Hi everyone, I have a basic question on statistics.(adsbygoogle = window.adsbygoogle || []).push({});

Suppose you have a biological assay to test a given property of some molecules.

At some point in time you have tested N different molecules M_{1}, M_{2}, ..., M_{i}, ..., M_{N}, and for each you have repeated the test a number of times R_{i}. The results are P_{i}.

Example. You have tested N=4 molecules doing R_{i}={3,2,1,1} repeats. The results are P_{i}={{5.5, 6.0, 5.7}, {7.9, 8.1}, {6.3}, {8.5}}.

Now, in practice the way results are reported (at least where I work) is: for each M_{i}, mean and standard error of the mean based only on the actual repeats for each molecule.

Which means, for molecule 3 above the standard error of the mean is quite small, for molecule 1 it's larger and for the last 2 molecules it isn't calculated.

And even more worryingly, when by chance two repeats give exactly the same result, you find s.e.m.=0 !

I can't help thinking that this is wrong. But my knowledge of statistics is limited, that's why I'm asking for help here.

Doesn't a 'method', and therefore an assay, have an inherent standard deviation SD that is based on the total observed variance? Shouldn't we express all results based on this single, general SD?

So in practice, wouldn't it be more correct to express the results as:

P(M_{i}) = mean(P_{i}) +/- SD/sqrt(R_{i})

This way, molecules that are tested only once would still get a standard error, and those for which repeats give close results wouldn't get an unreasonably small s.e.m.

Or am I wrong? What do you think?

Thanks

L

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# Standard deviation for a biological assay

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