The most distant Kuiper Belt objects (KBOs) appear to be clustered in longitude of perihelion and in orbital pole position. To date, the only two suggestions for the cause of these apparent clusterings have been either the effects of observational bias or the existence of a distant giant planet in an eccentric inclined orbit known as Planet Nine. To determine if observational bias can be the cause of these apparent clusterings, we develop a rigorous method of quantifying the observational biases in the observations of longitude of perihelion and orbital pole position. From this now more complete understanding of the biases, we calculate that the probability that these distant KBOs would be clustered as strongly as observed in both longitude of perihelion and in orbital pole position is only 0.2%. While explanations other than Planet Nine may someday be found, the statistical significance of this clustering is now difficult to discount.