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Consider I have two groups: control and treatment. The mean for glucose variable is written as $\mu_g$

How can I write mean for glucose for the control group and treatment group in mathematical notation?

I want to avoid using superscript e.g. $\mu_g^t$ because that is used typically for exponents

Kay
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  • It's not clear (to me) exactly what you are trying to notate, but one common idea is to put the subscript in parentheses, as $g^{(i)}$ or such. Otherwise, it isn't all that uncommon to just use superscripts as indices (see, for instance, Einstein notation). To be sure, this can definitely lead to ambiguity so care is needed. – lulu May 07 '23 at 10:03
  • hi Lulu, I have editied to give an example. Mean glucose I am representing by $\mu_g$ . But I want to distinguish mean glucose for test group v/s control group. How can I best write that? – Kay May 07 '23 at 10:09
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    I don't see a problem with superscripts, as in $\mu_g^t, \mu_g^c$. In writing I would definitely stress that these were indices, not exponents. You could use parentheses as well, but I think that clutters things up without really changing things. An alternative would be something like $\mu_{g,t}$. – lulu May 07 '23 at 10:11
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    People sometimes change the variable name. Thus $\mu_g$ might be the test mean and $M_g$ the control mean. This works well if, as appears to be the case here, you only have two variables to describe. If you had dozens, you'd need to use an index somewhere. – lulu May 07 '23 at 10:14

1 Answers1

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To summarize the discussion in the comments:

I. It is by no means unusual to use superscripts as exponents. Einstein notation is one typical example. To be sure, this can sometimes lead to ambiguities, but in context, with the proper warnings written out, people can sort it out.

II. Sometimes people use parentheses or brackets to distinguish between various sorts of superscripts. Thus $f^2(x)$ might denote the square $f(x)\times f(x)$, while $f^{(2)}(x)$ might denote a second derivative or an iterate ($f\circ f(x))$ and so on. Again, this can sometimes lead to ambiguities, so be sure to spell out what you intend at least once (and then be consistent).

III. You can just use multiple subscripts, as in $\mu_{g,t}, \mu_{g,c}$

IV. If, as appears to be the case here, you only need to distinguish between a small number of cases, a simple approach is to change the variable name. Let $\mu_g$ be the test mean, and $M_g$ the control mean. This is the least ambiguous method, but it is useless if you have many cases to distinguish.

lulu
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