However a prior question of the Mainstream model that might be relevant to this approach is: "What does Occam's razor do to Inflation, DM or DE?"
From that paper:
As shown in Table III our evidence for an anomaly is always above H = 3, i.e. “strong evidence”.
(emphasis mine)But even when different razors agree on an anomaly – such as the axis of evil – one should not trust the result blindly. The issue of systematics remains of paramount importance, as shown by the significant differences in H obtained from the various datasets and methodologies used to deal with the galactic foregrounds. And one should bear in mind that even the most enthusiastic “Ockhamist” would be unlikely to claim for his or her favorite razor a freedom from ambiguity better than H = ±0.3 or so. In addition it’s probably fair to say that the trouble of rewriting cosmology textbooks deserves in itself a penalty factor. This is hard to evaluate but it may translate into the requirement of a higher level of evidence than “strong”, at the phenomenological level. Perhaps the ever improving polarization maps will have a say on the matter and tilt the scales. This issue is currently being very actively investigated.
The question is exactly how 'strong' does the level of evidence have to be before people go to all "the trouble of rewriting cosmology textbooks"?
However the desire not to fall into the trap of making a false positive, (e.g. requiring an improvement in I(D, T ) of at least 5 for a decisive result,) i.e. saying the anomalies are there when really they are not, inevitably increases the chance of making a false negative, saying the anomalies and not there when really they are.According to some authorities, strong evidence for a theory over a “base model” requires an improvement in I(D, T ) by at least 3 (see xxx). The title of “decisive evidence” is not normally bestowed unless the improvement exceeds 5.
The paper deals with the low-l power deficiency separately from, and prior to, the Axis of evil, it concludes that the deficiency disappears after 'shaving' whereas the Axis stubbornly remains.
However these anomalies are not independent, for if the AoE actually exists and is caused by local contamination, then the low-l power deficiency becomes even more pronounced and I would guess would actually survive the stringent 'shaving' of this analysis.