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Equivalent Grading System

The following grading system precisely equates rubric, point, percentage, and letter grades using the following equation:

Rubric Base and Quality Points = (Percentage – 55) x .1

OVERALL PERFORMANCE	RUBRIC BASE	QUALITY POINTS	PERCENTAGE EQUIVALENT	PERCENTAGE RANGE		LETTER GRADE
Excellent	4	4.0	95		93.4-100.0		A
Excellent	4	3.7	92		90.1-93.3		A-
Above Average to Average	3	3.3	88		86.7-90.0		B+
		3.0	85		83.4-86.6		B
		2.7	82		80.1-83.3		B-
Average to Below Average	2	2.3	78		76.7-80.0		C+
		2.0	75		73.4-76.6		C
		1.7	72		70.1-73.3		C-
Needs Improvement	1	1.3	68		66.7-70.0		D+
		1.0	65		63.4-66.6		D
		.7	62		60.1-63.3		D-
Unacceptable	0	0	55		50.0-60.0		F

Percentage grades over 100 are averaged as 100
Percentage grades under 50 are averaged as 50

Rationale

Grades are typically given in a 12-step letter scale (A – F) but translated into a final 41-step quality point score (4.0 – 0) for averaging. Schools typically set letter grades and their point equivalents. Many faculty, however, use a 101-step percentage point score (100 – 0) some or all of the time for assigning or averaging grades before determining a final letter grade. To the consternation of some students, faculty members are typically free to use their own percentage system with most opting for what can be called traditional 7- or 10-point grading scales.
Since the final arbiter of a student’s academic achievement is generally his or her point score, one could argue the most appropriate percentage system is one that most accurately mimics point scores. Furthermore, one could argue that calculations should be made to the tenth place for accuracy and for making the differences between competing approaches to grading marginal. Calculating by 100ths makes differences even more marginal.
One could multiply each quality point by 25 to create a percentage system but that, of course, represents no academic challenge. Multiplying points by 10 and assigning them to the top of the percentage system (from 60 – 100) puts one closer to the mark but a direct translation would mean an A could only be achieved by the near impossible feat of averaging 100. Assigning percentages by working down from A instead of up from F would run an A from 97.1 – 100. While better, that is still too academically challenging and gives disproportionate weight to a D-.
When counting quality points by 10ths, there are 10 steps between whole grades. Therefore, assigning 10 percentage points to each letter grade range is logical. Because 0 is its own step on the scale, when counting percentage grades by 10ths, there is an extra 10th for the entire grading range that can either be assigned to the A range or the F range. Assigning it to the A range (90.0 – 100) is the normal convention but assigning it to the F range (90.1 – 100) is marginally more rigorous and arguably more accurate, since the extra step comes from counting 0.
Dividing those 10 steps by 3 creates minus, whole, and plus grades. Because dividing 10 by 3 leaves an extra 10th of a point, when counting by 10ths, each letter range also has an extra 10th that can be assigned to either the minus, whole, or plus range. While the minus range is marginally more rigorous and logic suggests the whole grade, mirroring quality points indicates it should be assigned to the plus grade.
As such, there are 6 possible combinations for assigning percentage ranges that can vary by as much as 2 10ths. The table above places the extra 10ths within the F range for marginal accuracy and rigor, and the plus of the letter range to mirror quality points. The use of other combinations is equally valid.
Since there are typically no A+, F+, or F- grades (although, if desired, they could be included in this system) those ranges should be added to their respective whole grade ranges.
In combining grades that originate as letters with other letter grades and percentage scores, it is necessary to assign each grade a number. Using a percentage equivalent score rather than a point score is sometimes simplest because grades originating as percentages do not need to be converted for averaging.
Dividing minus, whole, and plus grade ranges by 2 and rounding the result to a whole number creates percentage equivalent grades that can be equated to point and letter grades. A and F percentage equivalents should be calculated as if there were A+, F+, and F- percentage ranges. The result is an exact mapping of quality point scores from 55 – 95 percentage points using the formula: (Percentage – 55) x .1 = Quality Point.
As in quality points, with this system if an F is averaged with an A the result is a C. This becomes problematic, however, when a missing letter grade assignment is combined with a missing percentage grade assignment. Each would receive an F but one could be averaged as a 55 while the other could be averaged as 0. Therefore, if both letter and percentage grades are used, percentage grades less than 50 should be averaged as 50 (5 points below the F percentage equivalent). Conversely, to maintain parity, the maximum percentage grade should be 100 (5 points above the A percentage equivalent). An exception to the lower limit could be made in the case of cheating, so there is a simple and tangible penalty beyond that suffered for missing or poor work.
If a five-step rubric is created with 0 to 4 possible points, it can be directly equated to quality points and, hence, percentages. If the total value of a rubric equals forty points, for instance, ten areas with 0, 1, 2, 3, or 4 points, or five areas worth 0, 2, 6, or 8 points, then the total can be directly equated to percentages by adding 55.
Finally, the suggested overall performance descriptions are designed to straddle traditional definitions and inflated realities, allowing the flexibility to be more or less stringent, as desired.

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2013/01/07

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Equivalent Grading System

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