1. W HICH WORKSHOP … Workshop choices Session 1 1.30 – 3 pm Workshop ONE Multivariate Stats Workshop TWO Stats thinking & literacy 3 – 3.30 pmAfternoon tea Session 2 3.30 – 5 pm Workshop ONE Multivariate Stats (repeated) Workshop THREE Probability & literacy

2. Telling stories from data M ULTIVARIATE S TATISTICS “Statistical investigation is part of information gathering and learning process with is undertaken to seek meaning from and to learn more about observed phenomena as well as to inform decisions and actions. The ultimate goal of statistical investigation is to learn more about a real world situation and to expand the body of contextual knowledge”

3. I NTRODUCTION  Grant Ritchie and Dr Michelle Dalrymple Cashmere High School  Housekeeping (loos, afternoon tea, emergencies)  Junior Statistics focus Collated information from variety of resources  Plan for this session…

4. S TATISTICAL INFERENCE …

5. D ATA CARDS – WHAT ARE THE VARIABLES ? EthnicityAge in YearsYear Level Transport method to school Time to school (min)Height (cm) How school bag is carried Weight of school bag (g)Popliteal length (cm) Fitness levelIndex finger length (mm)Ring finger length (mm) Colour indicates gender KAREKARE COLLEGE: DATA CARD VARIABLES What would the survey questions have been? How was each variable measured? (units?) Possible outcomes for each variable? What type of data is this? Who would use this data? Introduce your student…

6. C@S LESSON PLANS …  http://new.censusatschool.org.nz/resources/level-5/ http://new.censusatschool.org.nz/resources/level-5/

7. NZ C URRICULUM Junior Statistical Inference NCEA Subject content Values & Key Comps

8. NCEA – S TATISTICS

9. CHS E MPHASIS Year 9  Introducing PPDAC – through Probability  Statistical Literacy Year 10  Theoretical Probability & Literacy  PPDAC Statistics (Making the call)

10. K ARE K ARE C OLLEGE EthnicityAge in YearsYear Level Transport method to school Time to school (min)Height (cm) How school bag is carried Weight of school bag (g)Popliteal length (cm) Fitness levelIndex finger length (mm)Ring finger length (mm) Colour indicates gender KAREKARE COLLEGE: DATA CARD VARIABLES

11. S AMPLES GIVE US AN IDEA ABOUT WHAT IS HAPPENING IN THE POPULATION

12. PPDAC CYCLE

13. I NVESTIGATIVE QUESTIONS Summary Comparison Relationship Other

14. W HAT MAKES A GOOD QUESTION ? Can be answered with the data Population of interest is clear Group(s) of interest is clear Variable(s) of interest is clear Intent (summary, comparison, relationship) is clear Someone is interested in the answer

15. I NVESTIGATIVE QUESTION ….  I wonder if heights of boys at Kare Kare College tend to be greater than heights of girls at Kare Kare College?  CHECK  Variable  Groups  Population  Direction of comparison

16. PPDAC CYCLE

17. T WO SMALL ASIDES … Shape Writing analysis statements

18. S KETCHING SHAPES Quickly sketch the general shape of the distribution

37. R EFLECTION : S EEING SHAPE  What did you look for when catching a glimpse of the plot?  Are your plots similar to your neighbours?  What is important to emphasise with your students?

38. D ESCRIBING SHAPE  Choose one plot and with your neighbour discuss how your Year 10 students would describe the shape  What sort of language would they use?

39. Normal (Bell-curved) Symmetric Uniform Unimodal Bimodal Trimodal Skew Right, Positively Skewed, Long Upper Tail Skew Left, Negatively Skewed, Long Lower Tail Outliers, Extreme Values G IVING STUDENTS STATISTICAL LANGUAGE FOR SHAPES

40. E NGAGING WITH SHAPE  One of the keys for unlocking the story behind the data  Develops the skill of what to look at and what to look for  Using their imagination, they start to notice what is interesting, unusual or unexpected. What are the data trying to tell us?

41. K ARE K ARE COLLEGE  Sketch what you expect the distribution of heights for girls and boys to look like?  Put a scale along the bottom of your sketch

42. D ESCRIBING DISTRIBUTIONS  We need to help students write good ANALYSIS comments every time we ask them to write.  Model for them  Give structures for them to use

43. S ENSIBLE ORDER TO STRUCTURE OUR ANALYSIS COMMENTS …  Centre  Spread  Shift & overlap  Shape

44. W RITING STRUCTURES  I notice…  I wonder…

45. W RITING STRUCTURES PEER  Used to craft each statement

46. W RITING STRUCTURES OSEM  O stands for Obvious observations:  Write down one thing you notice, then leave a gap, and write down something else you notice. Try to get 3 obvious things.  S is for Specific:  Under each obvious observation, explain what you mean so that another person would get it.  E is for Evidence:  Support each observation with numbers or calculations.  M is for Meaning:  So what? Write down what each of your points tells you about the original problem/situation. What else could we find out?

