I have an experiment with 2 mice of 4 different age levels. For each age, I analyse a mouse with method A and the other mouse method B (no mouse is analyse with both method). I want to see whether method A and B is comparable. I have constructed a graph and it shows some correlation. If I use Spearman's correlation on the average, there is strong correlation but not significant because there are only 4 data pairs. Is there any way to take into account all of the data points?
Try using a regression model instead of a correlation.
You are trying to show the difference between two methods A and B, given the age of a mouse. Define a linear model as follows:
LM <- lm(y ~ method + age) summary(LM)
y are the outcomes for either method,
method a dummy variable encoding whether method A or B was used and
age the age of the mouse. The summary will include an estimate for the difference between methods (
method:B will be the difference between A and B). The intercept will be that of method A.
If you believe the age has a different effect, depending on the method used, include an interaction term:
LM.with.int <- lm(y ~ method * age)
Since these are only three variables, you could visualize the entire dataset using a scatter plot with distinct colours/characters for age:
plot(y ~ x, col = age) # colour plot(y ~ x, pch = age) # character
If your study is underpowered, you must simply accept that you do not have enough mice to draw inference. This does not mean you should assess the adequacy of age as a predictor of the outcome, and assess the validity of paired analysis as an appropriate analytic approach. I would underscore, however, that if your research is disseminated like in a journal article, you should describe in detail all statistical tests that you tried. You had a prespecified analysis and you are now departing from it due to lack of statistical significance. This is p-hacking, and it will inflate the type 1 error rate.
It sounds like your sample comprises 8 randomly sampled mice, block randomized on age 1:1 to experimental conditions A and B. A loss of precision suggests that age is not (clinically) significantly prognostic of the outcome. While a paired analysis reduces the effective $n$ of the sample, the residual variability of the paired-differences should be halved, if not more, by design, thus improving efficiency... but only when paired clusters have a very high intracluster correlation. Block-randomized studies may or may not adjust for the blocking factor in some explicit way (multivariate analysis, fixed or random effects) or implicit way (conditional inference vis-a-vis paired t-test). Choosing not to adjust for the blocking factor relies on having balanced design for unbiased estimation of treatment effect and correct inference. You have that. So good! At this point a number of regression models should come to mind: a simple t-test, a regression model, or a mixed effects model.
I might suggest you can obtain powerful inference by using a simple permutation test. They perform well in small samples, the p-value does not depend on any sample characteristics even with such small $n$, like having approximate normality.