How do I analyse if two different samples significantly expressed different responses when exposed to certain environmental condition?

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Hi, I need help with my personal project, so will be very grateful if someone can guide me…

I have two different samples A and B to be exposed to two different temperatures, let’s call it low and high. Two samples A (A1 and A2) and similarly two samples B (B1 and B2) were taken from the same batch.

So I have

(italic to show low and bolded to show high temperature to spot differences quickly)

A1 and A2 exposed to low temperature throughout the experiment

B1 and B2 exposed to low temperature throughout the experiment

A1 and A2 exposed to high temperature throughout the experiment

B1 and B2 exposed to high temperature throughout the experiment

I measured the response (dependent variable) at increasing surface coverage (independent variable) of the sample.

At low temperature, I want to analyse if the response of A1 and A2 is significantly different from B1 and B2. Once this is analysed, I also want to do similar analysis for high temperature.

I also want to analyse if the response of A1 and A2 exposed to low temperature is significantly different when they were exposed to high temperature. Same analysis for B1 and B2.

Data for

A1 and A2 exposed to low temperature throughout the experiment

B1 and B2 exposed to low temperature throughout the experiment

A1 and A2 exposed to high temperature throughout the experiment

B1 and B2 exposed to high temperature throughout the experiment

So how do I statistically analyse them to answer the question?

I formerly tried selecting the common predictor (i.e. I didn’t analyse the entire dataset, e.g. A1 and A2), obtained the averaged response (e.g. from A1 and A2), created csv holding the relevant data and did

lm1 <- lm(response~log(predictor) * sample)
summary(lm1)

but I feel the approach is dodgy as I later feel I should analyse the whole dataset and perhaps perform lme but I have little experiences on doing it. Can someone help and give advices what stats I should do and how? Thanking in advance.

Hey catalyst,

you have three hipothesis tests here:

  • AVG(A1 U A2) is statistically different from AVG(B1 U B2)

  • AVG( A1 Lowers U A2 Lowers) is statistically different from AVG( A1 Highers U A2 Highers)

  • AVG( A1 Lowers U A2 Lowers) is statistically different from AVG( A1 Highers U A2 Highers)

Consider the U as the union of the two databases

For all three, you can use an parametrical or an non-parametrical hipothesis testing approach, depending if your data follows an normal distribution or not

here it have some testing that i think that you can use:

It seens that your groups are independent of each other, an normality often is not present in alot of datasets, soo i sugest that the best generical approach would be Unpaired Two-Samples Wilcoxon Test using the two.sided parameter.

it will return a p-value for your hipothesis testing confirming the null hipothesis or the alternative one.

let me know if it helps you

regards

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It was quite a while since I posted the question and now revisiting DQ and would like to thank you for your time in responding to my query. Nevertheless I have hired freelance statistician to provide solution for me and chose “Paired Samples Wilcoxon Test (non-parametric)” and applied linear mixed model to answer the question.