I am trying to understand how much an observation is compatible with other data, given that the sample size of this other data is very small ($n=5$).

In practice, I have several measurements: $x_{1}, x_{2}, \dots, x_{n}$. Given that $n$ is small the pure statisical error on the model is large. Now I have another observation $x_{0}$, and I would like to know how compatible this observation is with the rest of the data.

If I'm not mistaken (and I may since my background in statistics is bad), what I want is the likelihood of $x_{0}$ given $x_{1}, x_{2}, \dots, x_{n}$. For the sake of simplicity, I am assuming a gaussian distribution. But how to properly propagate the errors?


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