Making the call Year 10 Ppt - CensusAtSchool New Zealand

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 Ethnicity Transport to school

Age Time to school

Year level Height

Way of carrying school bag

School bag weight

Popliteal length

Fitness level

Index finger length

Ring finger length

Summary question

(give out strips)

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)

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?

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In pairs, take a sample of about 30 students Plot your sample (box and dot plot) Compare your plots 

What do you notice?

Summary question What are typical popliteal lengths of students at Karekare College? 

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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) 

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Get students to describe their sample distribution

Compare your plots – what do you notice? Location of centres, spread, shape, . . .

Comparison questions 

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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. 

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Show one population distribution relative to the other. Give a rough indication of the range of values expected. Collect and plot samples / data.

Comparison questions 

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Hand out students’ box plots for height and travel times Luxury of 18 samples for each question Box plots drawn without whiskers B G

Exploring the plots Take each question in turn  For each pair of plots (sample): 

Which group tends to have the bigger values? 

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Consider shift and overlap

Sort the plots wrt shift and overlap B G

Exploring the plots: for example Heights plots

B G 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

Exploring the plots: for example Heights plots

B G 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

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? 

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Consider shift and overlap

Sort the plots wrt shift and overlap B G

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

What do you notice over all samples? – BG: heights of boys & girls 

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? – BW: time to school 

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 amount

Small 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.

Formulating guidelines 

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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 At least one group’s median is outside the box of the other group. otherwise, it’s too close to call.

Formulating guidelines Make the call when At least one group’s median is outside the box of the other group. otherwise, it’s too close to call. Before we carry on: Please paper-clip your height strips and time strips back together

Visualising the suggested message  

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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!