Paired or unpaired test?

[#1]

Hi,

I have a dataset with samples measured after incubation for 0, 1 and 2 days.

Each sample was prepared in triplicates, and each replicate was then incubated at 0, 1 or 2 days. 

I'm interested in testing if the incubation time had any affect on the measurements.

Which test would be correct to use? Is it a paired test (matched pairs) or unpaired? The data is non-parametric.

Thanks.

[#2]

Hi @DI !

Looking at your situations and explanations, you have :

• 3 groups : 0, 1 and 2 days,
• Same samples for the three groups, since replicates come from the same original sample.

I would go for a Friedman test, which is a non-parametric paired test for more than two groups. You have your (source/original) sample ID as a blocking factor, and Time/days as your grouping variable (see example attached).

If you consider your different replicates are independent (not coming from the same sample source), then a Kruskall-Wallis test might be appropriate. 
More infos here : Nonparametric Tests (jmp.com)

I'm sure statistical experts in this community will have other ideas or questions for you to help you.
I hope this first answer will help you,

[#3]

Time is usually treated as a continuous variable, so you could regress Y against time and determine if there is a relationship. What do you mean when you say that the data is not parametric? What is the response? Do you have any groups or other variables changing in this study?

[#4]

Thank you for replying to my question. Sorry for not being clear. Data are not normally distributed.

Time is the only changing parameter. 

So, can I simply plot response vs. time (both as continous variables) by sample ID and see if they are correlated using a non-parametric correlation test? 

I've attached the data set.

[#5 · Accepted solution]

Hello @DI,

There are several ways to show if Time has a (significant) influence on your response :

1. Visualization by Graph Builder (image "DI_1") : This graph shows you quite easily that the response doesn't seem time-dependent, but more influenced by the samples variability.
2. Modeling through "Fit Model" platform (image "DI_2"): By creating a Mixed Model (with Sample_ID as a random effect) to see if evolution of the response is influenced by time, you can see that time doesn't seem to be a significant variable, in contradiction to random effect "Sample_ID" where the Wald p-value is close from 0,05. With a more simple approach (standard least squares with time and sample_ID as input variables), you'll see the same comparison : time as a not significant variable, and sample as a significant (or close to significant) one.
3. Analysis through Measurement System Analysis platform, to evaluate and compare the variance between inputs time and sample (image "DI_3") : By creating a MSA analysis with your response as response, sample_ID as "Part, sample ID" and Time as grouping variable (X), you'll see that 99% of the variance in the response of your experiments comes from your samples, not time.
4. Finally, you can also use the Multivariate platform, entering Time (as continuous variable) and your response, and in the red triangle checking "Non parametric correlations" -> "Spearman" (for example), and you'll see how little correlated and non significant is time related to your response (image "DI_4").

Looking at the different platforms outcome, the conclusion seems quite clear.
I'm pretty sure there are better analysis to do which may be more "statistically rigourous", but the combined overview with 4 different tools show an agreement.

I hope it helps you, 

[#6]

Thank you so much for the answers. Very helpful!