I am explaining the statistical setting that I am faced with, for which I have 2 questions.
1.
I have a simulation model running for 1 year (after the warm-up period) that simulates the patients coming into a clinic for their treatment (set up daily) (a patient may come in for their treatment once every week for the next 5 weeks on Mondays). One may consider this as a daily simulation termination.
The first question that I have regarding Independent and Identical Distributions (IID) is that I need to compare the number of patients that are present in the clinic (let us say, on Mondays). Yet, the number of patients each Monday may be different from Monday to Monday (this Monday, we have 100 patients; next Monday we have 105 patients; next Monday we have 97 patients). Each day is independent from the other, however, I do not believe that each day (in this case, Mondays) is identically distributed (taking in consideration that n is different). Thus, the question is: how can I compare, statistically independent days that are not identically distributed?
2.
A patient is scheduled for their first visit for 60 minutes (60 minutes window). Even through the doctors, nurses, pharmacists (and all the staff) have their own distributions regarding the time provided to the patient [thus, IID], the other problem that I face is that each patient has different needs: [for example]
Patient A: doctor + nurse.
Patient B: doctor + nurse + pharmacist.
Patient C: doctor + nurse + social worker.
Therefore, even if the patient is given 60 minutes for its appointment, because there are different staff interacting with the patient, are the durations of the patient’s visit IID in this context? They are independent [no link between patients]; they should be identically distributed as they (patient and staff) have only 60 minutes at their disposal, ….. yet…. I am not certain about this.
In the case where data-sets are not IID, how can they be compared?
Any help and guidance is very much appreciated.
Philip D DeWitt
Hello Philip,
Yes, the first assumption is correct: the data is independent.
#1. So, to see if I understand this correctly, if I compare Mondays to Mondays I should have the same Poisson counting process (with the same lambda); yet, if I compare Mondays to Tuesdays, the lambdas would be different. Is this correct?
#2. I do not model the wait time: I let the system provide me with the information (taking in consideration how busy or not the system/environment is). Your advice and comment makes sense.
The caveat: I do simulate patients with multiple visits. The first visit [60 mins] is the same for everyone. Yet, Patient A may have 5 visits, while Patient B may have 9 for their treatments (given 20 mins windows in the schedule). The number of visits is determined by a probability distribution [from which all the patients draw from it][this distribution was built from historical data). Why (how) would Patient A be dependent on Patient B?
Regards,
Alex
Andrew Paul McKenzie Pegman
Hello Andrew,
Thus, when in doubt, use the non-parametric tests. I used the Wilcoxon tests [signed rank and rank sum].
Thank you.
Yes, sorry, independence is required for non parametric tests too. You can check for independence using ICC (intraclass correlation) and test its significance. You might then have to address the non independence by using data that have different environments, randomise the data, or ensure the data is from different groups. But sadly, the experiments often have to be repeated to remove non-independence using those factors
- Badges
- Science topic