...
- points-based calculations : in which the ratio of an item's max points versus the total points possible for all items scored is used to establish the item's 'weight' within the gradebook
- weight-based calculations : in which the product of two assigned weights at the category and item levels is used to establish the item's 'weight' within the gradebook
Points Based Calculations
There are two cases for points based calculations, but the distinctions between the two are very slight. Whenever the 'organization' of the gradebook is set to "No Categories" or "Categories", points-based calculations will be used, independent of whether the "grade type" is set to "poe ints" or "percentages". In setting up the gradebook, an instructor must provide a maximum number of points per item, or if one is not entered, a default value of 100 will be used.
So, in "No Categories" mode, we might create the following gradebook:
In combination with these modes, there are a couple of additional parameters that influence how grades are calculated:
- #Project Extra Credit toggles whether extra credit calculations will be 'projected' or scaled against the overall gradebook or if they will be relative to only the items that have been already graded
- #Weight By Points allows an instructor to use points-based calculations to determine the relative weight of items within a weighted category, rather than requiring additional 'weights' to be set
Points Based Calculations
There are two cases for points based calculations, but the distinctions between the two are very slight. Whenever the 'organization' of the gradebook is set to "No Categories" or "Categories", points-based calculations will be used, independent of whether the "grade type" is set to "points" or "percentages". In setting up the gradebook, an instructor must provide a maximum number of points per item, or if one is not entered, a default value of 100 will be used.
So, in "No Categories" mode, we might create the following gradebook:
- My Default Gradebook
- Item 1 (25 points)
- Item 2 (25 points)
- Item 3 (25 points)
- Item 4 (25 points)
- Extra Credit Item (10 points)
This gradebook would have a total possible non-extra-credit point value of 100, with 10 extra credit points possible.
...
Of course when we include the ability of instructors to excuse an individual student from an individual item, we discover that P can vary on a student-by-student basis, as shown below:
Fig. 1
Student | Item 1 | Item 2 | Item 3 | Item 4 | Extra Credit Item | S | E | P | % score |
---|---|---|---|---|---|---|---|---|---|
Joe | 20 | 20 | 20 | excused | 10 | 60 | 10 | 75 | (60+10)/75 = 93.33% |
Melody | 20 | 20 | 20 | 20 | 10 | 80 | 10 | 100 | (80+10)/100 = 90.00% |
...
In "Categories" mode, calculations are still point-based, and work along the same fundamental principle, though when it comes to extra credit there is a further complication. By organizing the points into categories, we end up with the idea of an item that contributes extra credit to that category specifically, where it doesn't make sense to determine the category contribution to the overall score unless at least one non-extra-credit item has been graded for that category.
- My Default Gradebook
- Category 1
- Item 1 (25 points)
- Item 2 (25 points)
- Item 3 (25 points)
- Item 4 (25 points)
- Extra Credit Item (10 points)
- Category 1
So under this case, we have the same basic calculation as above, but if we add a student who only completed the extra credit item, we get another non-intuitive case:
Fig. 2
Student | Item 1 | Item 2 | Item 3 | Item 4 | Extra Credit Item | S | E | P | % score |
---|---|---|---|---|---|---|---|---|---|
Joe | 20 | 20 | 20 | excused | 10 | 60 | 10 | 75 | (60+10)/75 = 93.33% |
Melody | 20 | 20 | 20 | 20 | 10 | 80 | 10 | 100 | (80+10)/100 = 90.00% |
Francis | - | - | - | - | 10 | 0 | 10 | 0 | - |
...
Note | |||||||||||||||||||||||||||||||||||||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Alternative Points-Based Extra Credit CalculationOne way that we could conceivably implement the extra credit calculation would be to revise the calculation above by introducing an additional variable Q = sum of all non-extra credit points possible for scored and unscored items We would then revise the equation as follows: % score = S/P + E/Q In this case, our example above would look like this: Fig 3.
