One simulated experiment

balanced one-factor design
Group means
Group variances
n × var(means)
—
mean(variances)
—
Ratio = F
—
This computes F = n × variance(group means) / mean(group variances). When k = 2, this is exactly t² from the two-sample t demo using the same seed and draw order.

Accumulating F statistics

null F distribution plus simulated experiments