# R rpart cross validation and 1 SE rule, why is the column in cptable called “xstd”?

The rpart() function in R returns cptable that includes columns xerror and xstd. Here is an arbitrary example.

            CP nsplit rel error    xerror       xstd
1  0.161992664      0 1.0000000 1.0002790 0.01853630
2  0.043985638      1 0.8380073 0.8385070 0.01749290
3  0.030278222      2 0.7940217 0.7963870 0.01709283
4  0.013881619      3 0.7637435 0.7695997 0.01653832
5  0.010181164      4 0.7498619 0.7560406 0.01606136
6  0.008004043      5 0.7396807 0.7466449 0.01600352
7  0.007026176      6 0.7316767 0.7356289 0.01549501
8  0.006614587      8 0.7176243 0.7388091 0.01559568
9  0.005312278     10 0.7043951 0.7254237 0.01522645
10 0.004883811     11 0.6990828 0.7248227 0.01526605


Some argue that the tree should be pruned based on the minimum cross-validated error (xerror) and thus would prune at row 10, where the minimum xerror occurred. Other argue that "1SE rule" advises to look for the minimum but then go up 1SE because that tree is less complex. Using column xstd, that would suggest using 0.7248227 + 1*0.01526605 = 0.7400887 and thus pruning should occur at row 7. See also this post: How to choose the number of splits in rpart()?

My simple question: why is the column labeled "xstd" (presumably meaning cross-validated standard deviation), and yet people refer to this as the 1SE rule and not the 1SD rule.

• there is separate training tag in caret -- method = 'rpart1SE'.. Refer to topepo.github.io/caret/… – rbgh Oct 2 '18 at 4:12

• I don't think the labeling should be called poor. A standard error is by definition the standard deviation of the sampling distribution of a parameter estimate, generated by repeated sampling. xerror reflects the mean of the sample means (of the errors) from the ten folds; then xstd reflects the standard deviation of the sample means (of the errors) from the ten folds. Thus, xstd is a standard deviation of sample means, which is also known as the standard error of the mean. – Marjolein Fokkema May 16 '19 at 10:49