$ This is probably the most important (+1), but I would also add to strive for consistency. I don't understand why people write e.g. 'lasso', followed by 'LOOCV'. Either capitalize it all, or none of it. Personally, I think capitalizing is better, since it is immediately clear you're using an abbreviation. $\endgroup$ – Frans Rodenburg Jul 22 at 2:45

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