With Halloween on Monday night, it seems the government has tried to get into the spirit by once again attempting to scare the public into thinking the welfare system is bloated and wasteful. But as has been the case so many times on this issue, the only horror involved is that we have a government that continues to treat the public as idiots by using figures that collapse under the slightest scrutiny.

On Friday a story on the front page of the Australian relayed the views of the social services minister, ­Christian Porter, that the welfare system was flawed because “thousands of parents claiming government benefits are financially better off not getting a job”.

To support the need for welfare cuts to prevent this supposedly unjust situation, an example was provided of a person who despite not working would receive $52,523 from various government payments – an amount more than the $39,841 take-home pay of the median worker or even the $49,831 brought home by the median full-time worker.

As Kurtz would say, “The horror! The horror!”

Well no, actually.

Who is this shocking example that should have us gnashing our teeth over the bloated, bludger-inducing welfare system?

Why, a single parent with four children aged four, seven, 10 and 13 who neither receives any employment income, nor any child support from (presumably) the father, and who is paying $400 a week in rent.

It was a curiously specific example. It is rather odd that this government, which has steadfastly refused to provide the traditional tables in the budget detailing the impact on families of differing sizes and incomes, is able to now come up with such a precise example of a family when it wants to suggest welfare spending needs to be cut.

But it is patently absurd to hold up such a family as an example of anything, let alone the welfare system.

In 2012-13, of the 6.7m family households in Australia, just 580,000 or 9% were single-parent households with dependent children. Ben Phillips, from the ANU’s centre for social research and methods, estimates that only 4% of single parents have four or more kids and only about 2.5% are in a situation where their income would be such that they would be eligible for all the income this hypothetical person is getting.

So we are talking small numbers. And the example is both oddly specific and oddly vague.

$400 a week for rent? Where and for what type of house? If the three eldest children are of different genders that would mean at least two bedrooms for them and one for the four-year-old, plus one for the parent. A four-bedroom house for just $400 rent a week? Good luck finding that.

And it is worth noting that the $400 a week rent already accounts for 40% of her income.

But the real reason we should laugh with scorn at the example is not just that it seems utterly divorced from reality and at best represents a minute number of Australian households, but because it is also absurdly misleading.

Now it’s true that $52,523 is more than the take-home pay of a median wage earner, but that is a very disingenuous comparison. It is not comparing like for like.

The comparison would make sense only if median wage earners taking home $39,841 were also single parents with four children. And were a single parent to be earning only that amount, she too would have access to welfare like the family tax benefit A, which for four similar aged kids would be about $23,400.

As it is, the comparison is as stupid as trying to work out who is the better batsman by comparing David Warner’s test batting average with Steve Smith’s average in T20 matches.

Comparing household incomes means taking into account the size of each household. This is obvious when you think about it. A family of four needs more income than that of a single adult to achieve the same living standards, because it costs more to feed, clothe and house a family of four than a single person.

To compare households of different sizes economists use an “equivalised” measure.

The latest household, income and labour dynamics in Australia (Hilda) survey, released in July, estimated that the median equivalised household disposable income in 2014 was $45,505.

Now as that is still less than what this hypothetical single parent is getting in welfare, it sounds like a clear case of her getting too much. But that $45,505 amount is for a single person household.

Economists estimate that to maintain the same standard of living, you need to earn 30% extra per dependent child. So a single person who takes home $1,000 a week has the same standard of living as a single parent with one child earning $1,300.

So for a single parent with four kids to be on the median household income, she doesn’t need to earn $45,505. She would need to earn $100,111 – or almost double what this hypothetical (and extremely rare) single parent is receiving.

Or to put it another way, when you account for the size of her household, this hypothetical single parent, who apparently has no need to go back to work because life is so good on welfare, is equivalent to a single person earning $23,874 – or $459 a week. Not exactly living the high life.

But that is no shock. Never in the history of the world has being a single mother with four kids been considered a ticket to easy street.

That the government needs to resort to such an absurd example highlights not that the system is wasteful and is deterring people from working, but rather that it is actually quite targeted and that the government is bereft of a good case to justify the cuts it plans to make.

So try again, minister, and maybe next time leave the attempts at horror to the kids going out trick or treating.