I am currently working on a tool which calculates a score for each sample (i.e. patient biopsy) it is run on. Input samples can belong to one of two categories: case and control. Usually, a user would run the tool on a number of samples from both categories. For each case sample, I would like to report whether the sample's score is significantly different from the scores of the provided control samples. In other words, for each case sample I want to assess the likelyhood of seeing a score at least as extreme as the observed score if the sample came from the control distribution. My problem is that I don't know the real control distribution; I can only estimate it based on the control samples the user provides.
Currently, I am calculating the mean and standard deviation of the scores of the control group. For every case sample, I am then calculating the z-score with respect to the control group (i.e. I subtract the control group's mean score from the sample's score and divide by the control group's standard deviation). If the absolute value of the sample's zscore is > 2, I report the sample as significantly different. However, I a worried that with this approach I do not take the sample size of the control group into account. Other simple approaches like t-tests seem not appropriate here, since I don't want to compare means.
Could someone suggest a more appropriate test for this use-case? Any help would be greatly appreciated.