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The performance of plastic optical fiber is greatly influenced by the related but distinct effects of mode coupling and differential modal attenuation (DMA). We establish a method for estimating the matrix that governs both of these effects and allows us to distinguish the two. We obtain partial quantitative estimates of this matrix for a particular graded-index plastic optical fiber (GI-POF). The sample we studied exhibited strong but incomplete mode coupling over 100-m lengths, while DMA was largely limited to a centerline defect. We show that much of the loss of the fiber can be attributed to mode coupling between mode groups with similar effective indexes.