Hello,

I wrote a test which was too hard. I do not want to use the Canvas redistribution method because my scores are not distributed equally across the range; and I cannot add an equal number of fudge points because I do have some scores near 100%. The method that would make the most sense to adjust for this test is the square root method.

I think the best way to see how it works is to run the numbers on one of your own tests; here's a sample of resulting scores from mine.

Raw Score | Curved Score |
---|---|

98 | 98.99 |

70 | 83.67 |

45 | 67.08 |

18 | 42.43 |

References/resources:

https://sciencing.com/grade-using-square-root-curve-8541101.html

Square Root Curve Calculator » ClassCube.com

Also, for instructors new to or hesitant about curving, the results of curving should be available as a preview before finalizing, or possible to undo. Please search "Preview or undo for curving grades" to view and vote on this related feature request.

In the meantime, you can export the gradebook, manually calculate the desired values with Excel, and then reimport the gradebook back into Canvas.

When you export the gradebook, you need to keep the first (up to 5 depending on availability of SIS information) fields that identify the student and course. You can delete every column except for the one you're changing. I typically do that, so I'm left with 6 columns -- 5 identifying ones in columns A-E and 1 grading one in column F.

In column G, I apply the formula, staring with cell G3 = 10*SQRT(F3). Then I copy that formula down to the rest of the grades.Once that's done, I copy all the information from G3 to the end of column G and then paste it special as text over the original values, starting in cell F3. Then I delete all of column G, save the CSV file, and do the upload.

If it's a small class, it may be quicker to just re-enter the grades using the web interface.

I'm not sure whether your idea is to replace the existing curve method or to add an additional method to it.

The page you cited says it doesn't work well when the grade is not out of 100, but I'm not sure about their justification. The rounding to one extra decimal place only works because you're multiplying by 10, so I suppose it's for simplicity or because they don't really understanding what they're doing. I've never heard of the "Square root method" before, but what you're doing is known as the geometric mean. Most people are familiar with the arithmetic mean, which is the sum of the values divided by the number of values. The geometric mean is the n-th root of the product of n values. In this case, you have n=2 and are letting one of the values be the possible number of points and the second value be the score received. That makes it the square root of (possible * scored). The reason they mention 10 is because when the possible = 100, then the square root of possible = square root of 100 = 10.

If a student scored a 70 on a 100 point exam, then their geometric mean would be sqrt(70*100) = sqrt(7000) = 83.67 and your 18 becomes sqrt(18*100) = sqrt(1800) = 42.43. If they got a 7 (35%) on a 20 point quiz, then their geometric mean would be sqrt(7*20) = sqrt(140) = 11.83 (59.15%)

The geometric mean requires non-negative values, which shouldn't be a problem, but there is another interesting side-effect. My dad used to love to trick the unsuspecting with a baseball problem. He would tell them, "You take the number of runs the Cubs score in every game for a season and multiply them together, so if they scored 5 one day, 2 another, and 3 another, you'll have 5*2*3 = 30. I'll take the number of runs the Cards score in every game for a season and add them together, so if they scored 5, 2, and 3, I would have 10. I'll bet you that at the end of the season, I'll have more than you will."

In case someone hasn't figured that one out, at some point the Cubs are going to score 0 runs and the person betting on the Cubs will have 0 from then on. When using the geometric mean, the person who gets a 1 would get a 10, but a person who gets 0 gets 0. Both are better than the arithmetic mean where the 1 and 0 become 50.5 and 50 respectively.

Speaking of arithmetic means, which is what most people call "average", some people would prefer that approach be used and I will admit that the masses would understand it much better. If you had a 70, then you would get (70+100)/2 = 170/2 = 85. The 18 would turn into (18+100)/2 = 118/2 = 59. If you had 7 (35%) on a 20 point quiz, you would have (7+20)/2 = 27/2 = 13.5 (65%)

Others would say that the harmonic mean is the way to go (but only if no-one scores a 0) as the other methods give away too much. It is the reciprocal of the arithmetic mean of the reciprocals of the values. A 70 would become 1 / ( (1/70 + 1/100)/2 ) = 82.35. The 18 would turn into 30.51. A 7 (35%) on a 20 point quiz would become 10.37 (51.85%). The person gets a 1 gets a 1.98, but the person who got a 0 gets a division by 0 error, so you would have to check that the value was positive first.

Here's a comparison of the three common means on a 100 point exam. When all of the values are positive and there are at least two different numbers, the arithmetic mean is always the largest, the harmonic mean the smallest, and the geometric mean is in the middle.

Some want to assign a bell-curve to the grading. I've always resisted that one because a 45 one semester may turn into an A if the class does poorly and an F the next semester if everyone does well. That means that there is no consistency between semesters and an A may know less than someone who got a D. When they leave my class with a grade on their report card, the person looking at that grade isn't concerned with whether they were in a smart group or a challenged group, they want to know whether or not they know the material.

Others prefer to just add a constant to every grade, but that can make it go over 100, which some object to. Perhaps if you had some students that were near 100, then maybe those students are misplaced and you could just excuse the exam for them while adding a constant for the others.

Canvas has its own take on things as explained in How do I curve grades in the Gradebook? and Curving Grades in Canvas (PDF). This tries to normalize things, making sure that the top score gets 100%. Some see that as problematic -- if a 45 is the top score, do they really deserve 100%. The irreversibility of the process and the inability to know the grades ahead of time is troublesome.

The point being that there are lots of ways to curve grades and Canvas tries to do what is right (if there is a clear answer) or popular (as a second choice). They try to do that with a simple interface that is easy to use and understand. Note that I did not say that the procedure was easy to understand -- far from it -- just the interface.

It is unlikely that every curving scheme will rise to the popularity or correctness level needed to be added to the interface. The more you add to the interface, the more cumbersome and confusing it is to use. Thankfully, we can download the grades, adjust them on our own, and re-upload the results -- thus allowing us to have whatever scheme we like and double checking the results to make sure we're happy before committing.

Another option is the one I use -- I don't curve individual grades. At the end of a semester, I may take factors into consideration and that's when I would do the curving if I felt it was justified. That way I can look at more than just the score on one exam. At that point, the calculations needed for me to do that are all mental.