Jury members also looked on the internet for information about their case, despite being told not to by the judge, the research showed.
Other findings show that all-white juries do not discriminate against black defendants and juries convict more often than they acquit in rape cases, contrary to public perception.
The two-year study, led by Professor Cheryl Thomas of University College London, analysed 68,000 verdicts across Crown courts in England and Wales, and also staged simulated trials.
In relation to judge's directions - where a judge gives crucial guidance to jurors about what they have heard - the research team asked jurors at Winchester Crown Court to recall two key questions that the judge gave in a case where a defendant was charged with violence.
Only 31% of jurors accurately identified both questions, it was found.
A further 48% correctly identified one of the two questions, and a fifth did not correctly identify either question.
Researchers found a written summary of the judge's directions on the law for jurors improved their comprehension of the law.
Prof Thomas has recommended a pilot test of written juror guideline cards for a sample of courts to work out how they can be best introduced.
In 2008, the Lord Chief Justice suggested that courts might need to present more information visually to reflect greater use of technology like the internet.
The report, called Are Juries Fair?, also tested verdicts from all-white juries concerning white and black and Asian defendants.
It was found that verdicts at both courts showed no tendency for all-white juries to convict a black or Asian defendant more than a white person.
White defendants accused of racially motivated crimes were also not more likely to be acquitted by all-White juries than racially mixed panels.
More than a quarter (26%) of jurors saw internet reports of the trial, and 12% actively looked for information about their case, the study showed.
Jurors are directed by the judge at the start of a trial not to look for any information about the case themselves to minimise the risk of a miscarriage of justice.
Prof Thomas said some of the report's findings contradicted common perceptions about jury conviction rates - particularly in the case of rape trials.
"Contrary to popular belief and previous official reports, juries convict more often than they acquit in rape cases (55% conviction rate)," it said.
The report added: "While there is no doubt that the proportion of rape complaints to police that end in conviction is extremely low, it is also clear that this cannot be attributed to juries' failure to convict in rape cases."
Trials involving charges of making indecent photos of children had the highest conviction rates, at 89%, with threats to kill cases having the lowest, at 36%.
In response to the study, Justice Secretary Jack Straw said: "The jury system is working, and working well.
"The study's findings on the fairness of jury decisions, including for people from black and minority ethnic backgrounds, will help to maintain public confidence in juries and the jury system.
"But we cannot allow complacency about the justice system. We will carefully consider the recommendations for helping jurors do their job to the best of their ability."
Commenting on the findings, Lord Justice Thomas, Deputy Head of Criminal Justice, said: "Trial by jury is fundamental to the administration of justice, and confidence in the jury system is equally important."
He added: "One area of obvious and particular interest to the judiciary is the way in which the judge gives directions to a jury.
"The report recommends that work be undertaken by the judiciary in relation to ensuring the directions are readily understandable.
"Work has been under way in this important area for some time. For example, steps are being taken to ensure that more written material is available for juries. The Judicial Studies Board now recommends that written directions be given to juries in all but the most simple of cases and will consider, in detail, the recommendations made in the report.
"It must always be remembered that juries considering their verdict can ask the judge for clarification of any aspect of the case."
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