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**"Normalizing" standard deviation between two data sets**

I have a baseline set of data collected which has a standard deviation of

**X**, and then I collected another set of the data under a different condition (different temperature), and this has a different standard deviation

**Y**. How do I cancel out the standard deviations, to only see the difference of the actual data as it varies with the condition change (temperature)? I try to stay vague, but if this doesn't make sense of what I'm looking for, I'll give my application example. Just a general topic to point me to would help if nothing else.