A special government unit that has saved the NSW budget millions of dollars using behavioural psychology to "nudge" citizens to act differently will now turn its attention to helping apprentices finish their training, improving the experience of hospital patients and promoting diversity in the public service.

After early successes getting people to pay fines and taxes on time the behavioural insights unit in the Department of Premier and Cabinet is now applying its strategies to more complex policy challenges.

A new report on the unit's work shows how better wording of SMS reminders can deliver big cost savings and service improvements.

The unit ran a trial at St Vincent's hospital aiming to reduce missed outpatient clinic appointments which cost up to $125 for each no-show. Small changes to the text message reminders slashed the non-attendance rate by about 20 per cent. Messages that told patients how keeping appointments "avoided loss to the hospital" and "avoided loss to the patients at the hospital" were the most effective.