Social Housing Minister Amy Adams, on the other hand, says the number of homeless in New Zealand is actually around 4200.
The difference is that Adams - whose figure also comes from the Otago study - is referring only to people "without habitable accommodation".
Twyford is referring to the number of people sleeping rough, living in cars or garages, or living in emergency or temporary shelters.
While that may seem to capture a broad range of living situations, it actually matches the Government's official definition of homelessness.
The official definition was devised in 2009 by a working group of housing, statistics and welfare officials who concluded that it was important to recognise the "concealed homeless" if Government policy was to be effective.
The definition was peer-reviewed in 2015 by another working group, which approved it.
Conclusion: Fact (Though the homeless definition is broad by international standards).
Claim: New Zealand has the worst rate of homelessness in the Western world (Labour housing spokesman Phil Twyford)
The facts: New Zealand was ranked as having the highest homeless rate per capita in a piece of analysis published by Yale University last month.
The analysis was based on an OECD paper which said 0.94 per cent of NZ's population was homeless. The lowest homeless rate in the OECD was Japan, at 0.03 per cent.
The OECD paper said that NZ's high incidence of rough sleepers could partly be explained by its broad definition of homelessness.
As Social Housing Minister Amy Adams says, if NZ measured homelessness the same way Japan did, it would be ranked among the top of developed countries.
Japan only measures rough sleepers. According to the Otago study, New Zealand has around 1400 rough sleepers, or 0.03 per cent of the population - equivalent to Japan.
Conclusion: Mostly fiction. The study does not compare apples with apples, so it is unfair to say NZ has performed worse than every other country on the list.
