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I have a set of values of r squared from different robust estimators. The r squared values fall not fall from each other. I want to test if they are significantly different from each other. Is it possible? If yes, what test should i use? Should i use ANOVA? (i doubt myself for using ANOVA since my values are not from group means). Thank you very much

btw, here are the estimators i used and took the r squared values for each estimator

#estimation
OLS<-lm(dv~iv)
Huber1<-rlm(dv~iv,maxit=50)
Huber2<-rlm(dv~iv,scale.est="proposal 2")
Tukey<- rlm(dv~iv,psi="psi.bisquare")
LTS<-ltsReg(dv~iv)
S<-lqs(dv~iv,method="S")
MM<-rlm(dv~iv,method="MM", psi=psi.bisquare, maxit=50)

EDIT: The r squared values (which i computed manually) are close to each other. (i.e 0.40567,0.41003,0.40809 ... ) and i want to be sure that they are significantly different from each other.

the data i simulated has X~N(0,1).

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  • $\begingroup$ Could you please explain what it might mean for any set of numbers to be "significantly different from each other"? It isn't evident how that could be translated into any testable hypothesis, especially since you seem to be developing these statistics from the same data. Where is the randomness? Where is a probability model for the variation? $\endgroup$
    – whuber
    Apr 9, 2019 at 13:32
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    $\begingroup$ Also, given these values, why would you care if they are significantly different? They are practically identical. It's hard to think of a situation where these differences would matter. $\endgroup$
    – Peter Flom
    Apr 10, 2019 at 12:20
  • $\begingroup$ thank you sir. i just realized that i just have to accept that the robust estimations have similar r squared values given cases of leverage points in my dataset. i am working on my undergrad thesis and i'm literally panicking since they yielded similar results. thank you very much $\endgroup$
    – bel
    Apr 10, 2019 at 13:09

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