Hello. I'd like to run paired t-test about tree growth between control plot and treatment plot. I have 30 tree samples respectively and I measured diameters of trees 1 year ago and this year.
For running paired t-test, it requires approximately normal data so, I will do normality test before running t-test.
My question is, which data should I run normality test?
1) tree diameters in control and treatment plots of each year
or
2) the difference between 1 year ago and this year in control and treatment plots respectively.
1)
If you use paired t-test, you would want to use two tests: one to compare 0year-treatment to 1year-treatment and one to compare 0year-control to 1year-control.
The normality assumption for paired t-test considers the difference between the paired groups. So in your case it is e.g. the difference between 0year-treatment and 1year-treatment that should be normally distributed.
2)
You probably want to use a more complicated model than a paired t-test. Something like a repeated measures analysis that includes all four groups but still takes into account the repeated-measures nature of the measurements. A post-hoc analysis can compare among these four groups.
3) When you test for normality it is better to use a histogram or q-q plot and assess visually. This is better than using a formal test.
https://www.r-bloggers.com/normality-tests-don%E2%80%99t-do-what-you-think-they-do/
I agree with Salvatore. But I think that comparing the differences (year 1 - year 0) between the groups is perfectly fine. As long as there are no missing values I don't see any advantage of a more complicated model.
It might be worth thinking about how the change in diameter depends on the size (the diameter value). In your analysis you actually assume that this is independent, so if a small tree grows by 1 cm/year you would expect that a large tree also grows by 1 cm/year. Is this assumption sensible? I have no idea. But if you say: no actually not, because a larger tree will grow more (or less) then you might consider a model that accounts for this fact.
Another strategy is to consider your pretrial measurements as a covariate. With growth, growth will depend on initial size, and may be better expressed on a logarithmic scale (what percentage increase) rather than on a unit scale.
I'm thinking that if one tree is 100cm and another is 200 cm, what is the expected growth? 10cm or 10%?
Losing the baseline information by simply subtracting is removing an potentially important variable from the data generation process.
In answer to Kim's question:
"My question is, which data should I run normality test?
1) tree diameters in control and treatment plots of each year
or
2) the difference between 1 year ago and this year in control and treatment plots respectively. "
Answer:
1. In the first place, for paired samples t test, you will always run normality test on difference between two measures.
2. Whether the difference to check for normality is those of control or the treatment depends on the research question you want to answer. If you are interested in knowing whether there is significant change in treatment group as a result of your intervention, then select only the data for the treatment group and run your normality on their difference scores.
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