1. What is statistics really about? Neil Sheldon Royal Statistical Society Centre for Statistical Education & Manchester Grammar School

2. What is statistics really about? What sorts of things should we, as teachers of statistics, be doing in schools?

3. What is statistics really about? What sorts of things should we, as teachers of statistics, be doing in schools? What technical knowledge do we need?

4. What is statistics really about? What sorts of things should we, as teachers of statistics, be doing in schools? What technical knowledge do we need? What practical understanding do we need?

5. What is statistics really about? What sorts of things should we, as teachers of statistics, be doing in schools? What technical knowledge do we need? What practical understanding do we need? What interpretative skills do we need?

6. What is statistics really about? What sorts of things should we, as teachers of statistics, be doing in schools? What technical knowledge do we need? What practical understanding do we need? What interpretative skills do we need? How can we part of statistically sound decision making in our schools?

7. Understanding data What do you (and your students) know about the data of the world around us?

8. Understanding data What do you (and your students) know about the data of the world around us? What is the population of the world?

9. Understanding data What do you (and your students) know about the data of the world around us? What is the population of the world? At what rate is it growing?

10. Understanding data What do you (and your students) know about the data of the world around us? What is the population of the world? At what rate is it growing? At what rate, measured in planets, are we consuming the Earth’s resources?

11. Understanding data What do you (and your students) know about the data of the world around us? What is the population of the world? At what rate is it growing? At what rate, measured in planets, are we consuming the Earth’s resources? How does the rate of consumption vary from country to country?

12. Understanding data What about spotting, and correcting, inaccurate data?

13. Understanding data What about spotting, and correcting, inaccurate data? Trade between the US and Canada is reckoned to amount to $1 million per second (BBC). Is that correct? If not can you correct it?

14. Understanding data What about spotting, and correcting, inaccurate data? Trade between the US and Canada is reckoned to amount to $1 million per second (BBC). Is that correct? If not can you correct it? People in Britain drop about half a tonne of litter each per year (Highways Agency). Is that correct or in need of correction?

15. Understanding data The calorie counts used as the foundation for diet plans and healthy-eating guidance for the past 18 years may be wrong, a report suggests. The recommended daily intake of calories could be increased by up to 16%, a draft report by the Scientific Advisory Committee on Nutrition said. Intake levels are currently 2,000 calories for women and 2,500 for men.

16. Understanding concepts What level of conceptual understanding do you have? And how much of that conceptual understanding can you hope to convey to your students?

17. Understanding concepts Too often statistics can be seen as a set of ‘recipes’. Plug the numbers into the formula and don’t ask too many questions. Can you explain – would you expect your students to be able to explain – the principles of estimation or hypothesis testing or confidence intervals? Consider some specific issues …

18. Understanding concepts R A Fisher, one of the most distinguished of all statisticians, went to his death arguing that there is no role for the alternative hypothesis in significance tests. So why do we have alternative hypotheses in specifications, textbooks, exam papers?

19. Understanding concepts Suppose you are doing a chi-squared test for goodness of fit and the test statistic comes out to be very small – say, in the left hand 5% tail of the distribution. Some books tell you to conclude that the fit is ‘too good to be true’ and that the data have been fiddled. Other books reject this interpretation. Which is correct? And why?

20. Understanding concepts Exam question: Use the given data to find a 95% confidence interval for μ. State the probability that the true value of μ lies in your calculated interval.

21. Understanding concepts Exam question: Use the given data to find a 95% confidence interval for μ. State the probability that the true value of μ lies in your calculated interval. Exam question: A student says the probability that the true value of μ lies in a 95% confidence interval she has calculated is 0.95. Explain why that is wrong and give a correct interpretation of the confidence interval for μ.

22. Making decisions We live in information-based societies and an information-based age

23. Making decisions We live in information-based societies and an information-based age Decisions that affect all our lives should be based on evidence

24. Making decisions We live in information-based societies and an information-based age Decisions that affect all our lives should be based on evidence (Almost all) evidence needs statistical interpretation

25. Making decisions We live in information-based societies and an information-based age Decisions that affect all our lives should be based on evidence (Almost all) evidence needs statistical interpretation Statistical understanding is a vital life skill

26. The problem solving approach

27. Case Study: Value Added “The height of a man, in nine cases out of ten, can be told from the length of his stride. It is a simple enough calculation, though there is no use my boring you with figures.” – Sherlock Holmes in A Study in Scarlet by Arthur Conan Doyle

28. Case Study: Value Added stride height

29. Case Study: Value Added stride height

30. Case Study: Value Added

31. Mean GCSE score plotted against baseline score

32. Case Study: Value Added baseline outcome What is this line really telling us?

33. Case Study: Value Added baseline outcome And shouldn’t we actually be thinking about lines like this?

34. Case Study: Value Added A school sets pupils according to their performance on the baseline test, and keeps them in those sets.  How will eventual results compare from set to set?  How will value added compare from set to set?

35. Case Study: Value Added baseline outcome

36. Case Study: Value Added A school sets pupils according to performance in end of year examinations (re-setting each year).  How will eventual results compare from set to set?  How will value added compare from set to set?

37. Case Study: Value Added “Using Value Added allows fair comparisons to be made. Your pupils’ Maths results, for example, are compared with other pupils’ Maths results, so subject difficulty does not affect the outcome. Low ability pupils are compared with other low ability pupils, so a low ability intake is no disadvantage, while similarly a high ability intake is no advantage.”

38. Case Study: Value Added So, re-setting each year, average value added will be …?  independent of set  higher in the high ability sets  higher in the low ability sets

39. Case Study: Value Added baseline outcome

40. Case Study: Value Added

41.  “Standardised residuals are shown with confidence limits at 2 (95%) and 3 (99.7%) standard deviations.”  “If average standardised residual lies within [these] bounds you cannot draw any conclusions.”

42. What statistics is really about Neil Sheldon RSSCSE & Manchester Grammar School The purpose of statistics is insight, not numbers