Can I get an explanation for Simple Weighted Mean of Grades?

Can I get an explanation for Simple Weighted Mean of Grades?

by Jane Boyden -
Number of replies: 14

I've read through the different tutorials and forums to try to figure this out myself, but haven't had any luck. I also haven't had any luck figuring out the math behind it.

We've recently upgraded to Moodle 1.9.5 and with new Grade Book. We've also disabled all aggregation options except for "Weighted Mean of Grades," "Simple Weighted Mean of Grades," and "Sum of Grades." I have no problem figuring out Weighted Mean or Sum of Grades. But for the life of me, I can't get the Simple Weighted.

For a little background, I have the course set up as Weighted Mean of Grades. I've also created 2 categories, one with Sum of Grades aggregation method and the other with Simple Weighted Mean of Grades aggregation. For this example, both categories have equal weight. There are three assignments in each category: 10 Point Assignment, 20 Point Assignment, and 50 Point Assignment. There are 3 students in the class.

The Sum of Grades category is quite simple. To me, Simple Weighted Mean of Grades looks exactly like Sum of Grades as long as the MINIMUM is set to ZERO.

So my question is, is there actually a difference between Sum of Grades and Simple Weighted Mean of Grades as long as the Minimum is set to Zero (for Simple Weighted)? And secondly, can someone PLEASE explain to me the math behind what I have in the table below? I've changed the MINIMUM to illustrate what I'm talking about. Why does the point value change for the category total change? Why does the percentage for the category NOT change? Here's what I did:


 10 Point Assignment
 20 Point Assignment
 50 Point Assignment
 Category Total Points
 Category Total %
MAX = 80, MIN = 0




Student 1
 10
 20
 50
 80
 100%
Student 2
 9
 18
 48
 75
 93.75%
Student 3
 8
 15
 45
 68
 85%
MAX = 80, MIN = 20




Student 1
 10
 20
 50
 80
 100%
Student 2
 9
 18
 48
 76.25
 93.75%
Student 3
 8
 15
 45
 71
 85%
MAX = 80, MIN = 40




Student 1
 10
 20
 50
 80
 100%
Student 2
 9
 18
 48
 77.5
 93.75%
Student 3
 8
 15
 45
 74
 85%
MAX = 80, MIN = 60




Student 1
 10
 20
 50
 80
 100%
Student 2
 9
 18
 48
 78.75
 93.75%
Student 3
 8
 15
 45
 77
 85%

In reply to Jane Boyden

Re: Can I get an explanation for Simple Weighted Mean of Grades?

by Nicolas Connault -
The confusion comes from the sequence of mathematical operations, and the meaning of the category's "minimum" and "maximum". Let me explain that, using your first case and student 3:
  1. Before any weighting is done, each score is converted to a ratio:
    1. 8/10 becomes 0.8
    2. 15/20 becomes 0.75
    3. 45/50 becomes 0.9
  2. In the "Simple weighted means", the maximum value of the item is interpreted as its weight. So, once the weights are applied:
    1. 0.8 * 10 = 8
    2. 0.75 * 20 = 15
    3. 0.9 * 50 = 45
  3. These are then summed, then divided by the total weights (10 + 20 + 50 = 80)
    1. 8 + 15 + 45 = 68 (displayed in the "Category total points" column)
    2. 68 / 80 = 0.85
  4. When displayed as a percentage, 0.85 is 85% (displayed in the "Category total %" column)
Now, the category minimum: under normal circumstances there is no valid reason why you should want to adjust a category's minimum value. This will not "adjust" any raw scores, it will simply change the display of the total points.

If you think you have a strong case for using another minimum than 0, please explain and I will see if it's worth spending the time explaining the maths behind its calculation ;)
In reply to Nicolas Connault

Re: Can I get an explanation for Simple Weighted Mean of Grades?

by Bob Puffer -
"Simple Weighted Mean of Grades" confounds more than a few. I must confess I thought creating unnecessarily complex structures was principally the realm of academicians so please allow me to place my head on the chopping block and respectfully attempt to place Nicolas' explanation in my own words. Hopefully it will still be accurate. A student's grade resulting from all graded items contained in a category using the "Simple Weighted Mean of Grades":

  • WIll be the total points earned/ divided by the total points "earnable" (maximum points) as a percentage.
  • In the case where "Aggregate only non-empty grades" is turned on, only scores and maximums for graded items attempted will be considered
In other words... inside the category, a point's a point.
In reply to Bob Puffer

