I've collected fluorescence data from some bacterial cells.

Each cell has a gene in it which can be induced to fluoresce. However, even without being induced, the gene will still fluoresce a little.

I have subjected the cells to a series of concentrations of inducer, including 0% inducer, and measured the resultant fluorescence over time.

The fluorescence produced from cells that have not been induced is, effectively, 'background' fluorescence. Therefore, I would like to subtract the background fluorescence from the fluorescence measured in cells that have been induced in order to determine the fluorescence that is caused by induction.

$n = 3$ for all measurements.

My question is, can I take the mean fluorescence of the uninduced cells and assume that it is the true mean? I.e. assume that its $SE = 0$. If I can do that, when I subsequently subtract the mean background fluorescence from the mean induced fluorescence, the final calculated $SE$ will be lower.

Here's some example data:

 Inducer:       0%              5%
 1             3411            4965
 2             3427            4784
 3             3412            5379
 Mean          3416.666667     5042.666667
 SD            7.318166133     249.0385958

Given that the background will change for each experiment, I assume that the mean background measured is the true mean for that experiment. Is that not correct?

I must state that my maths/stats skills are rudimentary at best so please bear that in mind when answering.


No, you can't because the variance of the error term will be underestimated as a result. The simplest way to analyze your dataset is a two sample t-test where variances are not considered equal because they are clearly unequal for your data.The formula can be found here:


On the other hand, your proposition is similar to one-sample t-test, which is not the case here because the 0% mean is estimated rather than known.

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