# Statistical Test for Product Performance

#### DanMann

##### New Member
I work for a company that makes specialist printers. I need to determine/confirm the print speed performance of the printers, so I am planning to take a number of printers (A) and measure the print time for each of these printers a number of times (B). I then want to use that data to confirm that the print speed is better than a value (Y) with 95% confidence.
Which test would I use to determine this?
I feel like this is something I should be able to figure out, but I just can't seem to search for the correct terms.

#### obh

##### Active Member
Hi Dan,

So A and B are two models?

I can tell you the answer but you will learn more if you will try first yourself.
Did you try searching for:
"choose statistical test" or "statistical test decision tree"

#### DanMann

##### New Member
I had a look at the links in the forum sticky and I think I need a one way ANOVA because I have 1 continuous data dependent variable and 1 independent variable with more than two options. Is this right?

#### obh

##### Active Member
So A and B are two models?

Don't you compare two continuous independent variables?

#### DanMann

##### New Member
A and B are sample sizes; A is a number of printers and B is the number of printers from each printer. I want to show the performance of the printer.

#### obh

##### Active Member
Don't you compare two continuous independent variables? Two printers or two models

#### obh

##### Active Member
Ps there is overlap between tests, but let's try to think simple

#### DanMann

##### New Member
I didn't think they were continuous because the printers would be serial numbers, not continuous variables.

#### obh

##### Active Member
The time is continuous variable, please look for 2 sample t test and see if meets the assumptions

Just to be clear, you compare A printers of one model to B printers of second model? Or do you compare all the printers?

#### obh

##### Active Member
PS, if you compare the one way ANOVA test, and the two samples t-test (pooled), both tests are based on the same assumptions:
Normality assumption.
Equal standard variations assumption.

I believe that in the case you compare two groups, the two-tailed two samples t-test and the one way ANOVA (only right tail) will have the same result, so actually if meets the assumptions you are correct, but probably no one will use ANOVA test for two groups.

If your H0 assumption is that one printer type is faster, and you want to use H0: μ1 ≥ μ2, H1: μ1 < μ2 assumption you can only do it with one-tailed t-test

#### Dason

Obh I think you're misunderstanding them. It sounds like they have a single type of printer but they have multiple of these printer (and they have "A" of them). Each of these printer will print a number of pages ("B" being the number of pages). Then they want to test if this model of printer prints faster than a certain speed. It's not clear to me if they want to test of the average is higher than a certain value or provide the probability that the printers print faster than a certain speed.

@DanMann can you confirm/deny my understanding of your question and provide clarification on what you want to show?

#### obh

##### Active Member
Hi Dason
I read again from the start ...and you probably correct (shouldn't read too late ...) ... one model, A printers, and B pages for each printer.

#### DanMann

##### New Member
Hi,
Dason is correct: I have one model of printer, I have quantity A of this model of printer and I want to print on each printer B times and I want to use this data to show that the printer model prints faster than 30 s.
I tried the two-sample T and it appeared to do what I think OBH thought I wanted to do (i.e. compare the performance of one printer to another), but this isn't what I wanted to do.

#### DanMann

##### New Member
If it were a single printer, I would use either a capability study or a 1-sample T-test to determine the performance of the printer, but because I have multiple devices, I want to include the variability between devices as well as within the device and I'm not sure how to stack these together.

#### DanMann

##### New Member
Thanks OBH.
Dason - I want to show the probability that the printers print faster than a certain speed (i.e. 30 s).

#### obh

##### Active Member
Hi Dan,

If you want to analysis the variance inside each printer and the variance between the printers I think you can use: "confidence interval for a variance "

But as I understand you just interested in the probability that one print on one printer will be less than 30s?

If so maybe you can just take all data and run the one-sample t-test? (I assume that B should be equal for all the printers, or similar)
In this way, you will get both variances between printers and between prints.

Generally, one of the one-sample t-test assumptions is "independent of observations", using the same printers several times has a dependency.
But I think it should be okay since you plan a good random spread.
@Dason what do you think?

Anyway, I think you should also analyze the variance between the printers, you probably want this to be small.
for example, if the result will be that in 98% of the prints are faster than 30 s, you don't want that for some users 100% of the prints are faster than 30 s and for some only 20% are faster. Maybe repeated ANOVA will give you the division of the sum of squares between printers and between prints (but you need to print the same pages for each printer)

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