Bi-Variate Data( AS 3.9) Dru Rose (Westlake Girls High School) Workshop PD Aiming at Excellence

The Aims of this workshop Discuss some concepts in this standard that students appear to find difficult and share some possible teaching approaches Share some borderline A/M and M/E student work with our grading decisions and reasoning

2 Big ideas

How do we train students to use their eyes? Intially NO Technology(until they can identify key features of data and describe them in context.) Provide plenty of contrasting scatter plots with straightforward contexts

How do we train students to describe what they see in context? 1.Teacher modelling Student voice: “It’s a decreasing trend”

Activity: Where should the trend line go?

What do students appear to find difficult? 1.Scatter i.e. Variation in the vertical direction ( In a box-plot variation is about spread in the x- direction )

What does non-constant scatter really mean? X √

What do students appear to find difficult?

Start with data sets where it is obvious Tar content, nicotine content and weight are measured before the cigarette is smoked. The CO is emitted when the cigarette is smoked – hence must be the “outcome” variable.

Systollic BP (when heart muscle heart contracts) and Diastollic BP (when heart muscle relaxes between beats) Consider situations where it might not matter

Move on to a rich multi-variate set What might be a possible “outcome” variable? What might be possible predictor variables for that outcome? What are possible investigative questions we could pose? Gapminder 2008

What do students appear to find difficult? 3. What the trend equation tells us Linear Trend : Weight = * Height For every 1 cm increase in height, on average the weight of an American adult increases by about 1.08kg What does the tell us? Wt of a baby of zero height -Is it a useful measure in this plot? -NO

4. The correlation coefficient: inappropriate use of r When does it tell us something useful and when should it not be used? Technology does what the user tells it to. Students need to continually ask questions: Is it sensible to put a line on a non-linear graph? Does the line I have added actually describe the trend in the majority of the data? What do students appear to find difficult?

X caution √ X

What do students appear to find difficult? 5. Outliers and Groups They see outliers and groups where there are none They remove points or groups where they should not Key questions we want students to ask: Will this point (group) affect the position of the trend line(curve)? Will this point (group) affect the strength of the relationship? Do I need to do further analysis or further research or both?

iceland Brunei Luxembourg Why so different?

Outlier is clearly pulling trend line towards it- remove it to get an appropriate trend line for making a prediction

(tonnes/yr) Tonnes of oil equivalent per yr (toe) Not affecting trend line. No need to remove

Making a forecast: What do we expect at Merit and Excellence level ?

Research needed only Chad

What do students appear to find difficult? 6. Confounding (lurking) variables The association we are observing may be an indirect relationship, where both the predictor and outcome variables are correlated with another related variable (called a confounder) With the big multi-variate data sets now available in INZIGHT students can now test out their thinking regarding potential confounding variables

What other variable might be connected with low life expectancy and a high number of children per woman? (or the reverse ) Using INZIGHT we can quickly identify Chad as having the highest fertility rate. Why? Google question: Why does Chad have the highest number of children per wom an?

What do we expect for MERIT? Some research to help explain the reason for the posed question A demonstration of understanding of the context and any statistical jargon used Some discussion on the reliability and usefulness of the forecast : e.g. limited range of x values, wide prediction interval? An overall conclusion which does come to a final decision in answer to the question.

What extra do we expect for Excellence? Sound research, referenced and integerated into the report Deeper thinking, beyond a formulaic approach Ability to cope with the unexpected No inappropriate use of statistical techniques and /or serious misunderstandings Discussion of the limitations of the analysis