making the call year 10 some activities to immerse students in ideas about sample, population,...
TRANSCRIPT
Making the call Year 10
Some activities to immerse students in ideas about sample, population,
sampling variability and how to make a “claim” when comparing two groups
Aim of the workshop
To present some classroom activities to immerse students in ideas about:
sample, population, and the link between sample and population
the need to sample sampling variability shift and overlap when comparing two groups formulating guidelines for making a claim when
comparing two groups
Population ideas
Karekare College Students selected from 2009 C@S School is fictional 616 students (389 female, 227 males) 13 variables from C@S survey Each card represents a student Card colour indicates gender
Karekare College Data
AgeEthnicity Year level
Transport to school
Time to school Height
Way of carrying school bag
School bag weight Popliteal length
Fitness level Index finger length Ring finger length
What are typical popliteal lengths of students at Karekare College? How would you go about answering a question like this? (think like a student – Marina & Pip stories: the need to sample)
Summary question (give out strips)
Plots using data cards
Summary question
What are typical popliteal lengths of students at Karekare College? How would you go about answering a question like this? (think like a student – the need to sample)
What would the population distribution look like? In pairs, take a sample of about 30 students Plot your sample (box and dot plot) Compare your plots
What do you notice?
What are typical popliteal lengths of students at Karekare College? How would you go about answering a question like this? (think like a student) What would the population distribution look like? In pairs take a sample of about 30 students Plot your sample (box and dot plot)
Get students to describe their sample distribution
Compare your plots – what do you notice? Location of centres, spread, shape, . . .
Summary question
Comparison questions At Karekare College, do boys tend to be taller
than the girls? At Karekare College, who tends to take a longer
time to get to school; students who walk or students who travel by bus?
Comparison questions
For each question, ask students to: Predict and draw the population
distributions for the variable in the question. Show one population distribution relative to
the other. Give a rough indication of the range of values
expected. Collect and plot samples / data.
Hand out students’ box plots for height and travel times
Luxury of 18 samples for each question Box plots drawn without whiskers
Comparison questions
BG
Exploring the plots
Take each question in turn For each pair of plots (sample):
Which group tends to have the bigger values?
Consider shift and overlap Sort the plots wrt shift and overlap
BG
Exploring the plots: for example
Heights plots
In this plot:
Shift is small, boys values shifted slightly further up the scale – boys’ median is higher than girls’
Lots of overlap
Suggestive message: back in the two populations boys tend to be taller than girls
BG
Heights plots
In this plot:
Shift is large, girls value shifted further up the scale – girls’ median higher than boys
Little overlap
Suggestive message: back in the two populations girls tend to be taller than boys
BG
Exploring the plots: for example
Exploring the plots
Take each question in turn (start with BW: ‘time to school’)
For each pair of plots (sample): Which group tends to have the bigger values?
Consider shift and overlap Sort the plots wrt shift and overlap
BG
What do you notice over all samples? – BG: heights of boys & girls
Sometimes it’s the boys’ box shifted further up the scale and sometimes it’s the girls’. Sometimes the boys’ median is higher,
sometimes the girls’ median is higher, sometimes they are the same.
Small shift
In all samples, large overlap of boxes
Suggestive message is not consistent Not prepared to make the call which group tends
to have the larger values back in the two populations
What do you notice over all samples? – BG: heights of boys & girls
In all samples the bus box is shifted much further up the scale The bus median is always much higher than the
walk median
Large shift
Sometimes the boxes overlap, sometimes they do not, when they overlap it is only by a small amountSmall or no overlap
What do you notice over all samples? – BW: time to school
Suggestive message is consistent Make the call that students who travel by bus tend to take a
longer time to get to school than those who walk back in the two populations.
What do you notice over all samples? – BW: time to school
Formulating guidelines
Small shift and large overlap – not prepared to make a call, (‘too close to call’)
Large shift and small or no overlap – make the call
How large does the shift
have to be to make the call?
Formulating guidelines
At least one group’s median has to be outside the box of the other group.
Formulating guidelines
Make the call when
otherwise, it’s too close to call.
At least one group’s median is outside the box of the other group.
Formulating guidelinesMake the call when
otherwise, it’s too close to call.
Before we carry on: Please paper-clip your height strips and time strips back together
At least one group’s median is outside the box of the other group.
Visualising the suggested message
Show animations Raise hands to indicate which median is
higher. E.g.
boys higher – boys up the scale: right hand; girls higher – boys down the scale: left hand
Examples: Iron data 3 examples
Wrap Up
Presented some classroom activities to immerse students in ideas about:
the link between sample and population the need to sample sampling variability shift and overlap when comparing two groups formulating guidelines for making a claim when
comparing two groups
Thank you!