How to calculate 95% CI for accuracy and kappa in caret

Question

I am running k-fold repeated training with the caret package and would like to calculate the confidence interval for my accuracy metrics. This tutorial prints a caret training object that shows accuracy/kappa metrics and associated SD: https://machinelearningmastery.com/tune-machine-learning-algorithms-in-r/. However, when I do this, all that is listed are the metric average values.

control <- trainControl(method="repeatedcv", number=10, repeats=3, search="grid")
set.seed(12345)
tunegrid <- expand.grid(.mtry=4)
rf_gridsearch <- train(as.factor(gear)~., data=mtcars, method="rf", 
                       metric="Accuracy", 
                       tuneGrid=tunegrid, 
                       trControl=control)
print(rf_gridsearch)

> print(rf_gridsearch)
Random Forest 

32 samples
10 predictors
 3 classes: '3', '4', '5' 

No pre-processing
Resampling: Cross-Validated (10 fold, repeated 3 times) 
Summary of sample sizes: 29, 28, 30, 29, 27, 28, ... 
Resampling results:

  Accuracy   Kappa    
  0.8311111  0.7021759

Tuning parameter 'mtry' was held constant at a value of 4

Answer 1

It looks like it is stored in the results variable of the resultant object.

> rf_gridsearch$results
  mtry  Accuracy     Kappa AccuracySD   KappaSD
1    4 0.7572222 0.6046465  0.2088411 0.3387574

A 95% confidence interval can be found using a critical z value of 1.96.

> rf_gridsearch$results$Accuracy+c(-1,1)*1.96*rf_gridsearch$results$AccuracySD
[1] 0.3478936 1.1665509

Answer 2

The correct answer is this:

Upper interval = X_hat + z * (S/sqrt(n))

Lower interval = X_hat - z * (S/sqrt(n))

If you are dealing with proportions:

Upper interval = X_hat + z * sqrt( (p * (1-p))/n )

Lower interval = X_hat - z * sqrt( (p * (1-p))/n )