Mathematics employs logic, analysis and other quantitative techniques to gather, process and understand numeric measures. An analytical error is not an error in gathering information; it is an error in characterizing information. It is an error in logic. For example, mismeasuring a quantity might be an input error. Putting a decimal in the wrong place might be a computational error. But reasoning that three multiplied by three equals 10 is an analytical error.
Computer science is highly reliant on mathematics. Computers translate all information into a binary language upon which other logic-based languages are built. When programs are written in these languages they are all designed to take data, do something with it, and provide the result of of their computation. As with math, if the input is incorrect, the result of the function will be incorrect. If a logic error exists, the function is wrong. This is commonly known as a computer bug.
In medicine, analytical errors have a looser meaning. Medical treatment requires a degree of guesswork. Doctors don't necessarily know what's wrong with a patient; they deduce their diagnosis from medical tests and examinations. Analytical errors are errors in processing medical information. An incorrect diagnosis might not indicate an analytical error. A doctor can correctly analyze a patient but have bad results. A doctor can also improperly analyze a patient and get good results. An error is simply when the information gathered isn't reasoned appropriately.
Economics is another math-intensive discipline. Econometrics is a branch of economics that seeks to model economic dynamics. In econometric models, symbols represent real-life economic events. It is difficult to create models of understanding without oversimplifying so most econometric models isolate economic events. As with other analytical errors, it is the reasoning, not the accurate collection of data that constitutes an analytic error.