The correlation between close-in super Earths and distant cold Jupiters in planetary systems has important implications for their formation and evolution. Contrary to some earlier findings, a recent study conducted by Bonomo et al. suggests that the occurrence of cold Jupiter companions is not excessive in super-Earth systems. Here we show that this discrepancy can be seen as a Simpson's paradox and is resolved once the metallicity dependence of the super-Earth–cold Jupiter relation is taken into account. A common feature is noticed that almost all the cold Jupiter detections with inner super-Earth companions are found around metal-rich stars. Focusing on the Sun-like hosts with super-solar metallicities, we show that the frequency of cold Jupiters conditioned on the presence of inner super Earths is , whereas the frequency of cold Jupiters in the same metallicity range is no more than 20%. Therefore, the occurrences of close-in super Earths and distant cold Jupiters appear correlated around metal-rich hosts. The relation between the two types of planets remains unclear for stars with metal-poor hosts due to the limited sample size and the much lower occurrence rate of cold Jupiters, but a correlation between the two cannot be ruled out.${39}_{-11}^{+12}\mathrm{\%<img\; src="./W020240418469376285858.png"\; width="120"\; height="54"\; uploadpic="U020240418467858558352.png"\; data-uploadpic="U020240418467858558352.png"\; needdownload="true"\; data-needdownload="true"\; style="text-align:\; center;\; font-family:\; sans-serif;\; width:\; 50px;"\; oldsrc="W020240418469376285858.png"><span\; style="font-family:\; sans-serif;"></span><span\; style="font-family:\; -apple-system,\; system-ui,\; "Segoe\; UI",\; Roboto,\; "Noto\; Sans",\; Ubuntu,\; "Droid\; Sans",\; "Helvetica\; Neue",\; sans-serif;\; font-size:\; 16px;">,\; whereas\; the\; frequency\; of\; cold\; Jupiters\; in\; the\; same\; metallicity\; range\; is\; no\; more\; than\; 20\%.\; Therefore,\; the\; occurrences\; of\; close-in\; super\; Earths\; and\; distant\; cold\; Jupiters\; appear\; correlated\; around\; metal-rich\; hosts.\; The\; relation\; between\; the\; two\; types\; of\; planets\; remains\; unclear\; for\; stars\; with\; metal-poor\; hosts\; due\; to\; the\; limited\; sample\; size\; and\; the\; much\; lower\; occurrence\; rate\; of\; cold\; Jupiters,\; but\; a\; correlation\; between\; the\; two\; cannot\; be\; ruled\; out.</span>}$

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