More than 24,000 Scottish families are facing severe disadvantage, with Glasgow's population faring the worst, according to a new report.

The study ranks areas of the Scotland according to the hardship they face, and highlights vast differences in fortunes among groups.

The figures show one in ten families in Glasgow faces severe disadvantage – three times the national average.

The study published today by the think-tank Demos looks beyond purely financial measures of poverty and examines instead how a combination of issues such as unemployment, overcrowding and poor health can compound problems faced by families.

The study looked at low income, unemployment, physical and mental health problems and a lack of qualifications in 28,000 households in Scotland.

Families affected by four or more disadvantages were considered "severely disadvantaged".

Louise Bazalgette, the report's author, said the work recognises that hardship is about more than low income.

"It provides insight into the struggle thousands of families across Scotland go through on a daily basis coping with poverty, worklessness and poor health," she said.

"The extent of severe disadvantage in some areas of Scotland shows the scale of the challenge for some local authorities, who need to find effective ways to work with families facing a complex set of problems at a time of dwindling public resources."

Regions with the lowest proportion of very disadvantaged families included Grampian, east and west Dunbartonshire and Edinburgh. In Glasgow only 38% of families were unaffected by any of the social disadvantages surveyed. Some 11% were affected by four or more.

South Lanarkshire families were the next most likely to face major disadvantages, followed by those in North Lanarkshire and Fife.

However, South Lanarkshire was also shown to be more unequal than any other part of the country. The proportion of families without any significant challenges there – 58% – is higher than the national average, but so is the 7% with four or more disadvantages.

Across Scotland, on average 53% of families faced no disadvantages while 4% were affected by four or more.

The research also found households in Scotland with children in which the parents are unmarried are six times more likely to be severely disadvantaged than households in which they are married.

Lone-parent households made up 51% of those facing severe disadvantage, while 77% of the most severely disadvantaged were living in social housing

Ms Bazalgette said the report was the first phase of a project looking at family disadvantage in Scotland. The next stage will look in detail at the problems of families facing a complex mix of social barriers, and try to develop policy responses.

The research was supported by Quarriers, which supports struggling adults and children.

Chief executive Paul Moore said the charity was launching a new appeal to support families in Scotland.

"Multiple disadvantage has a compounding effect, creating a perfect storm of complex, interrelated hardships that feed off each other and are incredibly difficult to overcome," he said.

"Quarriers' mission is to step in to ensure the needs of these disadvantaged families are met – and we aim to do so through Scotland's Family Appeal

Research was conducted by Demos and NatCen, using statistics from the 2009-10 Scottish Household Survey.