The obvious disadvantage of this strategy is that instructors would not see extra credit points being awarded in the most straightforward common-sense way for students with excused items... so in Dela's case, even though she has been given 10 extra points, giving her 20 out of 20 points for the gradebook, she only receives a 60%, rather than a 100%. |
Weight Based Calculations
- My Default Gradebook
- Category 1 (60% of course grade)
- Item 1.1 (25 points) (25% of category, 15% of gradebook)
- Item 1.2 (25 points) (25% of category, 15% of gradebook)
- Item 1.3 (25 points) (25% of category, 15% of gradebook)
- Item 1.4 (25 points) (25% of category, 15% of gradebook)
- Extra Credit Item (10 points) (10% of category, 6% of gradebook)
- Category 2 (40% of course grade)
- Item 2.1 (15 points) (40% of category, 16% of gradebook)
- Item 2.2 (15 points) (30% of category, 12% of gradebook)
- Item 2.3 (15 points) (30% of category, 12% of gradebook)
- Category 1 (60% of course grade)
Weight based calculations are used whenever a gradebook is in "Weighted Categories" mode. In this
case the instructor must lay out the desired weighting of each category and each item within those categories.
...
So in the table below, the hyphen indicates unscored items, and otherwise a weight is provided to indicate the course grade weight that item will contribute:
...
Fig. 4
Student | Item 1.1 | Item 1.2 | Item 1.3 | Item 1.4 | Extra Credit Item | Item 2.1 | Item 2.2 | Item 2.3 |
---|---|---|---|---|---|---|---|---|
Joe | 15% | 15% | 15% | 15% | 6% | 16% | 12% | 12% |
Melody | 20% | 20% | 20% | - | 6% | - | 20% | 20% |
Francis | 60% | - | - | - | 6% | 40% | - | - |
Roderick | 100% | - | - | - | 6% | - | - | - |
...
w i = item weight within a category
W = sum of all included item weights within a category excluding extra credit items (the instructor's "best case" weights)
r = 1 / W
p i = percentage score for a given item (points earned / points possible)
x i = p * w (weighted score for a given item: x 0, x 1 . . . x N)
y i = w * r (scaled weighted score for a given item: y 0, y 1 . . . y N), though with extra credit items r is fixed at 1.00
Z = sum of all the student's scaled scores for a given r
...
So, if we were to calculate the "Category 1" grade for Joe, we first need to examine the desired category weights for each item, as in the table below:
Fig. 5
| Item 1.1 | Item 1.2 | Item 1.3 | Item 1.4 | Extra Credit Item W |
---|---|---|---|---|---|
Percent of Category | 25% | 25% | 25% | 25% | 10% 100 |
W = 1
r = 1
We can then look at Joe's actual percentage scores for each item and calculate W, r, w0..wN, x0..XN, and Z:
...
average = (0.95 + 0.80 + 0.87 + 0.79) / 4 = 0.8525 = 85.25%
Calculating the projected course grade
Once the category scores have been calculated, a similar procedure is followed to determine if the the category weights must be redetermined (for example, if a given category has no graded items below it).
g j = category grade for each included category, as calculated from algorithm directly above
c j = category weight for each included category
h j = g j * c j
C = sum of all included category weights within a gradebook (the instructor's "best case" weights) where g j for that c j is not null
r = 1 / C
v j = h j * r
% score = sum of all h's above (h 0, h 1 . . . h N)
So, if we were to calculate the course grade for Joe, assuming the following:
Category Name | Category Grade | Category Weight |
---|---|---|
Category 1 | 0.9525 | 0.6000 |
Category 2 | 0.8725 | 0.4000 |
C = 1
r = 1
Variable | Category 1 | Category 2 |
---|---|---|
g j | 0.9525 | 0.8725 |
c j | 0.6000 | 0.4000 |
h j | 0.5715 | 0.3490 |
v j | 0.5715 | 0.3490 |
% score = 0.5715 + 0.3490 = 0.9205 = 92.05%We can then repeat this calculation for some arbitrary "Category 2" scores for Joe:
| Item 2.1 | Item 2.2 | Item 2.3 |
---|---|---|---|
Percent of Category | 40.00% | 30.00% | 30.00% |
W = 1
r = 1
So again, we can calculate W, r, w0..wN, x0..XN, and Z:
Variable | Item 2.1 | Item 2.2 | Item 2.3 |
---|---|---|---|
w i | 0.40 | 0.30 | 0.30 |
p i | 0.85 | 0.88 | 0.87 |
x i | 0.3400 | 0.2640 | 0.2610 |
y i | 0.3400 | 0.2640 | 0.2610 |
Therefore,
Z 2 = 0.3400 + 0.2640 + 0.2610
Z 2 = 0.8650
Calculating the projected course grade
Once the category scores have been calculated, a similar procedure is followed to determine if the the category weights must be redetermined (for example, if a given category has no graded items below it).
