Solved – What do “$i$” and “$j$ ” subscript mean in statistics

notation

I'm just curious about what the meaning of $i$ and $j$ subscript in statistic formula. I think $i$ means individual and $j$ means higher level unit in a multilevel frame work. How did statisticians come up with these two letters? What are they short for?

Best Answer

The $i$ and $j$ are mathematical, rather than statistical, convention. The $i$ is because it is the first letter in the word index, and then $j$ comes after $i$. They have the benefit of being small, clear, and unobtrusive ($x_{ij}$ looks pretty good).

This is usually seen in the context of matrix entries, where $i$ indexes the rows, and $j$ indexes the columns. The matrix convention is followed far and wide in general branches of mathematics and science using linear algebraic machinery.

This is what I was told in my first linear algebra course in school, I know of no definitive reference.

Related Solutions

Solved – Feature naming conventions

With a lot of variables, at some point you are going to want to figure out what's what, and this will be easier if they are meaningful when put in alphabetical order. You are less likely to group them by whether they are logged or not than whether they are in the same "family". So, I'd rearrange your example as this:

gt_100k_income               income_gt_100k
is_missing_income            income_missing
lg10_income                  income_lg10
age_20_lt_25_age             age_ge_20_lt_25
zscale_age                   age_zscale
ratio_ln_income_ln_age       income_ln_over_age_ln

I realize that this is exactly the opposite of what some software does automatically (such as Excel pivot tables or Alteryx Summaries), but Bill Gates isn't right all the time.

It's probably more important to be consistent with your method, than what that particular method is.

Solved – Expectation Subscript

Normally it means that you are taking the expectation with respect to that distribution (or that probability measure). Sometimes we change the probability measure and therefore the expectations are taken with respect to the new probability measure. So they want to specify exactly with respect to which probability measure, they are taking the expectations.

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Solved – Feature naming conventions

Solved – Expectation Subscript

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