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WHICH WORKSHOP…
Workshop choices
Session 11.30 – 3 pm
Workshop ONEMultivariate Stats
Workshop TWOStats thinking & literacy
3 – 3.30 pm Afternoon tea
Session 23.30 – 5 pm
Workshop ONEMultivariate Stats(repeated)
Workshop THREEProbability & literacy
Telling stories from data
MULTIVARIATE STATISTICS
“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”
INTRODUCTION
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…
STATISTICAL INFERENCE…
DATA CARDS – WHAT ARE THE 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
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…
C@S LESSON PLANS…
http://new.censusatschool.org.nz/resources/level-5/
NZ CURRICULUM
Junior Statistical Inference
NCEA
Subject content
Values & Key Comps
NCEA – STATISTICSJunior
Statistics
Chance & Data
Questionnaire Design
Time Series
Stats Reports
Stats Reports
Bivariate Data
Bivariate Data
Multivariate Data
Informal Inference
Formal Inference
CHS EMPHASIS
Year 9
Introducing PPDAC – through Probability
Statistical Literacy
Year 10
Theoretical Probability & Literacy
PPDAC Statistics
(Making the call)
KARE KARE COLLEGE
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
KAREKARE COLLEGE: DATA CARD VARIABLES
Sort your data
SAMPLES GIVE US AN IDEA ABOUT WHAT IS HAPPENING IN THE
POPULATION
PPDAC CYCLE
INVESTIGATIVE QUESTIONS
• Summary
• Comparison
• Relationship
• Other
WHAT 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
INVESTIGATIVE 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
TWO SMALL ASIDES…
• Shape
• Writing
analysis
statements
SKETCHING SHAPESQuickly sketch the general shape of the distribution
0 20 40 60 80 100 120 140
0 2 4 6 8 10 12 14
0.5 1.0 1.5 2.0 2.5 3.0 3.5
1.5 2.0 2.5 3.0 3.5 4.0 4.5
0 20 40 60 80 100
16 20 24 28 32
0 200 400 600 800
0 100000 200000
0 20 40 60 80
REFLECTION: SEEING 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?
DESCRIBING 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?
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
GIVING STUDENTS STATISTICAL LANGUAGE
FOR SHAPES
ENGAGING 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?
KARE KARE 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
DESCRIBING 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
SENSIBLE ORDER TO STRUCTURE OUR ANALYSIS COMMENTS…
Centre
Spread
Shift & overlap
Shape
WRITING STRUCTURES
I notice… I wonder…
WRITING STRUCTURESPEER
Used to craft each statement
WRITING STRUCTURESOSEM
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?
PPDAC CYCLE
KARE KARE 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…
THIS IS A RANDOM SAMPLE OF STUDENTS FROM KARE KARE
COLLEGE
Write some analysis descriptions
Teaching world…
TO MAKE THE CALL BACK IN THE POPULATION
STATISTICAL 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?
WE LOOK AT MULTIPLE SAMPLES
Focus Direction of the shift
Consistency across samples
Developing a guide for ‘making-the-call’ back in the population
MULTIPLE 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
STUDENT IDEAS…SHIFT
LOC AT I ON OF THE BOXE S RE L AT I VE TO ONE AN OTHE 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
MESSAGE SHIFTLOCATION 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
STUDENT IDEAS… OVERLAPH O W M U CH T H E BOX E S ( M ID DL E 50% ) OV E R L A P O N E A N O T H E R
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
MESSAGE OVERLAP
HO W M U C H T HE BOXE S ( M I DD L E 50% ) OV E RL A P O N E AN O T H E R
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
STUDENT IDEAS… MEDIANSW H I C H M E D I A N I S H I G H E R ? W H E R E I S T H E M E D I A N LO C AT E D I N
R E L AT I O N T O T H E BOX 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
MESSAGE MEDIANSW H I C H M E D I A N I S H I G H E R ? W H E R E I S T H E M E D I A N LO C AT E D I N R E L AT I O N T O T H E B OX O F T H E O T H E R G R O U P ?
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
MAKING THE CALL…BACK 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?
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
MAKING THE CALL…BACK 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…
MAKING THE CALL…BACK IN THE TWO POPULATIONS…
COMPARING TWO POPULATIONSN = 30
WHEN TO MAKE THE CALL…LEVEL 5 GUIDE THE ¾-½ GUIDE
If the median for one of the samples lies outside the box for the other sample
e.g. “more than half of the B group are above three quarters of the A group”
make the call that B tends to be bigger than A back in the populations Restrict to sample sizes of between 20 and
40 in each group
MAKING THE CALL…
Write your conclusion
KEY IDEAS…
Writing good questions
Looking at a sample rather than the whole population
Writing good analysis statements
Statistical inference Level 5
ANY QUESTIONS…
WORKSHOP FEEDBACK…
On a piece of paper please give us some feedbackIt 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?....
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