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?

If you want to specify an amount that is "too small to be interesting", and you want a metric that will give you a metric similar to a p-value, you could do an equivalence test, i.e. you could do a test of whether $|\beta|<0.1$ (if that is your threshold of "interesting").
This answer points out that you can do a post-hoc equivalence test for a linear model/ANOVA using the emmeans package (see the vignette here).
But I do agree with other answers that showing effect sizes + CIs can be more useful than single numbers that measure the strength of evidence against a particular dichotomous hypothesis (e.g. $H_0$: $|\beta|<0.1$).
