Compare continuous temperature data across 4 different groups

[Geox]

Hello,

We've got an experiment which involved temperature monitoring of 12 chickens. Sampling rate of the temperature sensor was 25Hz.
Chickens were divided into 4 groups, 3 chickens per group. We tested 4 stressors A,B,C,D in each group on 4 consecutive testing days, but always in a different fashion. The data I will be working with is the normalized temperature data 1h prior and 1h post stressor induction.
The protocol was a fourth order latin square design:
Group 1 received A,B,C,D on 4 consecutive testing days (so day1:A, day2:B, day3:C, day4: D )
Group 2 received D,A,B,C on 4 consecutive testing days.
Group 3 received C,D,A,B on 4 consecutive testing days.
Group 4 received B,C,D,A on 4 consecutive testing days.

I am looking for a statistical method to get as much as possible information out of this conducted experiment. Difference between groups, differences within groups, is there something else I could do/conclude using this design? I do have some minor background in statistics and experimental design, but can anyone help me looking for some resources or suggest some methods/papers I should look into?

Thank you!

 

[staassis]

Estimate a one-way ANOVA model, where Group is the only factor. If the residuals are normally distributed (according to Kolmogorov-Smirnov, Shapiro-Wilk or Jarque–Bera test) run classic ANOVA F -tests. If the residuals are not normally distributed, run the counterparts based on bootstrap.

R allows all of this (and is available for free). SPSS allows most of this.

 

[Geox]

What do you mean by residuals?

 

[staassis]

It is a most basic concept in statistics, like several other concepts that you will have to learn to perform the analysis. I have given you the names of the right methods. Now you have to learn them. This will not be a 10-minute thing.

 

[Karabiner]

I am looking for a statistical method to get as much as possible information out of this conducted experiment.

Maybe we just start with using statistcs for answering your research questions.

Could you please tell us the precise research questions? In addition, is the design
feature of permuted sequences for A to D only meant to eliminate order effects,
or is some research question associated with this?

With kind regards

Karabiner

 

[Karabiner]

Estimate a one-way ANOVA model, where Group is the only factor. If the residuals are normally distributed (according to Kolmogorov-Smirnov, Shapiro-Wilk or Jarque–Bera test) run classic ANOVA F -tests.

But there are 2 repeated-measures factors? What would be the DV, it is measured 4*2 times.
And the between-subjects factor seemingly is only introduced to eliminate sequence effects,
it is not interesting by itself.

With kind regards

Karabiner

 

[staassis]

But there are 2 repeated-measures factors? What would be the DV, it is measured 4*2 times.
And the between-subjects factor seemingly is only introduced to eliminate sequence effects,
it is not interesting by itself.

Karabiner

Technically speaking, you are correct about the 2 factors. Yes, there is also a factor of time. However, due to the experimental design, we cannot test the intermediate time effect accurately. In each group time means a different thing. In one group the difference between t-1h and t + 1h is the effect of A, for the most part. In another group the difference between t-1h and t + 1h is the effect of B. The variance of Temperature(t+1h) - Temperature(t-1h) will be substantial when calculated over the 4 groups. And we can be sure that the distribution is not normal because, in fact, it will be a mixture of 4 distributions.

So what we can do is take the absolutely last value (time = 4d + 1h), subtract the first value (time = 1d - 1h) and compare the result over the 4 groups. Yes, the order is the only thing we are testing. Quite inadequate experimental design, if you ask me.

But you are correct, if we had 120 chicken we could do more interesting things with understanding the intermediate dynamics. Yes, formally speaking, there is the within-subject time effect.

 

[Karabiner]

This is probably not about time, but about conditions. Although the OP wasn't so kind as to
describe his research questions, I suppose that the effect of stressors A to D is of interest here, not
first stressor/second stressor/etc . So the first repeated-measures factor refers to the conditions
A to D. The sequence of conditions is varied in a complete Latin square design, and each variation
has the same sample size. This is supposed to elimiate the effects of order of stimulus presentation.
In addition, there is a second repeated-measures factor (pre-post).

With kind regards

Karabiner

 

[staassis]

This is probably not about time, but about conditions. ...
Karabiner

"Time" is just a name, reflecting the fact that Temperature(t1) and Temperature(t2) may be different for t1 < t2. Word "time" encompasses all the effects spread out in time. Please note: I did not say that "aging" is a supposed reason. But stress from testing can be.

In addition, there is a second repeated-measures factor (pre-post).
Karabiner

Which can be removed by considering Post - Pre =: Change.
And I have already explained why we cannot estimate any intermediate time effects accurately on 12 chicken only. Too much variability (in a form of a mixture of 4 distributions) for too little data.