How to ask if point is significantly different from a mean and stdev I am working with some groups of data, and I'm trying to find the best way of understanding if a data point is significantly or confidently above a baseline point. I am calculating the baseline point as the mean of a number of samples, and then a standard deviation to associate with it. However, for my sample being compared to the baseline, I have a sample size of one, so no mean or standard deviation.
Is there a good way to determine a confidence or significance that my sample point is elevated over the baseline point?
I was thinking something like this (in python):  
R = stats.t.interval(0.95,len(s)-1,loc=mean,scale=std/math.sqrt(len(s)))
 A: You don't need a standard deviation for your one point to know it it's an outlier. You just need to know its deviation from the average of the other points.
By finding the mean $\mu = n^{-1} \sum_i x_i$ and variance $\sigma^2 = (n-1)^{-1} \sum_i (x_i - \mu)^2$, you are effectively fitting a model to your data saying that points are being generated by draws from a distribution with that mean and variance. If you further assume that distribution to be normal, then you can actually compute the probability $Q$ to get a value $x$ with $z = (x - \mu)/\sigma$ larger than some deviation as $Q = {\rm erfc}(z/\sqrt{2})$. Conversely, given an acceptable error rate at which you will are willing to mis-identify outliers, you can compute the threshold $z$ over which you should classify a point as an outlier. Without some assumption for the shape of the distribution, you won't be able to associate a deviation with an exact probability, but $z$ is still a useful characterization of the degree of deviation.
