Shardendu Kumar Mishra Thank you for your valuable feedback and knowledge sharing. However, I would prefer a disattenuated correlation test if educational psychology or social science research uses self-report/self-rating questionnaires (involving reflective items). Honestly, errors exist in Pearson correlation (for example, test using IBM-SPSS software). Still, because of the Pearson correlation test limitation, the correlation value (involving the unknown error value) is possibly caused by the measurement (questionnaires) problem, and the correlation result/output does not represent the constructs. I will suggest researchers that test reflective constructs involving interval and ratio data rating questionnaires (reflective items) to conduct disattenuated correlation (please check the illustrated images I attached/shared). I hope the images can visualise what I try to express differently between these two tests. I try to encourage research tests and measure what they want to test with more suitable tests based on the research context (involving reflective questionnaire items).

Huey Shia Teo but isnt this a well known phenomenon? See for example this RG question some years ago: https://www.researchgate.net/post/Why-latent-variable-correlations-are-much-higher-compared-to-observed-variable-correlations

How are you planning to promote the use of disattenuated correlation or the correlation of latent variables?

Rainer Duesing Thank you for your valuable feedback and knowledge sharing. Good question: isn't this a well-known phenomenon? However, many still practice the Pearson correlation test instead of the disattenuated correlation. First, I should clarify that the disattenuated correlation test I am trying to highlight does not come from the latent variables in the same measurement construct variables (same questionnaires).

Usually, a measurement tool (questionnaires) needs to successfully go through EFA (pilot sample) and CFA (actual sample). CFA there, we also will test if the constructs have CMB (Common Method Bias) using a statistical test (Harman's Single Factor Test), and the CFA result also should make sure there are no multicollinearity exists among the constructs (in measurement model).

For example, some researchers are using the Pearson correlation test, some researchers try to see if the measurement construct relates to students ' achievement in specific subjects without checking the questionnaires with CFA, then directly produce the composite variable (mean value) and run the Pearson correlation and claim the relationship, even more worse talk impact when checking test, they conduct only Pearson correlation.

Honestly, I prefer to use SEM (CB-SEM) directly to test the model. If researchers are planning to use correlation (Pearson Correlation) to test the relationship between their measurement construct (reflective construct) and achievement (test result), please try to run a disattenuated correlation that will be more convincing.

Perhaps some researchers will say they plan to see the relationship between their measurement construct (reflective construct). The measurement model will help you in that case, but you should be aware of the multicollinearity problem.

In my opinion, there is no right or wrong; just a much more suitable test should make a preference, especially if you plan to generalize your findings to the public convincingly.

Huey Shia Teo you repeated good arguments, but again, this well know that you can explicily model the error with SEM and that this will imrove the estimation of correlations. You didn't answer my question how you are planning to promote the SEM approach?

Rainer Duesing Thank you for your feedback. My primary purpose is to share my knowledge and viewpoint on disattenuated correlation.

I should clarify that you mean "explicitly model the error with SEM and that this will improve the estimation of correlations." the estimation of correlations will not improve if the measurement (questionnaire) that consists of reflective constructs is too poor, which fewer researchers take note of.

My current research uses SEM (CB-SEM); with limited resources, I can only start promoting from my surroundings and keep sharing knowledge and ideas with possible platforms. I believe every researcher can be part of promoting the SEM (CB-SEM), and plenty of expert and knowledgeable researchers are working on it.

As a researcher, there is no right or wrong approach; most importantly, make sure tools, methods, and approaches fit your research purpose.

I hope this sharing will give insight into other research with the possible option when deciding on a correlation test such as disattenuated instead of Pearson correlation.

Huey Shia Teo, are you talking about the disattenuated correlation that Schmidt & Hunter describe here:

Schmidt, F. L., & Hunter, J. E. (1999). Theory testing and measurement error. Intelligence, 27(3), 183-198. https://doi.org/10.1016/S0160-2896(99)00024-0

See the attached PDF for a short excerpt showing the equations.

Bruce Weaver Thank you for your valuable feedback and knowledge sharing. We are on the same page, and I managed to get the full article here:

(PDF) Theory Testing and Measurement Error (researchgate.net)

"However, the bias introduced into estimates of correlations between constructs does not magically disappear when reliability reaches a particular level."(Schmidt & Hunter, 1999, p.192)

Which still has researchers who do not understand it. Thank you. Thumbs up!

While I agree with the points made by all so far in this discussion, I would add a caution. The statement that "disattenuated correlation enables the researcher to explain the correlation value- (without measurement error) ..." claims more than I think it should.

Disattentuation (either in its original sense of a direct adjustment for unreliability as estimated separately for each variable, or in the modern SEM sense of full-information estimation for all parameters in the model) only accounts for random measurement errors. Such errors deflate (i.e., attenuate toward zero) the true correlation, and hence disattentuation always increases the (absolute value of the) estimated correlation. However, potential non-random measurement errors (e.g., effects of A on indicators of B) are constrained to equal zero in your SEM model, and therefore the parameter estimates under that model take no account of them. Non-random or correlated errors (invalidity rather than unreliability), when ignored, can either inflate or deflate the true correlation between latent constructs.

Therefore, the statement I quoted should be framed more modestly, perhaps like so: "Disattenuated correlation enables the researcher to EXAMINE the correlation value- (WHILE ADJUSTING FOR RANDOM measurement error)..."

Burke D. Grandjean Thank you for your valuable feedback and knowledge sharing. Estimation methods play their role; when discussing estimation value, I understand there are too many estimate methods, and less research clearly explains which estimate method they used but explains their output/ result, perhaps questioning.

I agree with your statement that " Disattenuated correlation enables the researcher to EXAMINE the correlation-(WHILE ADJUSTING FOR RANDOM measurement error)..."

My point is that when a researcher conducts research that involves reflective items (reflective construct) from self-rating/ self-report questionnaires, I will suggest testing using disattenuated instead of Pearson correlation (composite/mean value).

I understand the possibility that you are trying to explain. Still, I believe that the suitable estimate method can overcome or minimize the potential since during the test (disattenuated correlation), I suggest running using IBM-SPSS-AMOS software (Maximum likelihood estimate), able to test the model fit value at the same time; this will help research more convincingly display that research model and data achieved good fit index.

Please check the photos I attached; I hope they help explain the possibility I am trying to express. Thank you.