Fact-checkers have been dissecting claims made during Thursday's vice-presidential debate between Joe Biden and Paul Ryan.

Both men accused the other of being misleading with their facts and figures, and Mr Biden memorably called one of Mr Ryan's criticisms "a bunch of malarkey".

Here are some of the assertions that went under the microscope:

Which small businesses?

During the debate, Mr Ryan said Mr Obama's tax plan would end up taxing about "53% of small-business income. It's expected to cost us 710,000 jobs."

Factcheck.org says at least one study backs Mr Ryan on the number of jobs lost, but it was commissioned by right-leaning groups including the US Chamber of Commerce, and assumed that revenue gained from the tax change would be used to finance higher government spending, instead of to reduce future federal deficits.

However, Mr Biden was judged to be correct in his response when he said some of the small businesses counted under the 53% statistic were giant hedge funds making hundreds of millions of dollars a year.

20 million to lose insurance?

Mr Ryan claimed 20 million people would lose their medical coverage if President Obama was re-elected, and if all of his healthcare reform act came into force in 2014.

Mr Ryan is apparently referring to a study this year by the non-partisan Congressional Budget Office on scenarios of what would happen to the number of people on employer-offered insurance.

He cites the CBO's worst-case scenario, and fails to mention how many would then get insurance through other sources. Another scenario in the study projects three million fewer people on employer-offered insurance and the most optimistic scenario adds three million.

"Usually, when Republicans cite this figure, they say 'up to 20 million', but Ryan did not even bother with that modifier, making his claim especially alarmist," the Washington Post.

'Tragic' end of war

PolitiFact gives Mr Biden negative ratings for cherry-picking Mitt Romney's statement on the drawdown of troops in Iraq.

"On Iraq, the president said he would end the war. Governor Romney said that was a tragic mistake, we should have left 30,000 [troops]," Mr Biden said.

He appears to be referring to a November 2011 speech by Mr Romney, but the former Massachusetts governor was not talking about the end of the war when he used the word tragic. He was talking about the speed at which Mr Obama removed the troops.

However, Mr Romney did say in a December 2011 interview with Reuters that "the president's failure to secure an agreement and maintain 10,000 to 30,000 troops in Iraq has to be one of his signature failures".