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How can I state the uncertainty about whether two stars are at a common distance using their parallax and standard errors of the mean? For example, the parallax of two stars are 12.1303 mas and 12.1159 mas and their standard errors of mean are 0.0354 mas and 0.0339 mas, respectively. What's the probability of both stars were at a common distance?

Hi,
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Willey

Hello!

One method to show the likelihood that the stars are both at the same distance away from the earth is to determine the significance value (in other words, the p-value) with a statistical test. I would suggest either a two-sample t-test (if the number of data points are below 30) or a two-sample z-test (if the number of data points are above 30). For these tests, you would need to know the mean, standard deviation, and number of data points/measurements. You can do this on a TI-84 calculator through STAT > TESTS or by doing a quick google search for two-sample t-test or two-sample z-test. The result will be a percentage called the p-value. The lower the percentage, the less likely it is that they are at a common distance.

I hope this helps!