Jeremy Corbyn set out his "mandate for change" in his speech to the Labour party conference today.
We've taken a look at some of his claims in topics ranging across investment, the Human Rights Act, self-employment, mental health, housing, tax credits and poverty.
"Britain at the bottom of the international league on investment. Just below Madagascar and just above El Salvador."
If he's basing this on the World Bank's figures, this isn't quite correct. The latest figures we have for El Salvador and Madagascar are from 2013. In that year, El Salvador invested 15.1% of its GDP, and Madagascar 15.7%. The UK finished a bit ahead of both that year, investing 17% of its GDP. Mr Corbyn's claim would have been correct for 2011 data.
The UK is quite low in the rankings for investment as a proportion of GDP. However, developed countries on the whole tend to invest less than developing countries.
Investment here is measured by gross capital formation—investment in new assets (things like roads, railways and trains), and on stockpiling unsold goods. It also includes spending on 'valuables' (things like gold or antiques), minus sales thereof.
If we ignore stockpiling of unsold goods, the picture's pretty much the same.
"The Tories want to repeal the Human Rights Act and some want to leave the European convention on Human Rights."
The Conservative general election manifesto did commit to "scrap the Human Rights Act, and introduce a British Bill of Rights" in its place.
Repealing the Human Rights Act, passed in 1998, wouldn't be as big a change as also leaving the European Convention on Human Rights (ECHR), which we ratified in 1951. It's not clear exactly what would be in a Bill of Rights or how different it would be from the Human Rights Act—the government has said it will bring out proposals for consultation "in the autumn".
But whatever is in it, staying signed up to the ECHR means that people could continue to bring cases to the European Court of Human Rights.
It's fair to say that some Conservatives would like to put a stop to that as well, but the government's policy for the time being is to remain in.
A previous version of the Bill of Rights proposals, published in October 2014, said that the Conservatives "would like the UK to remain a party" to the ECHR but could envisage a situation in which there would be "no alternative" but to leave as a last resort. The Daily Telegraph has reported that the party is "divided" on the issue, quoting Philip Davies MP as an example of a Conservative in favour of withdrawing.
Read more here.
"1 in 7 of the labour force now work for themselves... They earn less than other workers. On average just £11,000 a year."
This is right, according to the Office for National Statistics. Its latest figures show that just over 31 million people are employed, of which 4.5 million are self-employed. That's around 14.5% of all workers, or one in seven (measuring over May-July 2015). Read more here.
"In the last parliament at least half a million fewer homes built than needed."
There's a few different ways of looking at how many homes have been built and how many are needed. Either way it's reasonable to say the gap was roughly 100,000 homes in England in 2014 and the same gap has been similar since 2010.
We don't have a complete set of figures yet for 2014/2015.
For more detail, take a look at our factcheck.
"As three quarters of chronic mental health problems start before the age of 18. Yet only a quarter of those young people get the help they need."
We have very little up to date information on mental health services in the UK. The Chief Medical Officer has recently referred to both these figures, and although both its sources were more than a decade old they probably remain the best we have.
Research in 2003 found that three quarters of adults in New Zealand who had a psychiatric disorder had first experienced a mental health problem by the time they were 18. These were generally the same types of disorders, although not always. Researchers said that although the rate of mental illness was similar in New Zealand as in the US, there should be further work to replicate the finding elsewhere in the world.
24% of parents of a child with an emotional disorder had either contacted or been referred to mental health services when surveyed in 2004.
"Half a million more children in poverty".
The number of children in absolute poverty is up half a million after housing costs.
We can look at absolute poverty or relative poverty, before or after housing costs. Absolute poverty looks at the number of children living in households with an income below a fixed amount (after adjusting for household size). Relative poverty looks at children living in households with an income that's less than 60% of the amount the 'middle earning' household gets (again, after adjusting for household size).
The number of children in relative poverty (before and after housing costs) has fallen since the election, while the number of children in absolute poverty is up 200,000 before housing costs, and up 500,000 after they're taken into account.
"On the Question Time Leader's debate he said he had rejected child tax credit cuts. It's a shocking broken promise."
The Prime Minister appeared to promise not to cut child tax credit before the last election, though his wording was ambiguous. After the election, tax credit rates were frozen in the summer budget and some entitlements to them were cut.
The Conservatives claim he was referring to Child Benefit at the time. Labour also claimed the day after the Prime Minister made the 'promise' that "David Cameron is still failing to rule out cutting child benefit and tax credits again". So there was at least some room for interpretation in what he promised.
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