Correct Grammatical Form for RMSE? Which is preferred for use in journal publication:  Root-Mean-Square Error or Root Mean Squared error?  
Root-mean-square sounds a little casual, like "ice tea" instead of "iced." On the other hand, Cross-Validated's own tag uses just "square."
If there is a difference in usage across field, environmental science would be most relevant.
 A: Here are some textbook references:


*

*Page 546 of Ott and Longnecker says "recall that MS stands for mean square"

*Page 211 of DeGroot and Schervish (3rd edition) defines the mean squared error

*Page 30 of Draper and Smith (3rd edition) discusses the mean square.

*Page 158 of Draper and Smith, discusses MSE, which they call the residual mean square $s^2$.

*Page 202 of elements of statistics and Probability by Lippman defines mean squared error.


The two that mention the term RMSE directly, add the "d" at the end, but the others do not for the inner term mean square.
A: A google search of "root mean squared error" gives 318,000 results, while a search for "root mean square error" gives 1,660,000 results
A google scholar search of "root mean squared error" gives 61,300 results, while a search for "root mean square error" gives 224,000 results
I declare that "root mean square error" is preferred.
A: It's root mean square because it's the root of the mean of squares, not the square of the root of the mean.  
According to the Merriam-Webster's:

root–mean–square:  the square root of the arithmetic mean of the squares of a set of numbers

For a similar parameter, the International Electrotechnical Commission (IEC), in its Online Electrotechnical Vocabulary, suggests root-mean-square too.
Google Ngram viewer confirms the predominance of root mean square (also with error).
