Hi, I am a bit unsure about how the data should be preprossessed prior to performing a paired statistical test. Lets say I have two groups A and B where I measure something every day for twenty days. I would then test for normal distribution, and further use wither paired t-test or paired Wilcoxon test with dependency based on sampling day. Here where I am unsure. Lets say each group has four replicates. Should I;
1) take the mean of the replicates so that each group (A or B) is only represented by one value or
2) perform the test, and each group is represented by four values.
Option 2 gives me more degrees of freedom, and thus usually a more statistically significant value.
Madeleine
Hi Madeleine,
I am unsure that your choice of a paired t-test (or Wilcoxon) is relevant. Pairing by times is, in my opinion, a debatable choice because you will then "cancel" the effects of time which may/might be of interest. The choice of a non parametric test can not be justified only by a single normality test, beside the fact that this test has to be performed on _residuals_ : in your case the residuals of a two-way anova of 8 "subjects" crossed with 20 "times", hence 160 residuals with 7x19=133 degrees of freedom (with such a number a QQ-normality plot is highly more advisable than any test - in my opinion).
Still in my opinion, a better choice would be to treat your data as a designed experiment with 4 "subjects" nested in 2 "groups" (A/B) crossed with 20 "times".
If your measurements were not continuous but binary or categorical just go GLM.
You should better model the change over time per sampling unit (linear-, non-linear- or spline- regression).
Thank you for your answers.
The question I want to answer is; is there statistical significant differences between the groups? Can you do that with GLMs?
Your question is far too unspecific for an inferential analysis. If this is really what you want (to see some kind of difference) - then plot the data and find patterns or characteristics that are different.
If you want to test hypotheses (as you asked for t-test or signed-rank test), you should have a particular statistical model in mind, and the hypothesis should be a particular restriction in this model. If you have only two groups you may ask for the expected difference between the groups. Thus, the model describes the expectation as the sum of the expectation of group A (b0) and the difference between the two groups (b1), multiplied with an indicator for the group membership (0 for group A and 1 for group B). This model can model any combination of expectations for A and B, and the interesting difference is conveniently coded as a coefficient (b1). Based on assumption of the error distribution model one can construct a test of the hypothesis that b1 = d. If the error model is Gaussian, this leads to the t-test (usually, d is chosen to be zero).
So if you do a t-test, you scraped the surface of a GLM. The linear predictor is E(Y) = b0 + b1*X (with X being either 0 or 1, depending on the group y belongs to). The link functions is the identity, and the conditional distribution of Y is normal (Y|X ~ normal(E(Y), s).
If you do a linear regression, X is continuous and can take any real value (not just 0 or 1). If you transform the continuous predictor, you can model relationsships between response and predictor that are not linear.
You can combine group-effects and continuous regressors in one model, you can also model interactions (moderation, synergism/anatgonism) between them.
You can make other assumptions about the error model (Poisson, exponential, gamma, binomial, ...) and you can use smart link functions to get ensure that changes in the expectation due to changes in the coefficients are independent of the expectation itself.
You can model hierarchical error structures, so that for instance the model is aware that series of values were taken over time from the same individual, and that individuals may randomly differ in particular coefficients.
GLMs are a very general class of models. There is very little what you can't do with GLMs. The point is that you have to clearly specify the functional relationship between the predictors (time, group) and the response, and make sensible assumption about the error model, and to specify the hypothesis that should be tested as a restriction of that model.