In Saudi Arabia, Egypt and, most notably, Tunisia, the numbers of people backing the principle of free speech by social media users fell, said Northwestern University in Qatar's (NU-Q) "Media Use Survey 2015."
Respondents were asked if "it is okay for people to express their ideas on the internet, even if they are unpopular."
In Saudi Arabia, the number of people saying "yes" fell from 74 percent to 64 percent. In Egypt it dropped from 48 percent to 45 percent and, in Tunisia, from 57 percent to just 37 per cent.
In contrast, the survey found that support for free speech had risen slightly in Qatar – from 57 percent to 58 percent – and from 59 percent to 61 percent in the United Arab Emirates.
The survey also found that the number of people comfortable expressing their opinions online in post-revolutionary Tunisia and Egypt had fallen.
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In Tunisia, the number fell from 44 to 34 per cent over the two years and in Egypt from 43 to 33 per cent.
NU-Q's survey is the largest of its kind in the region and involved almost 6,100 interviews with people across six countries – Egypt, Lebanon, Qatar, Saudi Arabia, Tunisia and the UAE.
"This study is a systematic means of understanding the region, beyond news headlines and subjective commentary," said NU-Q dean Everette Dennies.
"The knowledge of how people use media, and what they think about them, offers insights about the social and political climate, as well as vital societal issues like freedom of expression."
The survey also found that almost half of all Lebanese, 48 percent, think there is an international news bias against their country.
In contrast, only seven percent of people in Qatar, which has been widely criticised in connection with its successful 2022 football World Cup bid, thought international news was biased against their country.
Northwestern University, based in the US state of Illinois, has one of the country's top journalism schools.