what‘s the difference bw One-way ANOVA and One-way ANOVA for repeated measures In R

Question

for example one-way : aov.res2 <- aov(mark ~ teacher, data=my_data2) one-way for repeated measures : aov(mark ~ teacher + Error(essay/teacher), data=my_data2)

what's the difference bw teacher + Error(essay/teacher) and teacher. 1.why add plus Error() after teacher & what's that mean? 2.why in the Error, we use essay/teacher not essay * teacher?

Answer 1

First, stackoverflow likely isn't the best place to ask such a theoretical question. There are other sites that lend better to your question. Try Cross Validated .

Having studied statistics extensively, I will give you a high level answer and then direct you to look for more details in textbooks or elsewhere online.

Let's make sure we understand what repeated measures data is. An example of such data would be measuring the blood pressure of a patient every day for a week. Hence we have several "repeated" measurements from one subject. If we did this for many patients/subjects, we then have repeated measures data.

Repeated measures data is inherently different from other data because we expect that the data we observe from the same subject, say over time, will be correlated. (Referring to our previous example, we expect that the blood pressure of a patient tomorrow will be related to the blood pressure of that same patient today.) If you have repeated measures data but don't model it as such, you are leaving out important information about how the data might be related within a subject. Modeling the data properly will then give you a more complete and accurate view, particularly in the variance. Said another way, the data collected from one patient does not vary the same way that the data varies between patients.

Hopefully this helps you understand the nuances of the two methods in question. Certainly I have not explicitly detailed the coding syntax, but I hope that this answer will help you understand why they are different. Once you understand the theory better, your questions will likely change and be more specific. Good luck!

Answer 2

I found the answer: The experimental object is measured multiple times, so there will be factors within the group. The factors within the group will be specially marked in the following form,

where "teacher" is the factor within the group, and "essay" is the ID of experimental object.