Suppose there are 1,050 students all age 15 and each student is randomly assigned to one of seven different teachers. However, teachers are allowed to decide how many students they want to accept in their classroom. One teacher is only willing to accept 32 students, for example. Another teacher is willing to accept 279 students. The distribution of students is shown below.
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The seven teachers are given one task only. In just 5 minutes, they are supposed to teach their class how to draw a pony. After the lesson has finished, each teacher must give her students a test which involves drawing a pony on a sheet of paper. The students cannot cheat when they are taking the test. They can either pass or fail the test. Passing (or failing) is completely subjective and entirely at the discretion of the teacher who taught the lesson.
The overall "pass rate" is 84% for the total of 1,050 students. However, some teachers are much lower than this rate, while others are much higher.
Using SAS, for each of the 7 teachers I want to be able to quickly know if the pass/fail rate is within an acceptable range, but I don't know how to calculate that given the fact that each teacher has a different class size. For example, at first glance it looks like teacher Rogers has a higher-than-average pass rate (86% versus 84%) but the significance of teacher Rogers having an 86% pass rate is affected by the fact that she only taught 32 students.
Also, if I compare each individual teacher's "pass rate" with the mean rate for all 7 teachers, there is a problem: The mean for the 7 teachers includes the pass/fail data for the teacher I am comparing. In other words, if I want to compare teacher Rogers with the other teachers (the "peer" group), I need to remove the data for teacher Rogers from the peer group, correct?
For example:
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I can manually write the necessary code to calculate odds ratios and test for significance with Chi square for each of the seven teachers, making sure to remove from the "peer group" the data for the teacher who is being compared to the control group. But that seems like a very slow and cumbersome process.
Can anyone suggest an easier and faster way to compare the pass/fail rates among the 7 teachers? I would be most grateful! =) Especially if it involves SAS.
The seven teachers are given one task only. In just 5 minutes, they are supposed to teach their class how to draw a pony. After the lesson has finished, each teacher must give her students a test which involves drawing a pony on a sheet of paper. The students cannot cheat when they are taking the test. They can either pass or fail the test. Passing (or failing) is completely subjective and entirely at the discretion of the teacher who taught the lesson.
The overall "pass rate" is 84% for the total of 1,050 students. However, some teachers are much lower than this rate, while others are much higher.
Using SAS, for each of the 7 teachers I want to be able to quickly know if the pass/fail rate is within an acceptable range, but I don't know how to calculate that given the fact that each teacher has a different class size. For example, at first glance it looks like teacher Rogers has a higher-than-average pass rate (86% versus 84%) but the significance of teacher Rogers having an 86% pass rate is affected by the fact that she only taught 32 students.
Also, if I compare each individual teacher's "pass rate" with the mean rate for all 7 teachers, there is a problem: The mean for the 7 teachers includes the pass/fail data for the teacher I am comparing. In other words, if I want to compare teacher Rogers with the other teachers (the "peer" group), I need to remove the data for teacher Rogers from the peer group, correct?
For example:
I can manually write the necessary code to calculate odds ratios and test for significance with Chi square for each of the seven teachers, making sure to remove from the "peer group" the data for the teacher who is being compared to the control group. But that seems like a very slow and cumbersome process.
Can anyone suggest an easier and faster way to compare the pass/fail rates among the 7 teachers? I would be most grateful! =) Especially if it involves SAS.