g j = category grade for each included category, as calculated from algorithm directly above
c j = category weight for each included category
h j = g j * c j
C = sum of all included category weights within a gradebook (the instructor's "best case" weights) where g j for that c j is not null
r = 1 / C
v j = h j * r
% score = sum of all h's above (h 0, h 1 . . . h N)
So, if we were to calculate the course grade for Joe, assuming the following:
Category Name | Category Grade | Category Weight |
---|---|---|
Category 1 | 0.9525 | 0.6000 |
Category 2 | 0.8650 | 0.4000 |
C = 1
r = 1
Variable | Category 1 | Category 2 |
---|---|---|
g j | 0.9525 | 0.8650 |
c j | 0.6000 | 0.4000 |
h j | 0.5715 | 0.3460 |
v j | 0.5715 | 0.3460 |
% score = 0.5715 + 0.3460 = 0.9175 = 91.75%
Melody's Case
So, if you remember from the table above and copied below, Melody had two items unscored or excused, one in each category. The result was that the overall course grade percentages for her graded items increased in value, as shown in this table. *Note that these percentages are not category weights, but course grade percentages, that is, the product of an item weight and a category weight:
Student | Item 1.1 | Item 1.2 | Item 1.3 | Item 1.4 | Extra Credit Item | Item 2.1 | Item 2.2 | Item 2.3 |
---|---|---|---|---|---|---|---|---|
Joe | 15% | 15% | 15% | 15% | 6% | 16% | 12% | 12% |
Melody | 20% | 20% | 20% | - | 6% | - | 20% | 20% |
Francis | 60% | - | - | - | 6% | 40% | - | - |
Roderick | 100% | - | - | - | 6% | - | - | - |
If we assign some arbitrary scores for these items, we can perform the same calculations we did above for Joe, but taking into account the excused/missing items.
Melody's "Category 1" Item Weights:
| Item 1.1 | Item 1.2 | Item 1.3 | Item 1.4 | Extra Credit Item |
---|---|---|---|---|---|
Percent of Category | 25.00% | 25.00% | 25.00% | 10.00% |
W = 0.75
r = 1.3333333 (repeating)
So again, we can calculate W, r, w0..wN, x0..XN, and Z:
Variable | Item 1.1 | Item 1.2 | Item 1.3 | Item 1.4 | Extra Credit Item |
---|---|---|---|---|---|
w i | 0.25 | 0.25 | 0.25 | 0.10 | |
p i | 0.89 | 0.93 | 0.98 | 1.00 | |
x i | 0.2225 | 0.2325 | 0.2450 | 0.1000 | |
y i | 0.2967 | 0.3100 | 0.3267 | 0.1000 |
Therefore,
Z 1 = 0.2967 + 0.3100 + 0.3267 + 0.1000
Z 1 = 1.0334
but since a category grade cannot contribute more than the desired weight for that category, we truncate this down to 1
Z 1 = 1.0
Melody's "Category 2" Item Weights:
| Item 2.1 | Item 2.2 | Item 2.3 |
---|---|---|---|
Percent of Category | 30.00% | 30.00% |
W = 0.6
r = 1.666666 (repeating)
So again, we can calculate W, r, w0..wN, x0..XN, and Z:
Variable | Item 2.1 | Item 2.2 | Item 2.3 |
---|---|---|---|
w i | 0.30 | 0.30 | |
p i | 0.87 | 0.91 | |
x i | 0.261 | 0.273 | |
y i | 0.435 | 0.455 |
Therefore,
Z 2 = 0.435 + 0.455
Z 2 = 0.89
Melody's projected course grade
Category Name | Category Grade | Category Weight |
---|---|---|
Category 1 | 1.0334 | 0.6000 |
Category 2 | 0.8900 | 0.4000 |
C = 1
r = 1
Variable | Category 1 | Category 2 |
---|---|---|
g j | 1.0000 | 0.8900 |
c j | 0.6000 | 0.4000 |
