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?
 A: The appropriate tests are in the book  by Stefan Wellek (2010)
Testing Statistical Hypotheses of Equivalence and Noninferiority, Second Edition:
 "6.2 Mann-Whitney test for equivalence" (pp126-135) and "7.5 A non-parametric k-sample test for equivalence" (pp 231-234).
The software package accompanying the book is at 
https://www.crcpress.com/downloads/K10408/TSHEQ_2ndEd_Programs_etc.zip.  The software consists of scripts for the freeware R Statistical Package (equivalent SAS macros are also included).  The script for the Mann-Whitney test for equivalence is called mawi.  According to Wellek (2010) p128, the input data required for mawi are the significance level, the two sample sizes and the name of a file containing the raw data.
The original published source of the Mann-Whitney test for equivalence may be more convenient:
Wellek, S. (1996), A New Approach to Equivalence Assessment in Standard Comparative Bioavailability Trials by Means of the Mann-Whitney Statistic. Biom. J., 38: 695–710. doi: 10.1002/bimj.4710380608  {onlinelibrary.wiley.com/doi/10.1002/bimj.4710380608/abstract}.
This extract from the abstract gives the idea of Wellek's approach:
"Let the two distribution functions be given by F(x) = P[X ≤ x], G(y) = P[Y ≤ y] with (X, Y) denoting an independent pair of real-valued random variables. An intuitively appealing way of putting the notion of equivalence of F and G into nonparametric terms can be based on the distance of the functional P[X > Y] from the value it takes if F and G coincide. This leads to the problem of testing the null hypothesis Ho P[X > Y] ≤ 1/2 - ε1 or P[X > Y] ≥ 1/2 + ε2 versus H1 : 1/2 − ε1 < P[X > Y] < 1/2 + ε2, with sufficiently small ε1, ε2 in (0, 1/2). The testing procedure we derive for (H0, H1), and propose to term the Mann-Whitney test for equivalence, consists of carrying out in terms of the U-statistics estimator of P[X > Y] the uniformly most powerful level a test for an interval hypothesis about the mean of a Gaussian distribution with fixed variance. The test is shown to be asymptotically distribution-free with respect to the significance level. In addition, results of an extensive simulation study are presented which suggest that the new test controls the level even with sample sizes as small as 10. For normally distributed data, the loss in power as against the optimal parametric procedure is found to be almost as small as in comparisons between the Mann-Whitney and the t-statistic in the conventional one or two-sided setting, provided the power of the parametric test does not fall short of 80%."
Clearly there are many other approaches to the problem, but Wellek's solution seems particularly suitable to this case.
