Who proposed the reflective correlation coefficient? The Wikipedia page for the Pearson product-moment correlation coefficient has a section on variants of the idea. This includes the reflective correlation coefficient, which has had a citation needed tag since 2011.
$$R_{\text{reflective}} \left[X, Y \right] = \frac{\mathbb{E}\left[ XY \right]}{\sqrt{\mathbb{E}\left[X^2\right]\mathbb{E}\left[Y^2 \right]}}$$
Trying a few search engines, I have not found a plausible origin of this statistic. While its construction is quite straightforward from the Cauchy-Schwarz inequality, I would rather cite it if possible.

I followed the link provided by Sycorax, and quickly searched each result for any sign of citations. Here are the results of that search.

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*Higgens 2008 has a document preview available, but I do not currently have access to the whole document. The term "reflective" appears in the summary of tables including "Table 5. Descriptive Statistics: Reflective" and "Table 6. Merged Responses for the HQPD Characteristic: Reflective".

*Li 2012 is not accessible to me. The document preview mentions correlation, but nothing about a "reflective" correlation.

*Zhu 2014 mentions a "reflective correlation coefficient" but does not provide a citation.

*Chen 2015 mentions and mathematically defines a sample "reflective correlation coefficient" as found in the Wikipedia article. They do not cite a source for it.

*Nilsson et al 2015 give a definition of the reflective correlation coefficient that matches the Wikipedia article. They cite an IEEE standard that I have not been able to access yet.

*Buckley and Doyle 2017 mention the term "reflective" multiple times in their paper, as well as the term "correlation". But here they appear to be independent usages.

*Miyazawa 2017 mentions and uses a "reflective correlation coefficient" in a way consistent with the Wikipedia page, but does not provide a definition or citation.

*Hodžić and Namas 2017 is beyond my current access. The available abstract and list of references is not clarifying here. But a related paper with the same authors and similar title mentions the "reflective correlation coefficient" as related to the Pearson correlation. No citation is given.

*Rui et al. 2017 mention "reflective correlation coefficient", however it is not clear prima facie whether this is physical reflection or not. They do not cite a source for this term, nor give the equation of interest.

*Malevich 2017 is not accessible to me. The document preview suggest that various correlations are calculated, but gives not hint of any of them being "reflective".

*Miyazawa 2017 mentions a "reflective correlation coefficient" in a usage that appears consistent with the wikipedia article, but skimming the article did not show any definition or citation.

*Kowalczyk et al 2018 mention "reflective correlation" in parentheses to "Pearson correlation", but do not cite, define, or clarify this term.

*Nilsson 2018 which appears to define the reflective correlation coefficient, but does not cite a source.

*Noda 2018 define reflective correlation in the same way as the Wikipedia article. They do not cite a source, but rather link to a Science Direct summary that does not contain the term.

*Cordova 2018/2019 has an abstract in English that suggests the term "reflective" was used in a psychological rather than statistical sense. An equation appearing equivalent to the reflective correlation coefficient does not appear in the thesis.

*Tølløse et al. 2021 uses the term "reflective correlation coefficient in the same sense as the Wikipedia page, however they give no citation for it.

*Miyazawa 2022 mentions their use of a "reflective correlation coefficient", but an explicit definition or citation is not given.


User Skbkekas in Wikipedia created the description of reflective correlation on Dec 4 2009. You can “talk” to him on Wikipedia, and ask why he called it such.
