10001036

– What do you call a tea party with more than 30 people? 
– A Z party!!! 
Joke #123 on http://www.ilstu.edu/~gcramsey/Gallery.html

2*SE is a popular convenient radius to eye 95% CI for t-test. Statisticians take t with df>=30 as z. However, I was incorrect to teach that 1.96*SE could be the precise radius when df>=30.

Guess what is the critical df to use decimally precise 1.96*SE. Larger than expected –

r<-qt(0.975,df=1:1000);
sum(as.integer(r >= 1.965))+1;
cat('\nNote: Only if df >= 473, 1.96 is decimally precise.\n');
##
sum(as.integer(r >2))+1;
cat('\nNote: If df >= 61, 2 is conservative.\n');
##
sum(as.integer(r >=2.05))+1;
cat('\nNote: If df >= 28, 2.0 is decimally precise.\n');
##
sum(as.integer(r >=2.5))+1;
cat('Note: If df >= 6, 2 is decimally precise.\n');
##
sum(as.integer(r >3))+1;
cat('Note: If df >= 4, 3 is conservative.\n');