h j | 0.6000 | 0.3560 |
v j | 0.6000 | 0.3560 |
% score = 0.6000 + 0.3560 = 0.956 = 95.60%
Summary of example scores
Student | Item 1.1 | Item 1.2 | Item 1.3 | Item 1.4 | Extra Credit Item | Z 1 | Item 2.1 | Item 2.2 | Item 2.3 | Z 2 | % score |
---|---|---|---|---|---|---|---|---|---|---|---|
Joe | 0.95 | 0.80 | 0.87 | 0.79 | 1.00 | 0.9525 | 0.85 | 0.88 | 0.87 | 0.8650 | (0.9525*0.6) + (0.8650*0.4) = 91.75% |
Melody | 0.89 | 0.93 | 0.98 | - | 1.00 | 1.000 | - | 0.87 | 0.91 | 0.8811 | (1.000*0.6) + (0.8900*0.4) = 95.60% |
Francis | 0.87 | - | - | - | 1.00 | 0.9700 | 0.76 | - | - | 0.7600 | (0.9700*0.6) + (0.7600*0.4) = 88.60% |
Roderick | 1.00 | - | - | - | 1.00 | 1.000 | - | - | - | - | 1.000*1.0 = 100.00% |
Note that, taking each student above individually, the hyphens above could be the result of any of the following:
- Dropping the lowest score in a category
- Excusing that student from that one item in that category
- Choosing not to enter a grade for that student for that item
Project Extra Credit
Anchor | ||||
---|---|---|---|---|
|
Basically the idea is that in "categories" mode, there are two options:
(1) Project Extra Credit = TRUE
(2) Project Extra Credit = FALSE
With (1) the instructor is saying that she wants to see extra credit contribute to the score ONLY as much as it will once all grades are entered. So if the total non-extra-credit points in a gradebook are 100, and you enter 5 points of extra credit, the percentage contribution of those 5 points will be +5/100 = 0.05
With (2) the instructor is saying that he wants to see extra credit contribute EXACTLY the number of points that are entered. So if only 1 non-extra-credit item (with 10 points possible) of the above gradebook is graded, then the percentage contribution of the 5 points extra credit will be +5/10 = 0.50
In "weighted categories" mode, the impact of "Project Extra Credit" is similar, but it has a substantially different impact on scores if you have an Extra Credit category with more than one item in it. That is, when "Project Extra Credit" is TRUE in "weighted categories", it means, assume that the extra credit contribution can be for the whole category weight even if only one item is graded. If "Project Extra Credit" is false, then the extra credit contribution will be bounded to the % grade for that item.
Weight By Points
Anchor | ||||
---|---|---|---|---|
|
Weight by points is only applicable when the mode of the gradebook is set to "Weighted Categories". The grade type can be any valid grade type: points, percentages, letter grades. In "Weighted Categories" mode a checkbox labeled "Weight By Points" will be visible for any category when editing.
Checking this box will recalculate the % category values for the items under this category to match the relative values of the underlying points and scaled as though the total points for that category represent 100% of the category weight. So if you have 10 items with 10 points each, of course they will each have 10%, but equally, if you have 10 items with 40 points each, they will have 10% each.