I am just wondering if qPCR data should normally be analysed with a two-tailed test because we are wanting to test the sig of expression in either direction (up- or down-reg).
But we can see the direction of expression before we run sig testing. So if there is a clear up-regulation or down-regulation is it acceptable to perform one-tailed testing.
Obviously, a two-tailed test will produce a more conservative p value and I think limit bias maybe... Also the experimental design dictates the test. Is bias the only reason or is there something blindingly obvious I am missing.
Please excuse my lack of statistical knowledge... But would there ever be a reason to present both values?
Thanks for your time :)
No there would never be a reason to present both values.
A hypothesis test (following Neyman/Pearson) is a tool that allows to control the (expected maximum) rates of false decisions. So please carefully reflect these two words: "rate" and "decision".
The first word tells you that a test is not an inference about a particular case. Actually, the particular case is of no interest at all! Gosh! Really! Consider the influence of a treatment on the gene activity. You can perform a hypothesis test (whatever one or tow-tailed). The test leads to either the acceptance or the rejection of a null hypothesis, determining your decision (e.g. to believe or to state that the treatment does or does not change the gene activity) (*) Where we are at the second word. So a test doe NOT tell you ANYTHING about your treatment. It is only to guide your decision, not to make too many wrong decisions in the long run.
The whole procedure makes sense when you have a process of repeated decisions to make, where the single decision has no meaning. An example in science (actually the only that I can think of) is a screening (by definition an automated process with a family of unspecified alternative hypotheses). Here, tests allow to control (family-wise) error rates or false-discovery rates.
So coming back to your question. If you do a test, you do it to control the rate of wrong decisions. If you would reject the null hypothesis for both directions, then this control is only provided by a two-sided test. The data can still wrongly show a more or less "clear" regulation in one direction, and as soon as you decide to use this (possibly wrong) information you will increase the rate of wrong decisions.
Further, if you perform a one-sided test, you have to specify the direction on theoretical grounds. If it then happens that you see a rather clear regulation but in the "unexpected" direction, you must not reject the null. If you specify the side of the test by looking at the data, you are using (uncertain) information twice (what the test does not consider), eventually leading to unwanteldy higher false-positive rates.
(*) NB: often such tests are performed without controlling the power, so the rate of false acceptances of the null hypothesis ["false negatives"] is not controlled; therefore the null hypothesis is often not explicitely "accepted" and the result after a "non-significant" test is undefined - a logical hogwash but nevertheless quite common practice).
Thank you Jochen for answering. You always explain your answers very clearly to me.
My investigation was to measure expression of a number of unrelated genes in "test" tissue vs control tissue. So really a two-tailed test is correct as any significant change in expression of the test relative to the control would be meaningful. But because of the basic design of my experiment, I could also hypothesis that expression will be greater in my test tissue; this was actually a real posibility.
The majority of genes were up-regulated, one down and a couple did not change when tested with two-tails. Clearly, if I test a data set that shows clear regulation in one direction with a one-tail test then the p value would be lower than it would be if tested the same data set with a two-tailed test, right. So, if a one-tailed test pushes the result below the significance threshold where a two-tailed test would't, this is a false-positive, right??? Because I have increased the rate of wrong decisions?
But if I had decided I was testing a one-tailed hypothesis for all my data sets and not a two-tail, does this then mean the one-tailed result is now meaningful and not false pos?
Having a signifiicant result from a one-tailed test that was non-significant on a two-tailed test is not neccesarily a false-positive. It is statistical issue, and it is about the procedure. If you stick to the procedure (i.e., specify a priori what direction would be relevant, and if you then decide to do a one-sided test, then call it only significant when the observed effect goes into the specified direction and call it non-significant otherwise [no matter how tiny the p-values for that direction might be!]), it guarantees that the rate of false-positives is controlled. If you don't stick to these rules you loose the control. You will never know which of your decisions is right or wrong. Test are not about a particular decision, they are about rates.
The results of one-sided tests are ok when you stated the direction before the test. For instance, when you state that the gene should/must(!) be up-regulated, and it the experiments shows a down-regulation, then you MUST NOT call this "significant", because following your hypothesis the treatmen CAN NOT cause the down-regulation and the observation MUST BE a "bad coincidence", by definition. The key problem with one-sided tests is that the reviewers must belief you that you would not have called a result "significant" if it was to the opposite direction.
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