I AM far from being an SNP supporter, but I do want to acknowledge the First Minister's honest assessment about the exams fiasco and her unpretentious apology for the mistakes made in the processing of exam assessments.

It is not often that we hear any government representative having the humility and good sense to make an apology over the government's errors of judgment, such apologies generally being rarer than hen's' teeth.

That is what was music to my ears today.

Nicola Sturgeon did try to use the political tactic, since leopards cannot change their spots, though they can try to hide their predatory party behaviour by dressing in sheep's clothing, of saying that her Government was merely following the same road as the other UK administrations in regard to processing exam results to mitigate her Government's folly in this situation.

Still there lurks in the back of my suspicious mind that her apology, which sounded as though it came from the heart, may have its true origin in the fear that her party could well lose popularity and votes as a result of this major gaffe.

While I must pay my due respects to her for having the courage to admit openly that her Government got it all wrong on the exam front, I feel that there are other areas where she should have shown more humility by resiling from the projected Hate Crimes Bill and the flawed gender identity programme her Government is determined to implement.

It took her Government long enough to ditch the much-criticised state guardian scheme proposed by John Swinney, who also happens to be at the helm for this current fiasco creating waves of poor publicity for his party, though it would not be any surprise if that scheme were resurrected and efforts made to slip it in through the back door of our labyrinthine political system.

However, we must congratulate our FM on not trying to defend the indefensible with regard to exam results and for issuing her wholehearted apology, whatever the motivation behind it.

Denis Bruce, Bishopbriggs.

MUCH of the debate surrounding the SQA results has been predicated on the widely held belief that the moderation process used was more likely to downgrade estimates for pupils from more socially deprived backgrounds. The idea of a "postcode lottery’ is now firmly embedded.

Reporters, researchers, politicians, and placards have all repeated various versions of Ruth Davidson’s claims in the Mail on Sunday that “the most disadvantaged pupils were more than twice as likely to have their grades lowered than wealthier students”. It has become such an article of faith for so many that it is incredible to realise that it all stems from a basic statistical misunderstanding of a single set of tables.

The only data thus far available to compare estimates and moderated results by relative social deprivation, are 3 tables in the SQA’s Equality Impact Assessment. These tables compare (for National 5, Higher, and Advanced Higher) the percentages that would have achieved a C-grade of better if the estimates had been accepted with the equivalent percentages after moderation was applied.

It is true that they show that the percentage achieving Grades A-C was reduced by a greater amount for pupils from areas of higher deprivation. The obvious interpretation is that such pupils must have been more likely to have had estimates downgraded. Simple conclusions from statistics are often misleading.

The tables tell us nothing about estimated As or Bs being downgraded to Bs and Cs and so provide no basis to conclude whether any group has been more likely to be downgraded.

Intuitively, the most likely phenomenon shown by this data is that the more deprived groups were likely to have included a larger number of estimated borderline passes. If all groups are then treated equally they end up with more such passes downgraded; but not because of unequal treatment.

For the statistically minded: imagine twp frequency distributions with different means and a pass mark to the left of those means. Now move them both left by the same amount. You’ll get tables very similar to those published by the SQA.

That of course is no consolation to the pupils who have narrowly missed a C grade, but what about the situation at other grades? Although the SQA has not published such statistics, it is likely that the situation is reversed at Grade A. Intuitively, because of the higher number of A estimates to begin with in less deprived areas. Or, for the maths geeks, repeat the thought experiment but with a higher cut-off point to the right of the mean. It seems very likely that the number of estimated As downgraded will have been higher for more affluent areas – this is just the reverse effect of what happens at Grade C.

If, as is starting to seem likely, the grades awarded are revised to match the estimates, the most striking feature might be the large number of extra A grades for rich kids. Such are the unintended consequences of basing policy on a simplistic analysis of data.

That nobody seems to have noticed this is perhaps the truest indictment of our education system.

Andrew Morrison, Dunfermline.

