# Statistics Question

## Main Question or Discussion Point

I am an instructor in a DOD academy. I am trying to show that the way that students are being graded in a particular performance test is a statistical improbability.

I have 200 students, all of which recieved a final grade of A in a course which consisted of 38 performance tests. These students consisted of 6 different classes which conducted these tests.

the academy works fon a graduate level 10 point grading system, i.e. 100-90 =A, 89-80 = B, 79-70 =C, 69 and below failure.

My logic tells me that it is impossible for 200 human beings with varying intelligence levels, all to recieve the grade of A for 38 individual performance tests.

I may not be providing sufficient amount of information, but if anyone out there can help, it would greatly appreciated.

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If P is the chance of a student getting A's on all 38 tests, then the probability of your event is P^200. For even odds of every student getting all A's, P would have to be as high as 0.996. Not very likely, unless the tests were all extremely easy.

HallsofIvy
Homework Helper
If P is the chance of a student getting A's on all 38 tests, then the probability of your event is P^200. For even odds of every student getting all A's, P would have to be as high as 0.996. Not very likely, unless the tests were all extremely easy.
But that last, "unless the tests were all extremely easy", is what makes such a statistical analysis invalid. You cannot say that the results are a "statistical improbability" without addressing just what it is that is being tested and how likely each individual student is to get an A on each individual test. I've known some P.E. classes where just showing up for the test guarenteed you an A!

If P is the chance of a student getting A's on all 38 tests, then the probability of your event is P^200. For even odds of every student getting all A's, P would have to be as high as 0.996. Not very likely, unless the tests were all extremely easy.
that is not good statistical reasoning. we're not trying to find the probablitiy of getting straight A's for an individual. we need an actual test for significance.

promethius is right, we need some more info: First, we need the complete set of numerical grades for each student (this can be anonymous, if desired; we only need the numbers). Second, we need you to give an approximation of what the typical grade for a student should be (based on the difficulty of the course). this doesn't have to be exact, as there can never be an "exact estimate", but give us an idea of what you think the average grade should be.

Provide these two components, then we can get into the specifics.

But that last, "unless the tests were all extremely easy", is what makes such a statistical analysis invalid.
Nonsense, I made a correct statement. I did not assert that there was necessarily any cheating going on. I simply said that either the tests were all extremely easy, or the result was very unlikely under the assumption that the grades were fair. One of those things is certainly true.

If you want something more statistical, you can observe that if you estimate the chance of a student getting an A at 0.986 or below, then the null hypothesis that the students' grades were fair is rejected at the 0.05 significance level.

Nonsense, I made a correct statement. I did not assert that there was necessarily any cheating going on. I simply said that either the tests were all extremely easy, or the result was very unlikely under the assumption that the grades were fair. One of those things is certainly true.
we are comparing a whole group, not "the probablity of a random student getting x number of A's in a row is y".

how do you even know what to reject or not when you dont even have the data?

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HallsofIvy and aznshark4 are correct in their reasoning.

My logic tells me that it is impossible for 200 human beings with varying intelligence levels, all to recieve the grade of A for 38 individual performance tests.

First, just to be a finicky arse, unless those 200 subjects were randomly selected, so there was no significant difference between them, would the experiment be properly conducted. I'm willing to bet that testees in this DOD environment would bias the sample.

Second, we need you to give an approximation of what the typical grade for a student should be (based on the difficulty of the course).
Exactly. There are tests that could evaluate the two samples--explaining those tests and why they are valid to a group of non-statistics students could be harder than the tests themselves, however...