First I will describe my problem (1), then solutions I found (2), and then pose the question (3).
1) I am a student making a simple program for statistical analysis of data for a biological laboratory. The situation is as follows: They have a protein and measure some property three times (to eliminate measurement error). Then they mix the same batch of protein with some chemical and measure the same property again twice. In the end they want to know if the measurements are different enough. (I know the number of measurements is low, but it is the maximum they can do).
2) If we assume that the samples are independent I would choose Welch's t-test, because we cannot assume the same variance. However they say that, due to the fact that we measure the same batch of protein three times, and then two times with some chemical, the before and after measurements are related samples. But for related samples I only found paired t-tests, which cannot be used here, because there are no explicit pairs. The only thing that comes to my mind is to pair each measurement from each set.
3) How does one measure statistically the difference of a property and test whether that difference is statistically significant given this design? We have 3 measurements of batch of protein before applying a chemical and 2 measurements after applying a chemical. Measurements are repeated to eliminate error in measurement device.