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Given a problem, we are asked to use a statistical method to come up with a conclusion. e.g. XYZ drug decreases heart diseases. (null hypothesis)

After searching on internet, I got a list of these tests:

Analysis of variance (ANOVA), Chi-square test, Correlation, Factor analysis, Mann–Whitney U, Mean square weighted deviation (MSWD), Pearson product-moment correlation coefficient, Regression analysis, Spearman's rank correlation coefficient, Student's t-test, Time series analysis

I presume all methods above can be applied. So I pick up student's t-test as my choice.

How could I know whether it is a maximum likelihood estimation which is unbiased, consistent and efficient? What I think is that we should know the Mean and Variance of the estimate to conclude. But it is nowhere in the notes I found online. =/

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Your question is unclear. Do you want to know how to check if an estimator is unbiased, consistent and efficient? Or do you want to find an estimator for a particular problem? – svenkatr Nov 27 '10 at 5:20
Your question is unclear. You make it sound like you can take any of these statistical tests and just apply them. Every test has its own assumptions based on the type of distribution you are working with. Typically one uses a method like the maximum likelihood estimation to figure out what distribution is best to apply to the data. Once you have a distribution, you can work with a test. – Tom Nov 27 '10 at 5:49
I am sorry for making this unclear.. Actually my question really is, what we make use of maximum likelihood estimation. To my understanding, maximum likelihood estimation(MLE) means we pick/"guess" the values of the parameters so that it resembles closest to the sample distribution. If population mean is the only parameter I am interested in, according to MLE, isn't it the same as sample mean? @Tom: can you please elaborate more on how MLE helps in deciding distribution to use? p/s: I picked t-test based on the assumption that the sample size is small and normal. – learnwhatever Nov 27 '10 at 8:46
MLE is a method devised to determine the parameters of a distribution, provided you already know what distribution underlies your data. It's useless if you don't know what your data mean. The best would be to use non-parametric tests if you have no idea at all about underlying distributions. – Raskolnikov Nov 27 '10 at 10:57
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I suggest you go ask on Cross Validated what a MLE estimation is and what a hypothesis test is. These are two different beasts. – Raskolnikov Nov 27 '10 at 12:01
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