# Number of Tests and Accuracy. Criteria?

• Bacle2
In summary, the conversation discusses the issue of accurately estimating class attendance as a measure of teaching effectiveness. The department head suggests switching from weekly to bi-weekly attendance, but the speaker is concerned about the potential distortion in the estimate of the true mean. The speaker considers three options for arguing against the switch, including using a difference-of-means test and the Law of Large Numbers. It is also suggested to take attendance every class and report the highest two numbers each week, as well as considering paired analysis to account for individual student attendance patterns.
Bacle2
Hi, All:

I have the following problem:

My department head wants to accurately estimate class attendance, as a measure

of the effectiveness of my teaching. For that, I used to take attendance weekly, i.e., once

each week, selecting the day at random, from which I would construct a confidence interval

at the end of the year. The department head wants me to switch from counting weekly to

doing so bi-weekly, since she must enter the data in the computer , submit, etc. I think

this is not a good idea, and I told her so.

I wonder what criterion I could use to argue that this swich is likely to cause a

non-trvial distortion in the estimate of the true mean weekly attendance.

What I have considered, so far:

1) I take the mean of all weekly attendance values, and I construct

a confidence interval. Problem (for me) is that the confidence interval will become

wider as N:= sample-size decreases. So, fewer measurements means smaller accuracy.

2) Trying a difference-of-means test, between the weekly measurements and the

biweekly measurements, and showing that the initial hypothesis is not accepted

at, say, a 95% confidence level.

3)Just a general argument that the Law of Large numbers suggests that more

measurements I get , the more accurate the estimate will be.

Do my arguments work? Should I consider anything else?

If we consider all class days to have the same distribution of attendance, number 2 is the only one that sounds reasonable and if you go to the trouble of doing that, you are proving that you can handle taking bi-weekly attendance.

Take attendance every class and report the highest two numbers every week. (Say that you thought "statistics as ordered" meant "order statistics".)

If we consider the class days to have different distributions of attendance then taking bi-weekly sampling is a "sampling without replacement". I doubt this line of thinking has any practical implications for your dilemma, but it is interesting to contemplate.

I would also suggest that you may even want to do some kind of paired analysis.

The reason I suggest this is because if certain students have a pattern of missing attendance then this information would be useful for you in demonstrating that this kind of behavior might be attributed more to the student than yourself.

If you had say a pattern of behavior where students with poor attendence history were unique with respect to other students that had high attendence history then even if you had some significant amount of people who didn't show up for class at all for the majority of the teaching period, then this would reflect more the student than yourself and it's important to take these kinds of things into account because if you didn't, the person you're under in the food chain will look at the statistic and then say 'this guy sucks' when given the other information, the person above you would say 'we seem to be accepting students that don't give a hoot' and that then becomes a separate administrative issue.

I'm sure there are more things like this but to me considering this is used to evaluate you, I thought it was important to bring it up.

## 1. What is the significance of the number of tests in determining accuracy?

The number of tests refers to the total number of times an experiment or observation is repeated. In scientific research, a larger number of tests can increase the statistical power and reliability of the results, leading to more accurate conclusions.

## 2. How does the number of tests affect the precision of the results?

The precision of the results is directly related to the number of tests conducted. The more tests that are performed, the smaller the margin of error and the more precise the results will be.

## 3. What is the ideal number of tests to ensure accuracy?

The ideal number of tests varies depending on the type of study and the magnitude of the effect being measured. In general, a larger number of tests will lead to more accurate results, but it is important to balance this with practical constraints such as time and resources.

## 4. What are some common criteria used to determine accuracy in scientific experiments?

Some common criteria include statistical significance, confidence intervals, and p-values. These measures are used to determine the likelihood that the results are not due to chance and provide a level of confidence in the accuracy of the findings.

## 5. How does the type of test affect the accuracy of the results?

The type of test used can have a significant impact on the accuracy of the results. Some tests are more sensitive and specific than others, meaning they can accurately detect smaller differences or variations. It is important to choose the appropriate test based on the research question to ensure accurate results.

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