Interesting bit from the Teaching, Learning and Technology group: "Absence of evidence is not evidence of absence". It's a reminder that no significant difference findings mean just what they say: there's no significant difference. Is there a difference? Maybe. Is there no difference? Maybe. But we simply cannot tell the effect from the research indicated. Just as we cannot overstate what research says, we cannot overestimate NS findings.
However, we're in education. Is a difference in one student's performance significant? Not statistically, but it's quite significant to that student. I don't believe that it is moral to withhold an educational condition from a student just because of NS results on an educational test.