Right Wing Nation

I finally solved the problem (without the help of MS customer support), and got MS Office 2007 installed on my new desktop (I installed Photoshop this morning, and I’ll install SPSS later today). Playing around with Excel reminded me of the reason I love Excel 2007, which in turn reminded me of, well, keep reading.

Months ago, I saw several dishonest statements on edublogs (sorry, it’s been months ago, and I have neither the time nor the inclination to find links at the moment), stating that zeroes are not valid scores. This is not dishonest in itself, but the threads upon which I commented were those in which the author claimed that zeroes were not statistically valid scores.

That is false.

Zeroes are often statistically invalid for calculating descriptive statistics for the class, such as means or standard deviations. But that does not imply that a zero is an invalid measure of a student’s performance. Note that I pointed this out in comments on these blogs, and got no reply. I assume, therefore, that the statements were made not out of ignorance, but dishonesty.

How does a student get a zero on an exam or assignment? Theoretically, a student might put his name in the exam, then get a zero because he didn’t know any of the answers, although the probability of this decreases as the number of questions increases (that is, it’s almost impossible on, say, a 100-question exam, but entirely possible on a 10-question quiz or assignment).

Assuming that each question has four distractors, and therefore that the probability of randomly getting any question correct is 0.25, the probability of getting a zero on a 10-question quiz is 0.056, or 5.6%; the probability of doing the same on a 100-question exam is 3.2072*10^-13, or 0.00000000000032, or 0.000000000032%.

A student could put his name on an exam, quiz, or assignment and answer nothing, that is, turn in a blank. But how frequently does this happen? How stupid can a student be to ensure a zero, when he could randomly answer, and get a somewhat higher score?

Or a student could not show up to take the exam or quiz, or not turn in the assignment. We’ll return to this scenario in a moment.

If you are calculating descriptive stats on a 100-question exam, and if you have zeroes from students who took the exam, but against all odds, managed to get zeroes (as I said, the probability of this is microscopically small), the zeroes are valid, and should be included in the calculation. Why? Because the students who got zeroes took the exam. Therefore, when calculating descriptive stats for the class, that is, answering the question, “How did the class do on the exam?” requires that you include the zeroes.

This, by the way, has never happened to me, in many years of teaching, grading, and calculating stats. The odds are far, far too small.

The same is true if instead of a 100-question exam, you are calculating class stats for a 10-point quiz or assignment (I have had this happen, quite often, because the probability of getting a zero is much, much higher).

To sum up: If you are calculating performance, and the measure of performance for some students is zero, those zeroes are statistically valid. Leaving them out will artificially inflate your class means.

But we have that other scenario, the one I said I’d address, where Johnny got a zero because he didn’t take the exam (or turn in the assignment). What about that?

Are you going to let Johnny make up the exam? If you are not, then his zero should be excluded from the scores when you calculate class stats, because he did not take the exam. Including his zero will artificially lower your class mean since he did not participate in taking the exam.

However, if you are going to let Johnny make up the exam, the question becomes when you let him make it up. If he takes the exam the day after the class took it, say, then include his score (whatever it may be) when you calculate class stats. But if you let him go a week or two, or worse, longer, before he makes up the exam, do not include his score when calculating class stats. By giving him all of that additional time, you make his score a different measure than those of the rest of the class. You cannot compare his performance on the exam to the performance of the rest of the class.

That leads us, of course, to the question of making up exams or accepting late assignments. This, I suspect, was the agenda of those edubloggers who falsely claimed that zeroes are not statistically valid scores, particularly since all were proponents of laissez-fâire grading policies.

If you work in the primary or secondary schools, your grading policy may very well be dictated from above, and you have no choice. But ignoring that, I hold that, at least in the secondary schools, such mushy gooey laissez-fâire grading policies are destructive.

Note that there are very good reasons for not showing up to take an exam, or not handing in an assignment on the due date. Grandmothers really do pass away. Students really do have religious holy days (well, at least some). It is only reasonable to allow students with valid reasons to make up exams or turn in late assignments. I refer here specifically to students who do not have valid reasons for showing up to take the exam (and “my alarm clock didn’t go off” is not a valid reason).

You teach students bad lessons that must be unlearned, with a great deal of pain for those students, when you let Johnny make up the exam. You teach Johnny that scheduling means nothing, that he may come and go as he likes, and do his work or not as he likes, without consequence. Johnny will not remember you kindly later in life when he fails his classes at the university, or is fired from his job because of the lesson you taught him.

Just as bad, perhaps worse, is that you teach the students who are responsible enough to have shown up for the exam that you have no regard or respect for them. You do not care that they are responsible and take education seriously, while Johnny does not. And if you’re sending that message, then you have no right to complain about students not taking education seriously, do you. You do not take it seriously, so why should they?

If you set your grading policies, and if you teach in the secondary schools or above, then there is no excuse for laissez-fâire grading policies, where you allow any student to turn in any assignment at any time he likes, unless none of your assignments is due on a specific date. You have no right to hold Johnny and the rest of the class to two different standards. It’s called fairness.

Of course, we always got a list of every possible religious holy day from every imaginable religion on the planet every semester, far too many to avoid scheduling exams or due dates on holy days. So we set a policy: If you cannot take an exam or turn in an assignment because of religious observance, tell your professor and make alternative arrangements before the date of the exam or due date, and we will happily accomodate you. Come afterwards and claim you couldn’t take the exam because you were at Good Friday services, and you get a zero. For “acts of God,” we only required documentation of some kind.

Still, I always got a few students who didn’t take the exam, and one or two who just disappeared, usually early in the semester, and didn’t drop the class. Those zeroes are invalid, and cannot be included in calculating class stats.

That leads us to Excel 2007. Because I always had zeroes that had to be exlcluded, I could never use the AVERAGE() function, and instead had to use SUM(range)/COUNTIF(range,”>0″). But Excel 2007 now has the AVERAGEIF() function, more than enough reason to upgrade. (Unfortunately, I don’t believe there is a STDEVIF() function.)

But back to zero scores. Yes, they are in many cases, valid scores. A zero is certainly a valid measure of how a student performed if he couldn’t be bothered to take the exam or do the assignment. In other words, a zero is a valid score for assessing that student’s performance. That student chose the zero when he didn’t take the exam. That it may not accurately reflect his knowledge is irrelevant, since by choosing not to take the exam, he made his knowledge irrelevant. Pandering to such irresponsibility undermines the educational mission, both with the irresponsible dolts and with the responsible students, and it undermines your creditiblity as an instructor.

By the way, there’s a rather entertaining article about multiple choice questions and probability here, if that sort of thing turns your crank. And if you’re curious, no, I have never used guessing penalties (you know, where you subtract a value from the score for each incorrect answer), but I did have an otherwise abominable professor in grad school who dealt with random guessing on tests by using paired T-F questions of the following format:

Statement A.
Statement B.

A. Both statements are true
B. Both statements are false
C. The first statement is true and the second statement is false
D. The first statement is false and the second statement is true

I thought it ingenious.