Re: Can I get an explanation for Simple Weighted Mean of Grades?

by Nicolas Connault -
In Mathematics, if you don't know what something does, don't use it :D
In reply to Nicolas Connault

Re: Can I get an explanation for Simple Weighted Mean of Grades?

by Bob Puffer -
I think that may be where our opinions mainly diverge -- I don't think someone should have to be a mathematician in order to use the gradebook.
In reply to Bob Puffer

Re: Can I get an explanation for Simple Weighted Mean of Grades?

by Nicolas Connault -
That's a very simplistic view of things, Bob smile "mean" and "weight" are not complex mathematical constructs, but even if they were, no one is "forced" to use these in the gradebook. Most people understand "mean", however, and they can just use that. Indeed, they don't have to be a mathematician! However, if they have mathematical background, they are in a better position to make better use of the gradebook. Is that wrong? I would add that if a person is better educated, they can make better use of Moodle. And if a person if is more clever, the same thing also applies. Do I make my point? ;)
In reply to Nicolas Connault

Re: Can I get an explanation for Simple Weighted Mean of Grades?

by Bob Puffer -
Nicolas,
I'm sorry my comments offended you. I do disagree that my interpretation is simplistic. I can only speak from experience in the US -- the overwhelming percentage of instructors with which I've had contact find the terms of the gradebook and the complexity in which they're enmeshed quite daunting. You are correct that no one is forced to use any of these terms, but in our case, their only recourse is to go to an external gradebook since they wish to weight their grades.

I would ask you if you think my explanation above is accurate -- I'd very much want to make sure I fully comprehend the nuances of the aggregation methods. If it is accurate, I'd also be interested in knowing what the difference is between the "Simple weighted mean of grades? and the "Sum of grades", aside from the fact that you can't exclude non-graded items from "Sum of grades"?
Thanks
In reply to Bob Puffer

Re: Can I get an explanation for Simple Weighted Mean of Grades?

by Nicolas Connault -
Bob,

You didn't offend me at all smile I was a bit frustrated that day about unrelated things, and my words didn't come across the way they should have, so I apologise if I gave you the wrong impression. What I was trying to say is that your comment about teachers needing to be "mathematicians" to understand the gradebook was somewhat exaggerated, given the fact they they can simply use "Mean" as a grading strategy, and the "Mean" is something I assume any teacher would know about.

The other aggregating methods are not very complex either. In fact the "Weighted mean of grades" is the equivalent of the method used in the 1.8 and earlier versions, and was only implemented in 1.9 to keep the grade totals identical during the transition of 1.8 to 1.9. It seems strange to me that suddenly we need to explain repeatedly how it works, when it has been working like this for years.

That being said, these aggregation strategies are documented rather thoroughly in the moodle wiki, as the following links indicate. However, these docs always have room for improvement, and if you feel that they could be improved upon, you are encouraged to write something in these pages' "Page comments" section. Your feedback will be reviewed and the documentation will improve that way.

http://docs.moodle.org/en/Category_aggregation
http://docs.moodle.org/en/Gradebook_1.9_Tutorial
http://docs.moodle.org/en/Grades_FAQ#What_is_the_difference_between_Weight_and_Extra_Credit.3F
http://docs.moodle.org/en/Using_%27Sum_of_grades%27
In reply to Bob Puffer

Re: Can I get an explanation for Simple Weighted Mean of Grades?

by Nancy Webb -
I THINK the difference between sum of grades and simple weighted mean of grades is that the total is a percentage of total points with simple weighted, but it is the just the total of all points with sum. 
In reply to Nancy Webb

Re: Can I get an explanation for Simple Weighted Mean of Grades?

by Bob Puffer -
Ah, Yes -- but depending IMO the display of the total makes them exactly the same, except you cannot exclude ungraded items from the Sum.
In reply to Bob Puffer

Re: Can I get an explanation for Simple Weighted Mean of Grades?

by Nancy Webb -

Every time I look at the difference between weighted mean and simple weighted mean I have to think it out again!

You ask if this is true about all graded items in a simple weighted mean of grades category:

  • Will be the total points earned/ divided by the total points "earnable" (maximum points) as a percentage.

I think you are right! a point is a point wth simple weighted. Thanks for putting it so succinctly.

