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Test of {macroscopic realism} (MR) is key to understanding the foundation ofquantum mechanics. Due to the existence of the {non-invasive measurability}loophole and other interpretation loopholes, however, such test remains an openquestion. Here we propose a general inequality based on high-order correlationsof measurements for a loophole-free test of MR at the weak signal limit.Importantly, the inequality is established using the statistics of \textit{rawdata} recorded by classical devices, without requiring a specific model for themeasurement process, so its violation would falsify MR without theinterpretation loophole. The non-invasive measurability loophole is alsoclosed, since the weak signal limit can be verified solely by measurement data(using the relative scaling behaviors of different orders of correlations). Wedemonstrate that the inequality can be broken by a quantum spin model. Theinequality proposed here provides an unambiguous test of the MR principle andis also useful to characterizing {quantum coherence}.

Loophole-free test of macroscopic realism via high-order correlations of measurement