Hi everybody,
I'm quite new in this kind of studies, my question is the following. I have a certain sample data set characterized by mean, standard deviation, standard deviation of the mean and confidence interval for the mean of the population. Then, I have a certain value coming from FEM analysis and I want to compare in order to understand "how much is good" the numerical result.
Which is from your POV the best way to do it? I don't believe that the comparison with the population mean is a good solution: my reason is the following. Suppose I have two independent data set coming from a normal population, and I am interested in the difference between the two means. From t distribution I have an interval estimate of the means difference, and of course standard deviation and standard error of the mean. Now if I compare FEM result with the mean of the first group, then FEM result with the mean of the second group I get relative errors below 5%, let's say. But if I compare the differences from FEM with the difference from statistical analysis I have a much higher error, let's say 50%.
Then do I have to simply say that my numerical values are within x+/-standard deviation? Or that they are within the confidence interval for the mean (or the difference between the two means)?
I usually trot out the usual suspects: Mean, Median. Mode, Max, Min and standard deviation. Plot on cartesian, semi log and log-log coordinate and see where the analysis leads me
I hardly understand what you actually want to do.
"comparing" a sample mean to a given fixed given value (usually) means to test the null hypothesis that the sample is from a population with the mean being that given value. You can check if the confidence interval of the sample mean covers the fixed value. If not, you can reject that null hypothesis.
However, I don't think than such a test is very meaningful. Imho it is more instructive to just interpret the confidence interval (as a whole, taken as a kind of interval that shows a range of possible population means which which the observed sample is not too incompatible) in relation to the given fixed value, based on subject matter knowledge / expert judgement.
Dear Rick Manner and Jochen Wilhelm
first of all, thank you for your answers.
As Jochen highlighted, my trouble is how to interpret my FEM results given the statistical analysis results. It seems that the best way is to use the confidence interval and simply show if FEM results are within it. I calculated the CI for the first group, the second group and for the difference between them; then, I just have to show if my FEM results are found in those CI, isn't it?
Thank you,
Luigi
"then, I just have to show if my FEM results are found in those CI, isn't it?"
Almost :)
To my opinion, it is better to interpret the CI as a whole - not just looking if the FEM result is within or without (this would be the same as a simple test where you either cannot or can reject H0, respectively).
You should look if the CI limits extend relevantly far from the FEM value or if the limits are irrelevantly close to the FEM value. What "relevant" is depends on the context, that judgement needs expert/subject knowledge (it's not a statistical question!).
If both CI limits are irrelevanly close to the FEM value, you may conclude that your sample provides sufficient evidence that the population mean your sample was taken from is very likely "practically similar" (only irrelevanlty different) to the FEM value. Otherwise, the data is still compatible with population means that are relevanly different to the FEM value, so that one might not want to state that the sample data confirms a population mean "similar" to the FEM value.
I hope that lenghly explanation made my point a bit clearer.
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PS: I know that this interpretation of a CI is Bayesian, what is not correct logically. However, given the prior is not highly informative or "strange", or the sample size is at least moderate, a maximum posterior interval would look not too different, and the interpretation of "relevance" usually leaves more room for arbitraryness than is solved by the academic distinction between CIs and posterior intervals, imho.
Wise and pragmatic words by Jochen, especially regarding the interpretation of CIs.
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