# Equivalence testing exam results

For reasons of economy, a college has moved from live lectures to videotaped.

They have exam results from the year/years before the change, and the year/years after.

They want to be reassured that the new method delivers exam results THE SAME AS, OR NOT WORSE THAN, the old.

We can assume they have taken proper steps to have all the exams comparable.

How is this to be framed technically, and what tests can be applied?

• This is called equivalence testing. Look at this topic for more info: stats.stackexchange.com/questions/139385/… Apr 22 '15 at 7:35
• Many thanks, alesc, especially for the topic name. I see a difficulty that distributions of exam results don't have exactly-paired values, but perhaps that can be overcome by grouping. Now to study the area.
– Bob
Apr 24 '15 at 4:52
• Do the exams have different questions each year, are the questions different or do they partly change? I ask because one thing that could be done is test equating: en.wikipedia.org/wiki/Equating that would make the tests have a common scale. However this needs you to have at least some questions to be answered by the same students or at least students with equivalent level of ability/knowledge. If you provide more detailed description I can write more on this method.
– Tim
Apr 24 '15 at 10:31
• Hi Tim; thanks for the suggestion - I read the Wikipedia article and I remember studying common item equating. That's what we have here - exam questions are drawn from pools of similar. Each year a fresh batch of students takes an equivalent exam.
– Bob
Apr 26 '15 at 6:24
• Hi @Tim; thanks - I read the Wikipedia article and remember studying common item equating. That's what we have here - exam questions drawn from pools of similar. Each year a fresh batch of students takes an equivalent exam. But I have to assume equivalent exams set to equivalent groups of students, ie that standardization has been done already by the subject specialists. The data I have is a sequence of distributions (ie the exam results for each year: how many students scored n%, n=1-100). If test equating can be applied to this, I'd be happy to know.
– Bob
Apr 26 '15 at 6:35