I'm trying to ascertain the accuracy of a device used to distinguish values from different populations.
Currently each device measurement contains a data point from 8 different sensors. The value recorded from this sensor approximately belonging to a normal distribution.
I have taken 30 measurements from two groups, say group A and group B, thus giving 60 measurements and a total of 2 * 30 * 8 = 480 sensor readings.
So the data can be described: $x_{gi} \in iid(\mu_{gi}, \sigma_{i})$ where $x_{ig}$ is an observation from population/group $g$ on sensor $i$.
I am now wondering how I could estimate the probability that a member from group A could be miss-identified as a member of group B. I am currently using a Nearest-Neighbour algorithm that identifies a data point by associating it to the group who's mean has the smallest euclidean distance. So say we had a measurement for group A, $\bar{x} = (x_{A1}, x_{A2}, x_{A3}, x_{A4}, x_{A5}, x_{A6}, x_{A7}, x_{A8})$ the euclidean distance to group A would be: $\epsilon_{A} = \sqrt{\sum_{i}(x_{Ai} - \mu_{Ai})^{2}}$, (note: $x_{Ai} - \mu_{Ai}$ is just the residual value) and to group B: $\epsilon_{B} = \sqrt{\sum_{i}(x_{Ai} - \mu_{Bi})^{2}}$
I have been looking for a while at chi distributions, however I am a novice statistician and cant seem to find a good way to calculate this probability just using values observed from the data: $\mu_{gi}, \sigma_{i}: \forall i \in \{1 ... 8\}$
