Stuff has the data:
Figures from the State Services Commission show government employees took an average of 7.6 sick days in 2012.
No official figures are kept for private sector sick leave, but an Employers and Manufacturers Association survey suggests the average could be as low as 3.7 days a year.
The discrepancy of nearly four days between public and private sector workers could be explained by a more relaxed public “workplace culture”, [Association employment services manager David Lowe said] said.
“There is an impression that the workplace culture in the public sector might not be as focused as in the private sector.”
So there is no comprehensive data on the private sector, which means that the numbers may well be incomparable, depending on the composition of the sample and nature of the survey. Even if we believe the difference is significant, there could be lots of reasons for it. It may be that public sector jobs are more dangerous, or just more stressful, which causes more sick days. It may be that the intense restructuring and job losses in the public sector have caused people to become disengaged with their organisation and take more sick days. It could be that private sector employees are paid more and public sector employees are compensated slightly with the perk of more lenient treatment of sick days.
There are plenty more reasons for the possible difference, but there’s no way that we can discern anything about the laziness of public sector workers from these numbers alone. Not without a healthy shot of prejudice, anyway.