Graphing Conundrum in Nursing Program: Fairness in Grading?

[jlittle13]

Hey all, I'm new to this forum and have a question I hope you guys can help me with. Some background on my math knowledge: I took pre-Algebra in 8th grade, Analysis I 9th, Analysis II 10th, Calculus 11th, Statistics 12th. (Yea, apparently I tested out of Algebra I-II but since I never took it, there is a lot that I never learned properly) I am now three years into college and have only taken college level statistics. In HS I was pretty good at math, now I'm very much out of practice. I am not entirely sure which forum I should put this on so Moderators feel free to move it.

My conundrum:
I'm currently in a nursing program and this question has to do with the way my school grades us for the semester (hang on with me, this does have to do with fairly difficult math, specifically graphing, let me explain)

Alright so this semester is split in half, and there are two units to take (each with three x 50 question tests), there are also two sections.
Unit A = Respiratory and Cardiac
Unit B = Gastrointestinal and Genitourinary
Section 001 takes unit A first, then unit B. Section 002 takes unit B first, then unit A. There is also a final test (HESI) that is worth 20% into whatever unit you take last.

We receive two final grades (that go onto the transcript and determine progression in the program), one for Unit A, one for unit B. The grading breakdown looks like this:
Section 001 -
Grade #1 = 100% Unit A grade.
Grade #2 = 80% Unit B grade + 20% HESI

Section 002 -
Grade #1 = 100% Unit B grade.
Grade #2 = 80% Unit A grade + 20% HESI

The overall passing grade for each final grade is 74.5.

I realized today that two individuals could score the same in both units and on the test, but be in different sections, and one could pass, and one could fail.

For instance:
Unit A grade = 90%
Unit B grade = 80%
HESI = 50%

Section 001 student
Grade #1 = Unit A grade = 90% Pass
Grade #2 = Unit Bx0.8 + HESIx0.2 = 80x0.8 + 50x0.2 = 64x10 = 74% = Fail
This student has to wait a year before (s)he can retake the failed class.

Section 002 student
Grade #1 = Unit B grade = 80% Pass
Grade #2 = Unit Ax0.8 + HESIx0.2 = 90x0.8 + 50x0.2 = 72+10 = 82% = Pass
This student progresses as normal.

As you can see, with the same grades on all tests, just taken in a different order, one would pass and one would fail. Not exactly fair.

This is my question:
The proof proves that this could be an issue in some cases, and I want to quantify the incidence of that issue.
Is there a way to plot these values on a graph (three dimensional maybe? maybe more than one graph? I'm really not sure) To show when the section difference matters and where it doesn't?

Some parameters would be:
Unit A grade = a number between 0-100 at intervals of 0.6(repeating)
Unit B grade = a number between 0-100 at intervals of 0.6(repeating)
HESI = a number between 0-100 at intervals of 2

I messed around with an online graphing calculator and am at a loss.

I hope that makes enough sense for you all to understand. If you need any clarification let me know. I'm planning on compiling the information and presenting it to the Dean, hopefully we can get a policy change to split the HESI 10% to each section.

 

[haruspex]

How about this:
Pick some HESI score, 50% say.
You can plot the pass/fail threshold as a graph of Unit A score (first) against Unit B score. Do the same again for the other order and observe the asymmetry. You could then repeat this for some other HESI scores (making sure not to make it too cluttered). Of course, the largest effect will be for the lowest HESI scores.

 

[jlittle13]

Making some progress. I realized that I can plot a line -4x+372.5 that represents the passing grades needed. The x-intercept is 93.125 (What you would need to get on your second half unit grade if you scored a zero on the HESI) and the y-intercept is 372.5 (the opposite, though impossible). Plot points to the left of the line are failing grades, points to the right are passing. The parameters of the graph would be 0-100 on the x and y axis.

Haruspex, is that what you were talking about? Then do a scatter plot of sorts with grades, do two different graphs (One for A one for B), and compare?

 

[haruspex]

Making some progress. I realized that I can plot a line -4x+372.5 that represents the passing grades needed. The x-intercept is 93.125 (What you would need to get on your second half unit grade if you scored a zero on the HESI) and the y-intercept is 372.5 (the opposite, though impossible). Plot points to the left of the line are failing grades, points to the right are passing. The parameters of the graph would be 0-100 on the x and y axis.

Haruspex, is that what you were talking about?

Yes, but that's just for the case of a zero score on HESI, right? I was suggesting taking a few different HESI scores (10%, 20% etc.) and doing this for each. Also, contrasting with the lines obtained by taking the units in the other order. These would just be the mirror image of the first set about the line y=x.

 

[jlittle13]

That's the case for all possible grades on one Unit and the HESI. The x-axis and values represent the unit grade worth 80% and the y-axis and values represent the HESI grade worth 20%. Here is a link to it. https://www.desmos.com/calculator/pqbjjs5oxg
Every plot point to the left of the line is failing, to the right is passing.

Could you explain to me how you'd do this in your way?

I'm conferring with my father and we are having a hard time trying to show the incidences in which it is different. We are tending to lean toward some sort of three dimensional graph? Because there are three different variables? I'm not sure. Thanks for the help!

 

[jlittle13]

OK. We are at a hospital waiting for my brother to get out of surgery and my father and I are having a lot of fun with this question while we wait.

We figured something out. Three dimensional algebra. I've never done it in practice so hang with me.
One equation is 74.5=0.8x+0.2y (a.k.a. y=-4x+372.5) representing the second half of the semester with the HESI.
The other is a straight line, z=74.5, representing the grade you need on the first unit in the semester.

Plot that, and any values where both z>74.5 and the point (x,y) lies above the y=-4x+372.5 line is passing. Any other values are failures. How can I graph that? Is it possible? Then I can find all passing values, switch z and x, and find where it is now failing. BAM. Then I have the incidence.

 

[haruspex]

Plotting in 3D is tough and doesn't necessarily make it any clearer.
I understand now what you did in post #3: you fixed the first unit result and plotted the pass/fail line for second unit v. HESI. All I'm suggesting is, instead, fix the HESI and plot Unit A v. Unit B. Do two plots, one assuming Unit A is taken first and the other assuming Unit B is taken first. This should make the asymmetry between the units clearer.
If you want to see how the asymmetry is affected by the HESI score, plot the same pair for different HESI values. Low HESI values will give the starkest result.

 

[jlittle13]

[EDIT:Actually, this doesn't work how I thought]
Another promising option is this. Just normal algebra here. We use the 74.5=0.8x+0.2y. We also use x(sub2)=74.5
the graph looks like this https://www.desmos.com/calculator/otlxdxutrs.

Anything to the left of both lines is a definite fail. Anything to the right of both lines is a definite pass. [STRIKE]Anything between the two lines represents the incidence. In the top area, the HESI holds up a Unit 2 mark under 74.5 that would have failed you out had you taken it first. In the bottom area, the HESI brings down a mark that would have passed had you taken it first.[/STRIKE]

 

[jlittle13]

Haruspex. Could you give me an equation for the plotting of that? Just an example to help me get an idea? I'm trying to wrap my mind around it but I'm pretty wiped.

 

[haruspex]

Haruspex. Could you give me an equation for the plotting of that? Just an example to help me get an idea? I'm trying to wrap my mind around it but I'm pretty wiped.

Suppose we pick HESI=50%. To pass, we need first unit >= 74.5% and second unit >= 80.625%. (80%*80.625% + 50%*20% = 74.5%). Plotting A as first unit and B as second unit, that gives us a rectangular fail region. Now swap the order of the units and you flip the rectangle about the axis y = x.