Donald Trump was, the researchers concede, an easy target. Having cringed themselves when he was on the campaign trail, they felt compelled to test their hypothesis: that the election of the 45th president of the US had prompted an upturn in national embarrassment.

The scientists, with no official records of the nation’s mood to pore over, turned to Twitter for an answer. After analysing tens of millions of tweets sent from US accounts between June 2015 and December 2017, they found references to embarrassment and variants on the word had risen 45% since the election, from an average of 909 per million to 1,319 per million.

Frieder Paulus, a social neuroscientist at Lübeck University in Germany, said: “Compared with the Obama administration, there was an increase in embarrassment since Trump was elected. Not only does it increase on average, you have very strong spikes in embarrassment too.”

The study could not prove Trump was the sole driver of any shift in national mood, or at least the mood of the US Twitterati. But the scientists present some intriguing evidence. They dived deeper into the data behind three large spikes in Twitter-expressed embarrassment and used word clouds to show references to Trump featured highly in all of them.

The first spike in embarrassment was on 10 October 2016, the day after the second presidential debate. The tweets that produced the spike were rich in the words “debate”, “Trump” and “country”. The second spike, on 18 March 2017, coincided with Trump apparently refusing to shake Angela Merkel’s hand, and saw “Trump”, “@realDonaldTrump”, “@Potus” and “Merkel” feature prominently in tweets. The third spike, on 28 May 2017, when Trump seemed to shove the Montenegro president at a Nato meeting, was driven by tweets referring to Trump and Nato.

“You can clearly see that the spikes are related to Trump,” said Paulus. The scientists more tentatively link other peaks of collective cringing on Twitter to Trump’s election day and inauguration, the administration’s withdrawal from the Paris climate agreement, Trump’s meeting with Vladimir Putin at the G20 summit, and his comments on the Charlottesville rally. Earlier spikes seen during the Obama administration may be the focus of future work, Paulus said.

The researchers, writing in the journal Frontiers in Communication, argue cringe peaks may arise when Trump appears to deliberately violate social and political norms. “At first it might have been easier for Americans to distance themselves and feel schadenfreude, but then he gets elected and they feel embarrassment on his behalf,” Paulus said.

“Donald Trump was an easy target, but we definitely need to look at other people, too. We shouldn’t think this is not happening on this side of the Atlantic.”