There are two groups; control and treatment. Sample size of each is 6. Treatment was given according the body weight of the sample and fat deposition is measured after few weeks. what is the best statistical design to analyze this experiment ?
Hello,
You can calculte 'delta(i) = weight (t1) - weight (t0) for each group (i), and compare between them using the avearge of each delta(i).
or simply you can use the regression function (in R software) :
lm(delta ~ group ), and estimate the parameter attached of group .
Or a two way ANOVA with repeated measures on one factor. The interaction of the ANOVA is equal to Chellai Fatih proposal, but has the advantage that you can also analysze the main effects of time and group seperately, if necessary.
But your experiment is absolutely underpowered and I would not trust any effects with such small samples. Small samples tend to overestimate the true effect size, see the following article:
Loken, E., & Gelman, A. (2017). Measurement error and the replication crisis. Science, 355(6325), 584-585.
The problem here dear Pr. Rainer Duesing is about the ANOVA assumptions ?
are they checked or not? as you mentionned above, the sample size (n=6) is a chalenge for ANOVA test.
Best wishes
Yes you are right, but I wouldnt trust any analysis with such small sample sizes.... the probability to get a wrong result due to measurement error ist way to high, see the above mentioned article, which used a sample of N=50 to show problems with small(!) samples!! Garbage in, garbage out.
P.S.: what are the assumptions for your proposal, is it assumption free? I guess not, if you use a linear model.
Thank you Chellai Fatih & @Rainer Duesing
But weight difference cannot take as response variable. Fat deposition & lean muscle development is measured in another specific method. The initial weight of the experimental unit (animal) is measured to decide the dose (size) of treatment and the weight of animals are vary. treatment also vary depending on the weight of the animal. want to relate the relationship of the treatment to the response.
Furthurmore the sample size is 6. so, I think we cannot use ANOVA. isnt it?
Sounds like a bad experiment... I think there is not much you can do, just report the descriptive statistics of each individual and the means. There is not much you could generalize to the underlying population or treatment effect in my opinion.
What was the goal of that all, why didnt you plan the whole experiment more throughful in the first place?
Thank you Mr. Rainer for helping.
I understand that the sample size is not enough. Actually this is not my research but i was helping & interested in it. The access and affordability was less to maintain large sample size with the available resources.
Thank you very much for supporting
Dear Madhuka Yasas it is not only the sample size, but also the setting. If the dosage is dependent on the animal weight, then these variables are inevitably correlated. Even with a large sample sizes this could cause problems, despite of a control group.
You barely get anything reliable with this sample size, otherwise I'd recommend a generalized estimated equation (GEE) and see what happens.
The best advice is: increase the sample size.
Dalton de Lima-Junior AND do an experiment where the dosage (factor levels) is independent of other (co-)variates.
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