I have a dataset of observations and want to test whether any of these observations is significantly different from the remaining observations. I could do this by performing a t-test on the mean of these remaining observations and test whether that is different from the one observation being trialled.
However, Not all observations should have the same weight. It's quite straight forward to use weights when calculating the mean, but how to do that for the standard error, and does this have consequences for the t-test that will be performed?
Any good suggestions will be highly appreciated.
Well we could indeed (for example) look at interquartile ranges and compare extreme distances from this range, but that would still not include giving weights to individual observations. Basically, we have more "trust" in some observations than others, and want to include that into the analysis. I'm not aware of any tests (t-test or outlier tests) that can do that.
Yes you can realize a weighted t-test. I did it with the package "survey" under the R statistical software. With this package, you can weight your mean and realised the t-test with the weighted mean.The command for weigthed t-test is : svytest()
No need for a package there. There is a weights argument for the linear model function (lm).
To answer my own question, I was notified of a great R-blog that provides a good alternative as well: http://www.r-bloggers.com/weighted-t-test-in-r/
Many thanks for all the contributions, really helpful!
Thanks Pablo! I will explore that package further. I haven't worked with it yet.
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