The planet-metallicity correlation serves as a potential link between exoplanet systems as we observe them today and the effects of bulk composition on the planet formation process. Many observers have noted a tendency for Jovian planets to form around stars with higher metallicities; however, there is no consensus on a trend for smaller planets. Here, we investigate the planet-metallicity correlation for rocky planets in single and multi-planet systems around Kepler M-dwarf and late K-dwarf stars. Due to molecular blanketing and the dim nature of these low mass stars, it is difficult to make direct elemental abundance measurements via spectroscopy. We instead use a combination of accurate and uniformly measured parallaxes and photometry to obtain relative metallicities and validate this method with a subsample of spectroscopically determined metallicities. We use the Kolmogorov-Smirnov (KS) test, Mann-Whitney U test, and Anderson-Darling test to compare the compact multiple planetary systems with single transiting planet systems and systems with no detected transiting planets. We find that the compact multiple planetary systems are derived from a statistically more metal-poor population, with a p-value of 0.015 in the KS test, a p-value of 0.005 in the Mann-Whitney U test, and a value of 2.574 in the Anderson-Darling test statistic, which exceeds the derived threshold for significance by a factor of 25. We conclude that metallicity plays a significant role in determining the architecture of rocky planet systems. Compact multiples either form more readily, or are more likely to survive on Gyr timescales, around metal-poor stars.
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