This paper investigates how black-box representation of sub-systems in a larger small-signal state-space model influences the results from participation factor analysis. The results show that the value of individual participation factors associated with the states of a black-box sub-system on diagonalized form can be misleading. To avoid this issue, participation factor analysis involving a black-boxed sub-system should be based on aggregation by the complex sum of participation factors associated with the subsystem. The reason is that individual participation factors of the diagonalized sub-system can assume high values that do not reflect a physical interaction with other sub-systems. However, the individual participation factors of any transparent part of the system model can still be studied according to established conventional methods. These findings are obtained from, and demonstrated by, analysis of the small-signal dynamics in an offshore islanded AC grid with two HVDC converter terminals applying grid forming control and two equivalent grid-following converters representing separate wind farm clusters.