Drawing an inference from an experiment: Level 8 Maxine Pfannkuch The University of Auckland.

Drawing an inference from an experiment: Level 8

Maxine Pfannkuch

The University of Auckland

Workshop Outline

• Background to Activity: Experiment– All levels: Plan and conduct surveys and

experiments using the statistical enquiry cycle

• Activity: Make an inference from an experiment– Level 8: Using methods such as resampling or

randomisation to assess the strength of the evidence

The statistical enquiry cycle

Orbital Express Experiment

• You work in the design and testing department for Orbital Express. The company has decided to start delivering packages by dropping them from orbit onto customers’ houses. It is testing two competing designs for the new re-entry vehicle.

Problem

Orbital Express Experiment

• Your job is to test the two designs and report which is better. The two designs cost the same to build, so your objective is to find out which re-entry vehicle gets the package closer to the target.

(Key Curriculum Press, 2005)

Problem

The re-entry vehicles

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Copier paper Tissue paper

Ruler – What’s this for?

Problem

What does it mean “closer to the target”?

What does it mean “closer to the target”?

What do I measure? How many trials?

Target area

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OutIn QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

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Categorical data Measurement data

Plan

Data collectionData

What can I conclude? Which re-entry vehicle is better?

Did 30 trials for each designBalls dropped from 50cm onto deskWhich is better, tissue or copier paper?

Analysis

• 30 trials for each design

• Balls dropped from three-storied building onto asphalt

• Is the copier paper better?

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What can I conclude? Which re-entry vehicle is better?

What can I conclude? Which re-entry vehicle is better?

• 30 trials for each design

• Balls dropped from 2m onto carpet

• Is the tissue paper better?

Analysis

Presenting findings Conclusion

Drawing a conclusion: Level 8

• Is the difference you see real or due to “chance”?• Does the result conform to the chance explanation or can

you argue the result is implausible under an all-chance model?

• To test the adequacy of a pure-chance account of the comparative difference in your data you must begin by conceptualising the operation of chance

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Resampling methodworksheet

Conceptualising chance explanation• On top axis plot observed /

experiment data• Chance explanation: there

is no link between paper type and distance from target. CUT LINK

• Scramble distance data, divide in half (9 each). By chance– 1 person copier measures– 1 person light measures

• Plot on paper. (Repeat scrambling 5 times)

• Question: Is the chance explanation plausible?

0.0 0.2 0.4 0.6 0.8Distance

Collection 1 Dot Plot

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Distance

Collection 1 Box Plot

Finding a way of “measuring the difference”

• Visually it appears that the chance explanation is plausible/not plausible. There seems not/seems to be a DIFFERENCE between chance plots and expt plot

• Want to compare chance plots with expt plot

• How do we compare things?– Look at how they differ

• How do we measure differences?

• All subtract same way then collate findingsmedian dist light – median dist copier

Finding a way of “measuring the difference”

• Under the chance explanation how often will you see the original observed difference of 0.2m or larger in the medians? A difference of this size or larger occurs about 15 times in 1000 through chance alone. Therefore, based on these data we claim there is ………… evidence of difference in median distances of light and copier balls from the target point.

0.2 = 0.2

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-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3DiffMed

Measures from Scrambled Collection 1 Histogram

Fathom simulation

Reflections on resampling method

• Why is this method in the curriculum?

• Emphasise the reasoning behind inference– Emphasising thinking– Building statistical concepts - part of a pathway

through the curriculum for students to understand the logic of inference

– Learning statistical reasoning and argumentation