How can I reduce a very large sample size for statistical significance (sampling methods)? In my biological study, I have around 14000 independent samples, and I study the evolution of a response variable over time. I have three groups to study.
Thus, I have two factors: factor "Group" (with three levels: CTRL, VC1, VC2) and a factor "Time" (with three levels: T0, T1, T2): I have a total of 3*3 = 9 conditions.
Thus, for each condition, I have around 1600 independent samples... Which is huge for statistical testing. I conducted a two-way ANOVA, but not surprisingly every comparisons (main effects and post hoc tests) are statistically significant due to a very big sample size. Basically, it finds significant p-values when they're not really significant (false positives) ...
> model <- lm(Variable ~ Group*Time, data)
            Sum Sq    Df F value    Pr(>F)
Group          705     2  61.597 < 2.2e-16 ***
Time          6495     2 567.686 < 2.2e-16 ***
Group:Time     713     4  31.152 < 2.2e-16 ***

> cohens_f_squared(Anova(model,type=2))

Parameter   | Cohen's f2 (partial) |           95% CI
-----------------------------------------------------
Group       |             9.56e-03 | [0.01,      Inf]
Time        |                 0.09 | [0.08,      Inf]
Group:Time  |             9.67e-03 | [0.01,      Inf]

How can I reduce the sample size to reduce the false positive rate? Is there a way for sampling my data?

YOU DON'T
People often want to deem differences interesting when $p<0.05$ and uninteresting when $p>0.05$ (or whatever $\alpha$ they pick...does not have to be $0.05$, even if that one is common).
This is incorrect.
A hypothesis test is extremely literal, and this is a feature, not a bug. You ask the hypothesis test if two quantities are equal, and if those two quantities are not exactly equal, the hypothesis test should tell you that.
However, you understand your subject. You know what is interesting. As I wrote in my comments, molecular biologists might be interested in distances of a few nanometers, while astronomers probably are not. You've identified $0.1$ as a threshold for being interesting. Go with that! Code that into your workflow so only the statistically significant and practically interesting results get displayed.
(Practically interesting but statistically insignificant is an annoying case, because the observed difference is interesting, but there is enough uncertainty that you may have, loosely speaking, just had some bad luck and gotten that large of a value as a fluke.)
You might be interested in reading the American Statistical Association's statement on p-values.
