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
Problem
• 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.
Orbital Express Experiment
Problem
• 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
Copier paper
QuickTime™ and a
TIF F (Uncompressed) decompressor
are needed to see this picture.
Tissue paper
QuickTime™ and a
TIF F (Uncompressed) decompressor
are needed to see this picture.
Ruler – What’s this for?
QuickTi me™ a nd a
TIFF (Uncompre ssed ) decomp resso r
are need ed to se e th is p icture.
What does it mean “closer to the target”?
What does it mean “closer to the target”?
What do I measure? How many trials?
TIF F
(U Q
are ncomuickTim
ne
pre
e
e
d
ed to ssed)™ and
see deco a
this mpre
pictu sso
re. r
Out
In
Plan
QuickTi me™ and a
TIFF ( Uncompressed) decompressor
are needed to see thi s pi ctur e.
QuickTi me™ and a
TIFF ( Uncompressed) decompressor
are needed to see thi s pi ctur e.
QuickTi me™ and a
TIFF ( Uncompressed) decompressor
are needed to see thi s pi ctur e.
Target area
Measure distance to target
Categorical data
Measurement data
Data collection
Data
What can I conclude? Which re-entry vehicle is better?
Did 30 trials for each design
Balls dropped from 50cm onto desk Analysis
Which is better, tissue or copier paper?
What can I conclude? Which re-entry vehicle is better?
• 30 trials for each design
• Balls dropped from three-storied building
onto asphalt
• Is the copier paper better?
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
What can I conclude? Which re-entry vehicle is better?
• 30 trials for each design
• Balls dropped from 2m onto carpet Analysis
• Is the tissue paper better?
Presenting findings
Conclusion
Drawing a conclusion: Level 8
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
• 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
QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
Resampling method
worksheet
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?
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 findings
median dist light – median dist copier
Finding a way of “measuring the difference”
Fathom simulation
• 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.
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