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 School is fictional 616 students (389 female, 227 males) 13 variables from 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 weightPopliteal length Fitness levelIndex finger lengthRing 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?

What does ‘tend to’ mean? Values for A are shifted further up the scale than values for B.

What does ‘tend to’ mean?

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 BGBG

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 BGBG

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 BGBG

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 BGBG 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 BGBG

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 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. 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 guidelines Make 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!