Statistics Question

[johnstewartjr]

Hello All,

I'm having a hard time understanding my BIOLOGY professors use of statistics in computation of my grade. I don't believe any of the students understand the true calculation but I believe it to be incorrect. Why would he add in my SEM and then divide by 4 thus only a curve of 2.5 points when the class avg. was 67. Please verify - thanks!!

The grading scheme for this course is as follows:​

Each student’s final grade is based on the average of four exam scores; all of these values are thenaveraged to calculate the overall grade average for the class – this average determines the middle “C”value for the class.Next, a statistical analysis (called a t-distribution) is used to determine the standard error of mean (SEM).The SEM is used to determine the range, or boundaries, for each letter grade. For example, if the classaverage is a 70, and the SEM is 10, then “C” range extends 10 points, with 70 in the middle, i.e., the C- cutoffis 65, the C+ cut-off is 75.For the BIOL 1353 course this past semester, the statistical values were as follows:Average 67.02StDev 14.55SEM 10.29​

Median 68.51

The SEM value above was then used to determine letter grade ranges as shown below:A 85.88A- 82.45B+ 79.02B 75.59B- 72.16C+ 68.73C 65.30C- 61.87D+ 58.44D 51.59​

Although the raw exam averages are used to construct the distribution and curve, each student’s actualletter grade is based on their adjusted average. The adjusted average is calculated by summing the fourexam scores PLUS the SEM value of the four exam scores and dividing by four (4). Calculating the SEM ofthe exam scores for each student is a way to reward students for demonstrating improvement over thesemester where they may begin with an initially poor score, but then showing significant improvementover the course of the semester. Such an exam score pattern typically shows a greater variance, and thusa greater SEM value that is averaged into the exam scores. Bottom line – this raises the grade averageanywhere from 2 to 5 or 6 points depending on the degree of variance.​

Next, any extra credit points earned during the semester are added to this re-averaged grade score togive the final adjusted average. Extra credit opportunities came from optional quizzes given during thesemester; 1 point was earned for each quiz passed with a minimum a score of 70 – a maximum of 4 pointstotal was possible. Additionally, another extra credit point was earned for writing a brief report onbacterial species of their own choosing. Thus, earning all extra credit could result in a gain of 5 points. ​

The letter grade for each student is determined by where their final adjusted average lies on the curve,according to the letter grade cut-offs listed above. To summarize, the formula for calculating the finaladjusted average is:[(Exam 1 + Exam 2 + Exam 3 + Exam 4 + SEM of 4 exam scores)/4] + extra credit points earned​

In addition to the above, as an added bonus, every student received a one point added to their finaladjusted average. The final adjustment to grades occurred when viewing all final numerical grades sortedfrom highest to lowest values. Students that were within 0.5 points of a letter grade cut-off were bumpedup to that next letter grade; such a change applied to 18 students.Final grade calculation is as follows:​

The adjusted average is= 54.36 + 38.26 + 44.14 + 72.53 + 10.62 = 219.91/4 = 54.98 + 2 extra credit points earned = 56.98Next a 1 point bonus was added giving​

57.98; this score equates to a “D”, however this value was 0.46 pointsbelow the D+ cut-off, thus the letter grade was bumped up to a D+, giving the final letter grade posted onPeopleSoft.​

 

[sous2817]

Without seeing every exam score to calculate the average and just going on the values you've posted, your professor's calculations are correct. Can you explain why you think the professor is incorrect?

 

[johnstewartjr]

54.36 + 38.26 + 44.14 + 72.53
(these are the 4 exams with average of 52.32)
I don't understand why he is taking the SEM and then dividing it by the number of exams, diluting the curve to essentially 2.5 points.

If Ivy league schools grade based on:
Grading of individual tests

they use +/- system and one standard deviation from the class average is a C-... which in this case would be
(67.02-14.55)= 52.47 would be bottom line C-

Even using his calc she had a 57.98, well into C range.. his system is obviously not to Ivy league standards and any other for that matter..

