# Compare between simulation and observation

Hello,

I have observed data collected from work field represent tasks time. I have simulate the work field activities and insert the same starting time of the real data. Now, I need to compare between the simulation output and real work output to see how much my simulation closer than the real work. My question is which type of t test should I run, paired t test or unequal variance t-test?
Please note that I have insert 2479 tasks to both system. However, the output of the real system is 2479 and the simulation 2214.
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Commented:
What is your data?  Time required to complete a task?  Are all the tasks the same?  Are all the workers equivalent?

How did you analyze and model the observed data?
Do you have more than mean and SD?  Does it fit a normal distribution?

What is your simulation based on?

>>  Insert 2479 tasks to both system. However, the output of the real system is 2479 and the simulation 2214.
What happened to the other 265 tasks?  Did the simulator run out of time?

If you run the simulation again (with a different random seed), do you get different results?
If you run it ten times, do some complete more than 2479 tasks and some less?
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Commented:
I don't know how you are analyzing the data or modeling the process.
But given the limited info I have, this is how I would proceed:

## 1.

There are 2479 observations of task time.  Find the mean and STD and try to fit it to a normal distribution.

## 2.

Sort the data, and plot it:      (1, t_min) (2, t_next) . . .  (2479, t_max)This will give you a monotonically increasing curve you can plot against the cumulative normal distribution.

## 3.

No matter what the data looks like, you can still model it by generating random numbers between 1 and 2479, and using that number to index the times in the sorted list.
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Author Commented:

the tasks are customers requests (customers problems and deal with that issues). in the real case, which I collect the data from the task arrive in specific time and takes time in process and then closed. I have designed the simulation based on the distribution of the process and insert the same time of arrival. I need to compare between the time from arrival until finish of the real and simulation to see how much the simulation is correct.

question is which test will be suitable for this kind of comparison. In my reading I found that t test the appropriate one due to the dame task will run in real and simulation and compare between its output.

Does my understanding correct?
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Commented:
>>  I have designed the simulation based on the distribution of the process

If the simulation is really based on the distribution (mean and variance) of the observed data, then the t-test should indicate that the means and variances are the same.

The t-test is usually used to compare two sets of observations, not one set of observations and a model.

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Author Commented:
in this time forget the disappear tasks. I need to know now how to compare using t test
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Commented:
You can use the t.test from Excel.
You can (but don't have to) use all of your data.

The parameters you have to decide on are:
Tails:  1 or 2    I don't know which would be appropriate, probably 1.

Type:   1    Paired                                           [If you choose equal sample sizes]
2   Two-sample equal variance       [If you want to unequal sample sizes or all of your data]
3  Two-sample unequal variance   [Your samples should have equal variance]
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