The uncertainty associated with a measurement is just as important as the measurement itself. A measurement without an error is next to useless.  In astronomy and astrophysical research, most initial uncertainty estimations come from the limitations of the telescope used in the observations. Other sources of uncertainty  could be the position accuracy of a source.

Signal-to-Noise

A researcher should always understand what the uncertainties are when making observations in order to interpret the results. For example, if you are observing an exoplanet transit, you would want an estimation of the noise in the field compared to the signal you want (this is generally referred to as the signal-to-noise ratio, SNR or S/N. Note: not to be confused with supernova remnant) Generally, anything with a S/N > 3 is considered a detection. A S/N > 5 is usually a significant detection.

Fitting Data

There are many methods for fitting data, all of which include ways to estimate errors. Below are links to some of the most common methods. Many of these are available in programs like Mathematica, Logger Pro, Excel, and exist in python libraries, so it is no necessary to do them by hand. That being said, you should always manually calculate a few results to convince yourself that the program is working the way it should be.

1. Least-Squares Fitting
   • For “Data that should fit a straight line”
   • Can be used for curve fitting too
2. Fitting a Gaussian