Is it “rows by columns” or “columns by rows”?

Question

I've got a data table like:

ID  Low Color    Med Color     High Color
 1        234          123            324
 2          4          432           3423

The rows are widgets, the columns are color levels. Would you call this table "widgets by color level" or "color levels by widget"?

Answer 1

"That depends." Rows are usually considered observations, and columns are variables. So I would say widgets by color level in your context. But it really depends on which are your dependent and independent variables (or how you're interpreting the data).

Answer 2

Of course you can view this table either way by transposing it. Conventionally, in a database rows represent objects and columns contain their attributes, whence this presentation would typically be viewed as a list of widgets, not a list of color levels.

Answer 3

Typically, we talk about a r(ow) X (c)olumn matrix, from Linear Algebra. So, a matrix with 2 rows and 3 columns is a 2 X 3 matrix. By that logic, I'd call your data frame a "Widgets by Color" table.

Answer 4

for a table like that, I say it the same way I'd say "n by k" for a matrix with n rows and k columns (i.e. rows first).