Determining whether investment results are due to luck or skill is no small task for even skilled analysts evaluating an active investment manager; given the amount of randomness inherent in markets, it can be very difficult to determine which is which. Fortunately, the field of inferential statistics exists specifically to analyze such situations and help to distinguish the signal from the noise, and determine when results are likely randomness and luck versus when there is at least a high probability that skill or some other factor is at play.
When inferential statistics is applied to evaluating active management, the results are questionable at best - a small subset of managers are clearly inferior, and for virtually all the rest, there are simply no clear indicators of skill at all; even when some modest level of outperformance occurs, the results are rarely ever statistically significant. Of course, just because an actively managed fund has outperformance that is not statistically significant doesn't mean the manager isn't actually generating real outperformance and adding value. It's just that the outperformance isn't large enough relative to overall market volatility to clearly show whether the results are due to luck or skill.
Unfortunately, though, the caveat is that given just how incredibly volatile markets really are, searching for "statistically significant" outperformance may actually be a lousy approach for evaluating managers; even if a manager really does outperform for an extended period of time, the available tests simply are not capable of distinguishing skill from market noise given the tenure of even long-standing managers. In fact, when tested to determine the effectiveness of the approach in the first place, the reality is that even if a manager is adding several hundred basis points of outperformance, annually, for more than a decade, there is still a more-than-90% likelihood that inferential statistics will FAIL to identify the signal that really is there.
In other words, if the goal is actually to determine which active managers really do add value, searching for statistically significant outperformance is an approach with an overwhelming likelihood to fail, even in situations where it should be succeeding! Which means in the end, failing to find statistically significant outperformance amongst active managers may actually be less a failure of active management itself, and more a problem with using an approach that was unlikely to successfully identify good managers in the first place!