I believe we use weighted means when we want to specify the weight for each item rather than having it be figured out based on the points. I created a little spreadsheet with two assignments, one is 10 points, the other 20. In simple weighted, a point is a point. But in weighted mean of grades, I can assign a weight for each item. In this example, I made each assignment an equal weight, rather than basing the weight on the points in the assignment. (Can weight it however I want, of course)

Simple weighted
Student Max Grade per item
Hmwk1 10 10 10.00
Hmwk2 18 20 18.00
Total 28 30 93% 93%
Weighted
Student Max weight Weighted Grade per item
Hmwk1 10 10 100.00 100.00
Hmwk2 18 20 100.00 90.00
Total 28 30 200.00 95%

Note that the student has a lower grade in simple weighted.

By giving each assignment the same weight in the weighted assignment, his 90% and 100% give him 95%, that is 190 out of 200 weighted points. But in Simple weighted, his 100% on the first assignment doesn't mean anything special, the student got 28 out of 30 points which is 93% of total points.

I think I'm right, but I am open to correction.  I used the formulas in the help topic for aggregation.

Nancy

In reply to Nancy Webb

Re: Can I get an explanation for Simple Weighted Mean of Grades?

by Mary Parke -
Nancy, in your example (under weighted) you weighted individual items.
Homework 1 is 10 points, worth 100%. Homework 2 is 20 points, also worth 100%. 18/20 is 90%. 10/10 is 100%. What you're doing is essentially Mean of grades aggregation in your weighting to 100% example - where each assignment is worth the same.

10/10 = 1.0; 18/20=0.9
1.0 +0.9 = 1.9
out of a total of 2.0 = 0.95 x 100 = 95%

So I wouldn't use weighted grades in the way that you were weighting, I would use mean of grades since you have everything weighted to 100% any way.

-------------------------------------

In weighted grading, most faculty look at it in terms of categorization - such as,

Homework = 25%
Exams = 50%
Participation = 25%

So the course would be set to weighted aggregation; a category for each subtopic (Homework, Exams, Participation) would be created using simple weighted means, and the weight would be easiest set at 25, 50, 25 respectively = adding up to a total of 100 for distribution to 100 in the course.

Under Homework, if I had 5 assignments like this:

HW1 = 10 points max
HW2 = 25 points max
HW3 = 15 points max
HW4 = 50 points max
HW5 = 50 points max

There are 200 points max for the homework category.

A student earned these scores:

HW1: 8/10
HW2: 15/25
HW3: 14/15
HW4: 33/50
HW5: 46/50

In the category (set to simple weighted mean) the calculation would first look like this (for simple weighted):
 HW1 8/10, HW2 15/25, HW3 14/15, HW4 33/50, HW5 46/50 category max 200:
 (0.8*10 + 0.6*25 + .93*15 + .66*50 + .92*50)/200 = 0.58 (or 58%)
Then I have to take into consideration the weighting of the entire category: 
0.58 * 0.25 (25% for homework category) = 0.145 or 14.5%
of the course total grade is what I've earned. So in essence, I had the chance to earn 25% of the course with from my homework assignments, but I was only able to earn 14.5% based upon my weighted work.

I *think* this is how the course final total will take into account the weighting applied to just this category - when the course is set to weighted grading, and the category is set to simple weighted grading.

And yes, I believe that simple weighted grading is a percent based upon total points earned out of total points possible - providing the category max is set correctly.

This is confusing to many.
In reply to Mary Parke

Re: Can I get an explanation for Simple Weighted Mean of Grades?

by Bob Puffer -
I believe with SWM the category total doesn't have to have the correct total points, it scales according to what the total is.
In reply to Bob Puffer

Re: Can I get an explanation for Simple Weighted Mean of Grades?

by Rod Spears -
That is correct Bob.

In my experience, that is one of the most confusing things about using SWM. You are required to enter a total number of points for the category and Moodle will scale the category grade to be consistent with the total points you have entered for that category.

If you have checked "Aggregate only non-empty" grades, Moodle will only count the non-empty grades. IF you have chosen to display the "real" grade Moodle will display the total number of points earned and if you are displaying the range as a "real" grade the student may get confused when they see the total earned/total possible points don't appear to calculate correctly.

That is why I don't display the "Real" grade when using SWM. I choose to display only the "percentage" grade or the "percentage/letter" grade.


In reply to Rod Spears

Re: Can I get an explanation for Simple Weighted Mean of Grades?

by Bob Puffer -
Well-put.

This gradebook, though best of the Moodle core by far, is heavily "weighted" toward displaying grades as a percentage.