# I Outlier or not?

1. Feb 16, 2017

### bacondoodle

Hi,

I have measured secretion of a hormone and I am normalizing it to the total cellular content of the hormone. I have used Grubb's test for determining outliers (GraphPads online calculator) and there are no outliers in the values for amount of secreted hormone, nor for hormone content. However, when I normalise it (secreted hormone / total hormone content) there are outliers in the resulting values. Should I exclude them even if there are no outliers in the original data?

Thanks

2. Feb 16, 2017

### Staff: Mentor

Generally you do not exclude outliers unless there is a specific experimental reason to do so. Like a machine malfunction or user error.

Outlier tests should not be used as a basis to exclude data. Instead they should be used as a basis to examine specific cases and see if there was some kind of experimental error.

3. Feb 16, 2017

### Stephen Tashi

As I understand the situation, both secreted hormone $S(i)$ and total hormone content $T(i)$ vary from sample to sample. Grubbs test assumes you are testing a normally distributed population. If $S$ and $T$ are normally distributed, the ratio $S/T$ isn't normally distributed. So, theoretically, Grubbs test does not apply to $S/T$.

In practical situations it isn't impossible that a random variable that is not normally distributed by theory can still be approximated by a normal distribution. However, you should determine that the normalized values $S/T$ do have an approximate normal distribution before paying attention to the results of a Grubbs test for outliers on the normalized values.

4. Feb 16, 2017

### FactChecker

I agree, with one caveat. Suppose there is some reason to know that a data point can not be correct or is just way too rare to be expected in a sample of that size. In my opinion, it can be excluded even without understanding what may have gone wrong experimentally. The reason requires knowledge of the subject that is independent of the experimental result.

5. Feb 16, 2017

### Staff: Mentor

In the end, the important thing is to disclose the exclusion of the data and explain the reasons. Then, the scientific community can agree or disagree through peer review and citations.