The functions requires that the factors have exactly the same levels.For two class problems, the sensitivity, specificity, positive
predictive value and negative predictive value is calculated using the
positive argument. Also, the prevalence of the "event" is computed from the
data (unless passed in as an argument), the detection rate (the rate of true events also
predicted to be events) and the detection prevalence (the prevalence of predicted events).
Suppose a 2x2 table with notation
rcc{
Reference
Predicted Event No Event
Event A B
No Event C D
}
The formulas used here are:
$$Sensitivity = A/(A+C)$$
$$Specificity = D/(B+D)$$
$$Prevalence = (A+C)/(A+B+C+D)$$
$$PPV = (sensitivity * Prevalence)/((sensitivity*Prevalence) + ((1-specificity)*(1-Prevalence)))$$
$$NPV = (specificity * (1-Prevalence))/(((1-sensitivity)*Prevalence) + ((specificity)*(1-Prevalence)))$$
$$Detection Rate = A/(A+B+C+D)$$
$$Detection Prevalence = (A+B)/(A+B+C+D)$$
$$Balanced Accuracy = (Sensitivity+Specificity)/2$$
See the references for discusions of the first five formulas.
For more than two classes, these results are
calculated comparing each factor level to the remaining levels
(i.e. a "one versus all" approach).
The overall accuracy and unweighted Kappa statistic are calculated. A p-value from McNemar's test is also computed using mcnemar.test (which can produce NA values with sparse tables).
The overall accuracy rate is computed along with a 95 percent confidence interval for this rate (using binom.test) and a one-sided test to see if the accuracy is better than the "no information rate," which is taken to be the largest class percentage in the data.