

Significance of Correlation Coefficients 

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ClaudiaB posted on Monday, April 08, 2013  1:38 pm



Hi, significance of correlation coefficients is usually only dependent on the N of the sample and the correlation coefficient r. I ran a correlation model in Mplus and there the significances of the correlation coefficients (WITH) are calculated basing on the ratio of the coefficient to its standard error. In my data I get the following: Estimate S.E. Est./S.E. PValue A WITH B 0.300 0.088 3.413 0.001 C WITH B 0.293 0.078 3.766 0.000 Thus the strongest correlation (.30) is less significant than the smaller one (.29), which in the usual way of calculating significances would not be possible. Is there some way to get "normal" significance values in Mplus? Or do you have some literature I could refer to when reporting significances as calcultated in Mplus? Thank you 


Please send the output and your license number to support@statmodel.com so we can see the full situation. 


You are right that there is a simple formula for the standard error for a correlation that depends on only the correlation coefficient value and the sample size. But that simple formula is for a correlation among two observed variables that are normally distributed and where the variables are not part of an overidentified H0 model as in SEM. The correlations you point to involve latent variables and a categorical observed variable which are part of an overidentified H0 model estimated by WLSMV. In that case, the simple formula is not applicable. Instead, standard errors are computed using WLSMV. Their sizes depend on many factors including the model structure in complex ways. 

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