# Test significant difference question

#### doie

##### New Member
Hello everyone, I'm a new member (with low degree of statistical understanding) hoping someone can clarify a question for me.

We run laboratory testing and often check sets of data for significant difference to confirm that test results are not changing. I usually get a sample to be tested 6 times and then later get the same sample repeated 6 times again. I then compare the 2 sets of 6 data results by t-test and get a p score telling me if the 2 sets of results are significantly different or not. As I say - this is done using replicate analysis of the same sample so sets of results would be similar to e.g. set 1 (2.33, 2.45, 2.38, 2.44, 2.51, 2.40) versus set 2 of (2.44, 2.36, 2.48, 2.34, 2.50)

My question is can a t-test function be allied to sets of data that have much wider ranges of data e.g. could a set of data like (11.21, 15.24, 9.79, 0.74) be compared using the t-test to set containing (12.22, 24.48, 8.59, 14.34) or is it not appropriate ?

#### fed2

##### Active Member
I guess technically speaking you can apply a t-test as you describe but it will be 'unequal variance' t.test, ie t.test(,,3) in excel.

Real question is are the variances equal. In an assay validation context it may indicate precision is not what it used to be.

#### doie

##### New Member
I had an instinct that the t-test wouldn't be appropriate but you can't convince someone with with your instinct. It's much clearer when you've identified that I'd be looking at the variance between the two sets which, in my case, won't tell me anything useful.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Another test if your description is accurate to the actual context, would be a permutation test. It would assign each observation to each group across all permutations, then tell you how likely your results would be given every permutation possible.

@fed2 brings up a good point with the variance comment. The centrality of data may not differ but their variance may, which is important to know in quality control. @Miner may also have some input given this seems in his wheel house.

Thanks for posting and welcome to the forum!

#### Miner

##### TS Contributor
My question is can a t-test function be allied to sets of data that have much wider ranges of data e.g. could a set of data like (11.21, 15.24, 9.79, 0.74) be compared using the t-test to set containing (12.22, 24.48, 8.59, 14.34) or is it not appropriate ?
Are these data being collected in the same manner as you described for your first scenario? Or are these collected across multiple samples?

#### doie

##### New Member
Sorry for the delay in getting back.
Data is collected as I originally described i.e. same source repeated at different times to compare. I know I could possibly compare precisions as an option but but I think that will only determine one part of the process for me i.e repeatability across the 2 sample runs .

#### Miner

##### TS Contributor
You can still use a t-test for unequal variances.

#### doie

##### New Member
Thanks for all the feedback guys. It's a great help to have knowledge available like this, particularly when you're struggling like me. Much appreciated.