Now a television campaign by the National Society for the Prevention of Cruelty to Children (NSPCC) is to urge Scots not to delay in reporting suspected sexual abuse.
The poll, by the society and YouGov, found just 17% of those questioned would report concerns as soon as potential evidence of abuse came to light.
This is supported by the NSPCC's own findings that almost half of people (47%) in Scotland who contact its helpline with a serious concern about a child have waited more than a month to get in touch.
The charity is now to launch a six-week, UK-wide television campaign called "Don't wait until you're certain".
Matt Forde, head of services for the NSPCC in Scotland, said: "Child sexual abuse is not a problem that died with Jimmy Savile.
"It is a problem that continues today, with children across Scotland suffering at the hands of a minority of adults.
"While the uplift in reports of abuse and new figures indicating that people are more willing to speak out is very welcome, it's also clear that people are still waiting for that elusive certainty that something is definitely wrong before taking action.
"People clearly have the desire to act but are unsure how or when to do it."
He added: "The truth is you will probably never be certain because of the hidden nature of abuse, especially sexual abuse.
"Our poll also shows that 59% of people are not confident that they could spot the signs if a child they knew was being sexually abused. This is why we are taking our 'Don't wait' film, directed by Amanda Boyle, to a wider audience as a television advert."
Originally produced for use online, the video will now be shown on television across the whole of the UK.
The poll found that the main barriers to reporting child abuse would be fear of being wrong (59%), fear of making it worse for the child (39%), fear of splitting up the child's family (17%) and fear of repercussions for the accused (17%).
Dr Linda Papadopoulos, a psychologist, said: "Jimmy Savile was allowed to abuse in part because people were not certain what they were seeing was abuse, and in part because the children themselves were not listened to or believed.
"It's vital that people listen to what children are saying, and that they report concerns immediately even if they are not certain.
"People are understandably concerned about being wrong or making things worse for the child if they say something, but all the time they spend procrastinating that child could be in real danger.
"To a child who is being abused, every day the abuse is allowed to continue can feel like a lifetime."
Between April 1, 2011 and March 31, 2012, 186 of the 1475 contacts with the NSPCC from people in Scotland were about child sexual abuse.
Two-fifths of contacts from people in Scotland about child sexual abuse were so serious they had to be reported to the police or local authorities.
Anyone with concerns about a child or who wants advice can contact the NSPCC free, 24 hours a day, by calling 0808 800 5000.