 

[sous2817]

The professor does explain why you add the SEM before dividing:

Calculating the SEM ofthe exam scores for each student is a way to reward students for demonstrating improvement over thesemester where they may begin with an initially poor score, but then showing significant improvementover the course of the semester. Such an exam score pattern typically shows a greater variance, and thusa greater SEM value that is averaged into the exam scores. Bottom line – this raises the grade averageanywhere from 2 to 5 or 6 points depending on the degree of variance.

In your case, it added 2.5 points to your grade. Had you had a wider variation, it would have added more points.

Also, you're using the wrong number to calculate the grade range, try using 10.29. On top of that, 10.29 is the WHOLE RANGE for a letter. So you need to divide that by 2 (giving you a value of 5.145). So you take 67.02 +- 5.145 and you get the upper and lower bounds of a C grade (72.165 - 61.875).

I don't see how or why the Ivy league ties in to it but you're trying to compare how one professor curves versus another for a particular course. If it's any consolation, when I took biology, there wasn't a curve. A "C" grade was between a 79 - 70, period. No curves, no extra points, nothing like that. So in my class, given the exam scores you posted above, you'd end up with a 52.3225...or an "F".

 

[johnstewartjr]

your reply makes no sense at all, first of all it's obvious how he comes to his grade range with 10.29 split between each range.. that wasn't the question.

second - what you received in biology is irrelevant and I don't remember you posting what the class average was.. so I could really careless if it was 70-79 seeing how I don't know what the class average was or if it was worth a curve. I would guess in the case of professor reviews, if he were to not give a 2.5 point curve or whatever the case may be based on each students variation, then the average for the class would be a D (would probably warrant dean/dept chair attention).

Columbia was used as a benchmark example as to how curves are used using standard deviations..


look forward to more RELEVANT replies as to how the SEM (true meaning) applies to his calculation and why he is using it or is it an arbitrary way to add it in to the exam averages and then divide by # of exams.. is this standard procedure.. and why this methodology over standard deviation as in the example I used.

 

[johnstewartjr]

Additionally if SEM is the ST dev of population / Sq. Rt of sample size then that would equal 14.55/2 = 7.28. So he has my SEM as 10.62, which I believe to be an incorrect calculation by him.

 

[sous2817]

Sorry...didn't realize you were applying how a class you're not enrolled in curves to your grade so you can justify a higher grade.

I was using my biology grade as a benchmark much like how you used your Columbia example...to point out that there are numerous ways to curve (or not curve in my case) a grade. The arbitrary class from an arbitrary school you picked in your 2nd post uses standard deviations. The class you mentioned in your first post uses a t-distribution and my class didn't use any. Your posts boils down to you not agreeing with the methodology the professor used. Math is correct, theory is correct, end result is correct. You're going to have to ask the professor why they decided to use the method they did. There isn't a "right" or "wrong" answer...just an answer that you either agree with or disagree with. I don't think you're going to get the answer you're looking for on an Excel forum..maybe a forum on statistical theory (Statistics Help @ Talk Stats Forum) or a rate the professor (Rate My Professors – Find and rate your professor, campus and more – RateMyProfessors.com) type of website would be a better fit.

I don't think you'd want to go to your professor showing that they calculated your SEM too high. Wouldn't a SEM of 7.28 give you a lower final score...

 

[johnstewartjr]

yes, it does, but it proves a point to the dean/chair, etc that atleast he will be on their radar going forward (so maybe future students will benefit?) as I don't believe a one hundred level freshman biology prof. should be applying this degree of statistics to his curving methodology as well as being incompetent in his calculations if he can't simply compute my SEM...

 

[sous2817]

Well the main thing is that you hopefully get some closure. Either way, best of luck moving forward!

 

[xenou]

Hi johnstewartjr,
If you want to prove your prof is wrong you had better not simply accuse. Show the maths. I don't see any facts in your complaints - you merely claim that the teacher is wrong with offhand references to curving at other schools (which the teacher is in no way obliged to follow as standards). This is not the way to go to the dean.
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