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W HICH WORKSHOP … Workshop choices Session 1 1.30 – 3 pm 3 – 3.30 pm Session 2 3.30 – 5 pm Workshop ONE Multivariate Stats Workshop TWO Stats thinking & literacy Afternoon tea Workshop ONE Multivariate Stats (repeated) Workshop THREE Probability & literacy “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” M ULTIVARIATE S TATISTICS Telling stories from data 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… S TATISTICAL INFERENCE … D ATA CARDS – WHAT ARE THE VARIABLES ? KAREKARE COLLEGE: DATA CARD VARIABLES Ethnicity Age in Years Year 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 level Index finger length (mm) Ring finger length (mm) Colour indicates gender •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… C@S LESSON PLANS … http://new.censusatschool.org.nz/resources/level-5/ NZ C URRICULUM Subject content Values & Key Comps NCEA Junior Statistical Inference NCEA – S TATISTICS CHS E MPHASIS Year 9 Year 10 Introducing PPDAC – through Probability Theoretical Probability & Literacy Statistical Literacy PPDAC Statistics (Making the call) K ARE K ARE C OLLEGE KAREKARE COLLEGE: DATA CARD VARIABLES Ethnicity Age in Years Year 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 level Index finger length (mm) Ring finger length (mm) Colour indicates gender S AMPLES GIVE US AN IDEA ABOUT WHAT IS HAPPENING IN THE POPULATION PPDAC CYCLE I NVESTIGATIVE QUESTIONS • Summary • Comparison • Relationship • Other 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 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 PPDAC CYCLE T WO • • SMALL ASIDES … S KETCHING SHAPES Quickly sketch the general shape of the distribution Dot Plot Collection 1 0 20 40 60 skips 80 100 120 140 Dot Plot Collection 1 0 2 4 6 8 m nth 10 12 14 Dot Plot 2007fullsample 0.5 1.0 1.5 2.0 reaction 2.5 3.0 3.5 Kiw ipop 1.5 2.0 Dot Plot 2.5 3.0 3.5 4.0 4.5 weight Dot Plot 071107 yr11 2006 Maths all 0 20 60 40 AttendancePercentageHalfDays 80 100 2007sample 16 Dot Plot 28 24 20 rightfoot 32 Dot Plot Manurew a High School_1 0 200 400 Score 600 800 Dot Plot Collection 1 0 100000 De bt 200000 Dot Plot 2007sample 0 20 40 hairlength 60 80 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? 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? G IVING STUDENTS STATISTICAL LANGUAGE FOR SHAPES 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 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? 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 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 S ENSIBLE ORDER TO STRUCTURE OUR ANALYSIS COMMENTS … Centre Spread Shift & overlap Shape W RITING I notice… I wonder… STRUCTURES W RITING STRUCTURES PEER Used to craft each statement W RITING STRUCTURES OSEM O stands for Obvious observations: S is for Specific: Under each obvious observation, explain what you mean so that another person would get it. E is for Evidence: Write down one thing you notice, then leave a gap, and write down something else you notice. Try to get 3 obvious things. 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? PPDAC CYCLE 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… T HIS IS A RANDOM SAMPLE OF STUDENTS FROM K ARE K ARE C OLLEGE Write some analysis descriptions TO MAKE THE CALL BACK IN THE POPULATION 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? 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 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? Heights Travel time S TUDENT IDEAS … SHIFT L O C AT I O N O F T H E B O X E S R E L AT I V E TO O N E A N O T H E R 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 M ESSAGE SHIFT L O C AT I O N O F T H E B O X E S R E L AT I V E TO O N E A N O T H E R Heights Travel time Inconsistent message Consistent 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 In all cases the bus travel time to school box is located further to the right than the walk travel time to school box S TUDENT IDEAS … OVERLAP H OW MUCH THE BOXES ( MIDDLE 5 0 % ) OVERLAP ONE ANOTHER Heights Travel time Most of the time the boys totally overlapped the girls Most of the time there is no overlap Sometimes there was a partial overlap Occasionally there is a small overlap M ESSAGE OVERLAP H OW MUCH THE BOXES ( MIDDLE 5 0 % ) 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 S TUDENT IDEAS … MEDIANS W HICH MEDIAN IS HIGHER? W HERE IS THE MEDIAN L O C AT E D I N R E L AT I O N TO T H E B O X O F T H E O T H E R G R O U P ? 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 M ESSAGE MEDIANS W HICH MEDIAN IS HIGHER? W HERE IS THE MEDIAN L O C AT E D I N R E L AT I O N TO T H E B O X O F T H E O T H E R G R O U P ? Heights Travel time Inconsistent message Consistent message Sometimes the boys’ median height is higher The bus median time to school is always higher Sometimes the girls’ median height is higher Median heights are inside the overlap One of the median times to school is nearly always outside the overlap 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? M AKING THE CALL … B ACK IN THE TWO POPULATIONS … Heights Large amount of overlap Little or no overlap Medians within the overlap At least one median is outside the overlap Due to sampling variability another sample could easily give a different picture Travel time Don’t know which box is to the right back in the populations Therefore we don’t know who is taller 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 … 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… C OMPARING TWO POPULATIONS N = 30 W HEN TO MAKE THE CALL … L EVEL 5 GUIDE T HE ¾-½ GUIDE e.g. “more than half of the B group are above three quarters of the A group” Restrict to sample sizes of between 20 and 40 in each group M AKING Write your conclusion THE CALL … K EY IDEAS … Writing good questions Looking at a sample rather than the whole population Writing good analysis statements Statistical inference Level 5 A NY QUESTIONS … 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?....
