How did the Government statistician get his figures in the smacking referendum petition?
There's been a bit of misinformation around the smacking petition. I've seen news reports, blogs and media releases that have all provided incorrect figures, while correctly stating that the petition has been deemed by the Government Statistician not to have a valid 10% of signatures.
According to petitioners, they handed in 324,511 signatures on February 29, (not 324,316 as DPF noted). The sample was 1/11th - so 29,501 signatures were checked. That's a pretty high sample size meaning there is a higher margin of error.
Of those signatures checked, 25,754 were valid, meaning 3,747 were not. Of those signatories not qualified 3,373 could not be found on the electoral roll, 214 were illegible, 158 were duplicates and 2 triplicates. So 25,754 x 11 = 283,294. The number required is 285,027 so this indicates a shortfall of just 1,733 signatures, give or take errors.
However the Government’s Statistician's best estimate is just 266,903 or a shortfall of more than 18,000; nearly 17,300 greater than the 1/11th sample would indicate. The standard error is +/- 1600. He did a one sided hypothesis test at the 95% confidence level -and at the top confidence level (99%), that's 269,500. So why use the highest confidence level? How did he get his 266,903 number?
He used the estimator of Goodman and Kiranandana. No idea what that is. Can anyone tell me?
Update We have answers. Over at No Right Turn,Idiot Savant turned to google god to subvert the satanic statistics to assist me. Because there`s 160 replications, that suggests there will be a further 1600 replicates in the rest of the population at minimum, and up to a further 1,600 x 10 hidden replicates in the population as a whole. You also check the invalids (see comments for explanations of all this). So it may well not be as dodgy as Family First's Bob McCoskrie makes it out to be. Just pretty complicated.They`ll get the signatures.
Update 2After comments here, I have added in an extra sentence and shortened the post for clarity. And I see Gordon Copeland is also querying this.