What kind of anomalous data, and what is the explanation for it? This is the first time I'm hearing that atheists or science ignores data...
The following dissertation is a good summary of the arguments against Physicalism. You will find many scientific studies mentioned therein on paranormal phenomena (mostly ESP). These scientific studes are basically the "anomalous data" that mainstream science chooses to mostly ignore:
http://repositories.lib.utexas.edu/bitstream/handle/2152/ETD-UT-2009-12-682/SMITH-DISSERTATION.pdfFurthermore:
- the studies of Masaru Emoto on the effects of consciousnesss on water
- the UFO phenomenon with thousands of recorded cases that have no conventional explanation
- the scientific studies on the events of 9/11 and why the official version of these events is a lie
- plus a lot more
Another good source that sums of up the scientific evidence for the Conscious Universe is the book "The Source Field Investigation" by David Wilcock.
There are a number of other phenomena such as reincarnation, ghosts & spirits, cryptozoology, mythological history (e.g. Atlantis), "free energy" devices, and even some philosophical arguments which also fit into this expanded worldview.
The model that explains all this, to put it very briefly and incompletely, is the following:
The Universe is essentially One Conscious Being and we parts of that being. We are foremost eternal spirits having a brief human experience. Consciousness is the primary property of the Universe and influences matter (i.e. mind over matter). There many more "dimensions" or layers of existence above and beyond this material realm. There are many ET civilizations existing on other planets and the higher realms. Planet Earth has been put in a kind of quarantine for several thousands of year for the purpose of spiritual growth. For this purpose certain powerful, "evil" groups were allowed to take control over the Earth manipulating the people into believing the current limited worldview. Their reign is ending now though (this year). Humanity's distant past is far different than what is told in the history books, for example there were ancient, highly advanced civilizations that existed many thousands of years ago (and also on Mars).