Is there a way to calculate a probable range for the next single datapoint?
Given a number of experimental results (n-datapoints), I find a range of reported values. I can use that set of data to calculate a confidence interval (t-distribution or normal). However, the confidence interval tells me nothing about the probable range that my next datapoint will fall within. The confidence interval is actually a probable range for the mean of my datapoints. In other words, it only applies to predicting the next mean of n-datapoints. Is there a way to calculate a probable range for the next single datapoint?
The more datapoints I have the narrower the confidence interval. Which makes sense, because the more data I have, the more confident I am that the true value is represented by the mean of those points. At some point, more datapoints will tell me nothing new about the range of values that I can expect to see. Additional redundant values is why the standard deviation decreases and the confidence interval narrows. But, if I'm attempting to establish acceptable limits to ensure that future datapoints are not showing a trend, I need a range that encompasses all of the individual datapoints that are considered to be valid. Each future point needs to be scrutinized by itself as being acceptable or not.