The interaction between the El Niño–Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD) has been noted in many previous studies. However, the interaction is often presumed to exist in a robust manner. This paper questions this assumption and looks for statistical evidence for the robust existence of the ENSO–IOD interaction rather than chance co-occurrences. Consistent definitions of ENSO and IOD events were developed so that ENSO and IOD events identified are comparable in nature, strength, persistence, and time of occurrence during the year, relative to their natural variability. We applied a combinatorial probability test to the probability tables of ENSO and IOD events to test for robustness of our results and those computed from two published works. Our findings show that there is an asymmetry in the interaction between ENSO and IOD. The interaction between El Niño (EN) and the positive and negative phases of the IOD (pIOD and nIOD, respectively) is more robust, enhancing the EN–pIOD co-occurrence and suppressing the EN–nIOD co-occurrence. On the other hand, the interaction between La Niña (LN) and either phase of the IOD cannot be said to exist with the same robustness; the interaction suppresses LN–pIOD co-occurrence, but the occurrence of LN–nIOD might be coincidental. Further research is needed to determine the cause and mechanisms for the asymmetry in the interaction between LN and pIOD/nIOD.