The treasurer, Joe Hockey, has again said Australians work six months of the year for the government – a claim that is untrue since the top marginal tax rate of 45 cents in the dollar cuts in only for earnings over $180,000.

Hockey said in an interview on Melbourne’s 3AW: “I want to give families a bit of a break with cost of living and that’s certainly Tony Abbott’s very strong view. We should put more money into the pockets of Australians. It’s their money. When Australians spend the first six months of the year working for the government with tax rates nearly 50 cents in the dollar, it’s a disincentive.”

“You’re working July, August, September, October, November, December just for the government and then you start working for yourself and your own household income after that for another six months, it is a disincentive, so we’ve got to bear that in mind. We’ve got to bear in mind that bracket creep is going to take middle-income Australians into the second-highest tax bracket over the next few years, which is a disincentive for people to work,” he said.

The 2% Medicare levy and the 2% budget repair levy do bring the marginal tax rate for high income earners to 49 cents in the dollar, with the temporary budget repair levy also cutting at for incomes over $180,000.

But 49 cents in the dollar is the marginal tax rate for high income earners – paid only on earnings over $180,000, not the average tax rate.

An analysis by the Australia Institute last year, after the treasurer made similar comments, found that even the top 1% of earners – on more than $290,000 a year – had an average tax rate of 39 cents in the dollar. The top 3% of earners, on more than $180,000 a year, had an average tax rate of 32%. Those in the second-highest tax bracket – earning more than $80,000 – had an average tax rate of 25%.

A spokesman for the treasurer said Hockey had been speaking “in very broad terms.”