Same Folds, Paired Comparison

Two models scored on the same five folds:

fold	model A	model B
1	0.81	0.83
2	0.79	0.80
3	0.88	0.87
4	0.76	0.79
5	0.86	0.87

The means are 0.820 and 0.832. Fold-to-fold standard deviation is 0.050 for A and 0.038 for B, so the two means carry standard errors of 0.022 and 0.017, both wider than the 0.012 difference between them. Does this evidence favor B?

The comparison is invalid: each model needs its own cross-validation split, otherwise the second model is scored on folds the first has already been fitted on.

Yes. Both models ran on identical folds, so the informative statistic is the per-fold difference: +0.02, +0.01, -0.01, +0.03, +0.01, mean +0.012 with a standard error near 0.007. Most of the fold-to-fold spread is difficulty shared by both models, and it cancels in the pairing.

No. The means are 0.820 +/- 0.022 and 0.832 +/- 0.017, the intervals overlap heavily, so the models are statistically indistinguishable.

Yes, and the 0.012 gap is a reliable estimate of the difference on new data, because averaging over five folds removes the variance that a single split would carry.