The Panini-Test

The Panini-Test
Daniel J. Stekhoven
CEO Quantik AG
Statistician
Activation of mTORC1 is necessary and sufficient for the alert
phenotype.
JT Rodgers et al. Nature 000, 1-4 (2014) doi:10.1038/nature13255
Activation of mTORC1 is necessary and sufficient for the alert
phenotype.
JT Rodgers et al. Nature 000, 1-4 (2014) doi:10.1038/nature13255
16 days ‘til…
Copyright ©1994 - 2014 FIFA.5
And the most important thing before the world cup starts…
© 1997-2014 Panini SpA
410 stickers
8
blister
box
5 Stickers
50 Blister = 250 Stickers
© 1997-2014 Panini SpA9
?
10
20 Minuten – Panini-Box – 21. März 2014
Gut feeling and hypotheses
 Complete box  not so many doubles
 Single Blisters bought at different stores  many doubles
«Null», because there is no system behind the filling of the boxes
 «Null hypothesis»:
 Stickers filled randomly into the boxes
 Alternative hypothesis:
 Stickers are filled systematically into the boxes, such that not many
doubles are present
How can we decide between
these two hypotheses?
12
Hypothesis test
 I bought a box with 250 stickers and I could fill 242 of these
stickers into an empty album (410 possible pictures).
 If we assume that the null hypothesis is true:
 Is it plausible, that I could glue 242 pictures into the album?
 Do the null hypothesis «randomly filled boxes» and the event
«242 stickers at once» fit together?
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Problem: What is «normal»?
• If I was able to put many more stickers than «normal»
into the album, then the boxes were probably not filled
at random
• If we assume that the null hypothesis is true – how
many stickers can we put into an album normally?
• Level of significance: How «abnormal» does an
observation has to be, such that we do not believe in
the null hypothesis anymore?
– e.g. 1/1’000’000  we reject the null hypothesis if we
observe something that is less probable than 1/1’000’000
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Solution: computer simulation
1
186
2
192
1 mio
193
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Number of albums
Resultat der Computersimulation
Number of stickers
16
Number of albums
How «abnormal» is our observation?
Number of stickers
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Conclusion
• If we assume that the stickers are filled into the boxes at
random:
– The probability for observing an event with 242 stickers put
in a new album coming from a single box is less than
1/1’000’000!
 Our observation and the simulation (the null hypothesis
world) do not fit together!
Stickers are not filled randomly into the boxes
18
20 Minuten – Panini-Box – 21. März 2014
Summary
1.
2.
3.
4.
5.
6.
Model: Draw 250 sticker with replacements from 410 possible stickers
Null hypothesis: «stickers are randomly filled into the boxes»
Alternative: «systematically filled-in, such that less doubles appear»
Test statistic: Number of stickers put into a new album when we buy a box of
250 stickers.
Distribution of the test statistic under the null hypothesis: computer simulation
Level of significance:  = 1/1’000’000
Critical region of the test statistic:
The computer has not observed more than 211 stickers in one album using 1
mio iterations  critical region: K={212, 213, …, 250}
Test decision: The observed value (242) is within the critical region. This is why
the null hypothesis will be rejected on the level of significance of 1/1’000’000
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Acknowledgment
• Original idea by Markus Kalisch
Copyright ©1994 - 2014 FIFA.
• …it’s all about
collecting data
© 1997-2014 Panini SpA