Peter Miles, 61, his 58-year-old wife Cynda, daughter Katrina, 35, and Mr Cockman's four children - daughter Taye, 13, and sons Rylan, 12, Arye, 10, and Kadyn Cockman, eight - were found dead at the Miles' Osmington property, northeast of Margaret River, on Friday.
"The members of this family were deeply connected to the town of Margaret River", Commissioner Dawson said.
"We try and get back to business as normal, the community will certainly be endeavouring to do that, and I guess as time goes on you talk a little less about it".
"We thank the community for their support and ask that our privacy is respected as we grieve". It is such a small community and it will have such a huge effect.
"At this point in time, we don't have any information to raise further public concern".
Australian Medical Association president and West Australian local Michael Gannon said the trauma of this incident would no doubt be visited on every person in the town.
Felicity Haynes, who lives on a neighbouring property, told broadcaster ABC the family involved were "caring neighbours".
"They were good people".
Mass shootings are uncommon in Australia and Friday's was the deadliest since a 1996 massacre left 35 dead at Port Arthur in Tasmania. Neighbors reported that the children were home-schooled there.
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"Like all other jurisdictions across Australia, Western Australia's gun laws have also been eroded as pro-gun lobby groups continue to place pressure on governments", said Sam Lee, chairman of Gun Control Australia. Applicants are also required to undergo firearms training, and weapons and ammunition must be stored separately, according to the law.
The generally accepted definition of a mass shooting - four deaths excluding the shooter in a single event - has been met only once in Australia since then.
He noted, however, that there were no significant changes in gun-related homicides in the country.
But researchers say it is hard to determine with much certainty how the changes affected gun violence over all.
In an editorial a year ago, the Age said it respected citizens' rights but that there are "some freedoms that have no place in a civilised society, and none more so than the carrying of illegal firearms".
Mr Cockman, who was estranged from Katrina, said he had not spoken to Peter and Cynda "since they cut me off from my kids" but being angry served no objective.
"I actually spoke to him the night before the incident", said Richard Dosser, who lives about two kilometres down the road.
On Saturday, Commissioner Dawson confirmed three longarm firearms were recovered at the property, all of which were licensed to Peter Miles.
"This is a very distressing day for Western Australia", he said. They would identify victims only after next of kin had been notified, said the police.