We've had a national testing program (Naplan) for quite a few years now, testing numeracy, literacy and writing skills in years 3,5,7 and 9. It's not much use as a diagnostic teaching tool because it occurs too late in the school year to be of any help to the teachers, who by then already know which kids are having trouble in these areas.
For about the last 4 years the results for each school have been published on the net and parents and others tend to judge schools by the complicated statistics - graphs and bands - which is unrealistic given that the students are only asked 30 multiple choice questions for numeracy and the same for literacy.
Even worse, the teachers are now under such pressure to deliver results that they spend excessive amounts of time teaching the tests rather than really educating their students in the broadest sense.
Our newspapers are forbidden to use the test data to produce league tables of top schools but that doesn't stop parents deciding a school is doing really well based on the colours used to shade the scores. Green (above average) is better than red. I noted that a fundamentalist Christian school near us, with very few students and half the teaching staff unqualified, seemed to score very highly on literacy. I'm not surprised because they spend most of their day isolated in booths reading from an imported 'christian' curriculum and answering comprehension questions. Then they learn the answers by rote without any discussion. This is not enough to build a balanced education for the 21st century but if all you are looking at is the scores, then it looks pretty good.
One aspect of the tests that is reasonably good is the tracking from year 3 to year 5 and also from year 7 to year 9. You can see if a particular school is "value adding" to a particular cohort. Again it depends on whether the tests are actually a good measure of progress.
Our tests are done on paper using a pencil and are marked electronically. I'm not sure what it costs but if all you are spending money on is an expensive test program, without the resources being made available to overcome educational deficits, then the money is being wasted.