47. PPDAC CYCLE

48. K ARE K ARE COLLEGE  I wonder if heights of boys at Kare Kare College tend to be greater than heights of girls at Kare Kare College?  Take a random sample of 30 boys and 30 girls  Dot plot  box plot…

49. T HIS IS A RANDOM SAMPLE OF STUDENTS FROM K ARE K ARE C OLLEGE  Write some analysis descriptions

50. Teaching world… T O MAKE THE CALL BACK IN THE POPULATION

51. S TATISTICAL INFERENCE …  “Making the call” means making a statistical inference…  From our sample, can we say if heights of boys at Kare Kare College tend to be greater than heights of girls at Kare Kare College?

52. W E LOOK AT MULTIPLE SAMPLES Focus  Direction of the shift  Consistency across samples  Developing a guide for ‘making-the-call’ back in the population

53. M ULTIPLE SAMPLES I wonder if heights of boys at Kare Kare College tend to be greater than heights of girls at Kare Kare College? I wonder if, at Kare Kare College, students who walk to school tend to get there faster than students who take the bus? HeightsTravel time

54. M ULTIPLE SAMPLES  Sort your two sets of samples (heights & travel time)  Make observations within one group of samples  What is similar?  What is different? Consider SHIFT OVERLAP MEDIANS  Make observations between the two sets of samples  What is similar?  What is different?

55. S TUDENT IDEAS … SHIFT L OCATION OF THE BOXES RELATIVE TO ONE ANOTHER Heights  In nearly every case, the boys box has shifted to the right Travel time  The students who walk boxes are shifted to the left every time

56. M ESSAGE SHIFT L OCATION OF THE BOXES RELATIVE TO ONE ANOTHER Heights  Inconsistent message  Sometimes boys’ height box (middle 50%) is located further to the right of the girls’ height box  Sometimes girls’ height box (middle 50%) is located further to the right of the boys’ height box  Sometimes the boxes completely overlap Travel time  Consistent message  In all cases the bus travel time to school box is located further to the right than the walk travel time to school box

57. S TUDENT IDEAS … OVERLAP H OW MUCH THE BOXES ( MIDDLE 50%) OVERLAP ONE ANOTHER Heights  Most of the time the boys totally overlapped the girls  Sometimes there was a partial overlap Travel time  Most of the time there is no overlap  Occasionally there is a small overlap

58. M ESSAGE OVERLAP H OW MUCH THE BOXES ( MIDDLE 50%) OVERLAP ONE ANOTHER Heights  For the heights the middle 50% (box) overlaps a lot or completely Travel time  In most cases the boxes do not overlap  In some cases there is a small overlap

59. S TUDENT IDEAS … MEDIANS W HICH MEDIAN IS HIGHER ? W HERE IS THE MEDIAN LOCATED IN RELATION TO THE BOX OF THE OTHER GROUP ? Heights  Most of the medians for boys and girls are very similar  The boys is slightly higher than the girls sometimes  The girls is slightly higher than the boys sometimes Travel time  The median than the bussing is always higher than the median for walking

60. M ESSAGE MEDIANS W HICH MEDIAN IS HIGHER ? W HERE IS THE MEDIAN LOCATED IN RELATION TO THE BOX OF THE OTHER GROUP ? Heights  Inconsistent message  Sometimes the boys’ median height is higher  Sometimes the girls’ median height is higher  Median heights are inside the overlap Travel time  Consistent message  The bus median time to school is always higher  One of the median times to school is nearly always outside the overlap

61. M AKING THE CALL … B ACK IN THE TWO POPULATIONS …  Which situation would we trust to make statements about what is happening back in the two populations?  The heights or the travel time?  What are the key features of the two situations?

62. Heights  Large amount of overlap  Medians within the overlap  Due to sampling variability another sample could easily give a different picture  Don’t know which box is to the right back in the populations  Therefore we don’t know who is taller Travel time  Little or no overlap  At least one median is outside the overlap  Even with sampling variability we expect another sample to give a similar picture  Expect that the bus box is to the right back in the population  Therefore we are pretty sure that bus travel time takes longer M AKING THE CALL … B ACK IN THE TWO POPULATIONS …

63. Heights  I wonder if heights of boys at Kare Kare College tend to be greater than heights of girls at Kare Kare College?  It is too close to call…  Explain why you have made this conclusion (EVIDENCE)  If I took another sample… Travel time  I wonder if, at Kare Kare College, students who walk to school tend to get there faster than students who take the bus?  I can make the call that …  Explain why you have made this conclusion (EVIDENCE)  If I took another sample… M AKING THE CALL … B ACK IN THE TWO POPULATIONS …

64. C OMPARING TWO POPULATIONS N = 30

65. W HEN TO MAKE THE CALL … L EVEL 5 GUIDE T HE ¾-½ GUIDE

66. M AKING THE CALL …  Write your conclusion

67. K EY IDEAS …  Writing good questions  Looking at a sample rather than the whole population  Writing good analysis statements  Statistical inference Level 5

68. A NY QUESTIONS …

69. W ORKSHOP FEEDBACK … On a piece of paper please give us some feedback It can be for about these workshops, or for CMA generally 1. Please keep doing… 2. Please stop doing… 3. Please start doing… 4. Anything else you want us to know?....