In an exercise it is usual for a piece of work to be assessed twice. A student assesses their work before submitting it and the teacher then (re)assesses the work. The teacher's assessment uses the student's assessment as the starting point. An exercise allows the teacher to award a proportion of the grade to the student's assessment, the remainder of the grade is allocated to the teacher's assessment of the work. (The maximum grades for these are called "Grade for Student Assessments" and "Grade for Submissions" respectively.) Note that the grade from the student's assessment is not used. The student's assessment is given a grade based on how well it matches the teacher's assessment.
The degree of agreement between the student's and teacher's assessment is based on the differences between the scores in individual elements (actually the squared differences are used). The mean of these differences must be converted into a meaningful grade. The "Comparison of Assessments" option allows the teacher a degree of control on how these comparisons are converted into grades.
To get some idea on what effect this option has, take the (fairly simple) case of an assessment which has ten Yes/No questions. For example the assessment might use questions like "Is the chart correctly formatted?", "Is the calculated profit $100.66?", etc. Assume there are ten such questions. When the "Very Lax" setting is chosen, perfect agreement between the student's and teacher's assessment gives a grade of 100%, if there is only one question which does not match the grade is 90%, two disagreements give a grade of 80%, three disagreements 70%, etc.. That might seem very reasonable and you might be thinking why is this option called a "Very Lax" comparison. Well, consider the case of a student doing a completely random assessment where the answers of the ten questions are simply guessed. On average this would result in five of the ten questions being matched. So the "monkey's" assessment would get a grade of around 50%. The situation gets a little more sensible with the "Lax" option, then the random assessment gets around 20%. When the "Fair" option is chosen, random guessing will result in a zero grade most of the time. At this level, a grade of 50% is given when the two assessments agree on eight questions of the ten. If three questions are in disagreement then the grade given is 25%. When the option is set to "Strict" having two questions out of sync gives a grade of 40%. Moving into the "Very Strict" territory a disagreement in just two questions drops the grade to 35% and having a single question in disagreement gives a grade of 65%.
This example is slightly artificial as most assessments usually have elements which have a range of values rather than just Yes or No. In those cases the comparison is likely to result in somewhat higher grades than the values indicated above. The various levels (Very Lax, Lax, Fair...) are given so that the teacher can fine tune the comparisons. If they feel that the grades being given for assessments are too low then this option should be moved towards the "Lax" or even "Very Lax" choices. And alternatively, if the grades for the student's assessments are, in general, felt to be too high this option should be moved to either the "Strict" or "Very Strict" choices. It is really a matter of trial and error with the best starting point being the "Fair" option.
During the course of the exercise the teacher may feel that the grades given to the student assessments are either too high or too low. These grades are shown on the exercise's Administration Page. In this case, the teacher can change the setting of this option and re-calculate the student assessment grades (the "Grading Grades"). The re-calculation is done by clicking the "Re-grade Student Assessments" link found on the administration page of the exercise. This can be safely performed at any time in the exercise.