How to delete groups containing less than 3 rows of data in R?

One way to do it is to use the magic n() function within filter:

library(dplyr)

my_data <- data.frame(Year=1996, Site="A", Brood=c(1,1,2,2,2))

my_data %>% 
  group_by(Year, Site, Brood) %>% 
  filter(n() >= 3)

The n() function gives the number of rows in the current group (or the number of rows total if there is no grouping).

Throwing the data.table approach here to join the party:

library(data.table)
setDT(my_data)
my_data[ , if (.N >= 3L) .SD, by = .(Year, Site, Brood)]

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