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?

Hypothesis testing with p-values is useful in some situations where you need to make a crisp decision from one experiment. You don't. Instead of worrying about p-values, compute confidence intervals for the differences or ratios you care about. If a confidence interval only spans differences (or ratios) that you consider trivial, then you have good evidence that that difference (or ratio) is trivial. If the interval spans differences that would be nontrivial, then you've found something that is not negligible.
The big picture here is that you don't seem to be asking "Is there a difference or not?". You are asking "how big is the difference". Answer that with a confidence interval to quantify precision and interpret in the scientific context of your data.