IN the past twenty years there has never been a release of school examination results that met with universal acceptance. It will never happen. It cannot happen. Politics demands it so.

Previously, any cohort of students in any subject, which had two or three per cent increases yearly, would be criticised as showing subject matter being "dumbed down". Conversely, if two or three per cent reductions are recorded yearly, then criticism is voiced that exams are being set too difficult. If subject results are static, then the complaint is that progress is not being made.

The usual subjects – CfE badly designed/poorly implemented, teachers' pay too low and staff over-stressed, classroom assistants under resourced and the like – have all been eclipsed this year by the Covid 19 pandemic.

The option of having no results awarded this year would never have flown.

The assessing by teachers resulted in high over-estimates and the SQA algorithm model is the outcome.

A wonderful coalition has now come together through Ian Gray, Donald Ross, Willie Rennie and Jamie Green united in favour of taking teachers' assessments at face value and removing any SQA equalisation to past pass levels. (Bear in mind that an election is due in nine months).

Just how does this now work?

With pass marks this year raised 20% on last year, come 2020/21 in12 months time, are we to see every student in every exam receive a top grade? Why bother with examinations? Alternatively, next year sees a huge fall in pass marks to equalise this year's leap?

The total number of places at Scottish universities and colleges will never equal the number of secondary schools passes. Therefore even if every student received A graded passes there will still be an entry sifting process and disappointment is now moved from the school pass stage to the tertiary selection stage.

Every possible solution offered in this matter will fail some faction in society.

Robert Wolfenden, Biggar.

THE calls for John Swinney to resign are ludicrous. We have to recognise that teacher estimates are far from infallible. I once predicted a D for a pupil and in the exam he scored A – although my other predictions were broadly consistent.

A moderation process was essential, since the average prediction was 25 per cent better than typical of former years' exam results. To have allowed the predictions to stand unmoderated would have been unfair to pupils of previous years.

If ire is to be directed anywhere it should be towards the school, or even the individual teacher, whose predictions in previous years had been seen to be consistently over-optimistic. With due consideration at appeal, we would hope that cases of genuine underperformence will be recognised and rectified.

James McKelvie, Carmunnock.

NOW that the SQA has developed a robust algorithm to adjust results down, it can be used regularly in the future to adjust for deprivation by increasing grades. This would have the effect of allowing for inequality, encouraging effort, boosting self-confidence, and achieving the policy goal of reducing the attainment gap. Win, win and unarguable logic given the current detriment logic.

Bob MacKinnon, Inverness.

IS there room for an alternative view of the importance of examinations and education in these stressful times?

Writing as someone who left school with a couple of dodgy Highers, I can tell young people who have been disappointed in their results that this is not the end of the world or even the road, it's only the beginning. Having sought employment in an occupation which genuinely excited me, I was interviewed by some "suits" in London. The interview ended in a bit of a barney between one of the interviewers and my rather bolshie self about politics (Harold Wilson was the subject, which dates me). I left the interview room thinking "Oh well, I'll just have to think of something else."

I was rather surprised therefore to be accepted on to a training course against some quite stiff competition, and which led to a long and interesting career. It turned out that they were looking for bolshie young people who would stand up for themselves.

However, that was only the beginning of my education. I eventually graduated with honours in History with French (2:1 since you ask) from the Open University, at the age of 64. As most people of my age will tell you, education is a life-long experience, both for good and ill. I spend more time reading and learning now than I ever have before.

My message to young folk at this (seemingly) crucial time in their lives is: believe in yourself; stand up for yourself; argue your point with anyone who will engage and just make friends with those who won't; above all keep learning from every experience you encounter and don't worry if you fail from time to time.

John Jamieson, Ayr.

WHILE I agree that the disruption to young people's education has a massive effect, I would say that a positive outlook has to be kept. I did not have the opportunity to go to university, but I have always read widely, and I educated myself. In agreement with Mark Twain, I did not let my schooling interfere with my education.

Margaret Forbes, Kilmacolm.

Read more: Letters: Let's end the school examination and certification process