1. Statistics
Jonas Ranstam PhD

2. Statistics
A scientific report
The idea is to try and give all the information to help
others to judge the value of your contributions, not just
the information that leads to judgment in one particular
direction or another.
Richard P. Feynman

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Description of observed data
mean, median, mode (central tendency)
standard deviation, range (dispersion)
Presentation of uncertainty
p-value, statistical significance (hypothesis testing)
confidence interval, SEM (interval estimation)

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What uncertainty?
Generalization uncertainty, for example:
- From one sample of rats to all rats (the uncertainty
caused by biological variability)
- From a single measurement on a single rat to all
measurements of the same kind on the same rat
(the uncertainty caused by using imperfect
measurement instruments, i.e. reliability)

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What determines the degree of uncertainty?
1. The number of observations
2. The variability

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What is important when presenting results?
1. The number of observations
2. The variability

7. Reported mean concentration with ±SD (bar chart)

8. Observed mean concentration (dotplot)

9. Estimated mean concentration with 95% confidence intervals

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Why use CI instead of SEM?
Because the CI is the better measure of uncertainty
n SEM CI (for a mean value)
2 ±1 50%
3 ±1 58%
4 ±1 63%
6 ±1 64%
7 ±1 65%
∞ ±1 68%

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Other problems related to generalization uncertainty
1. Independence of observations
2. Gaussian probability distribution
3. Multiplicity

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1. Independent observations (2 treatments, 4 rats, n = ?)
n=4
n=8
n = 96

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Independent observations
Distinguish between:
1. Biological variation
2. Measurement reliability
Describe the sources of variation clearly in the manuscript!
How many animals, repeated observations, technical
replicates, etc. have been analyzed?

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Recommended reading
Churchill GA. Fundamentals of experimental design for
cDNA microarrays. Nature Genetics 2002;32S:490-495.

15. 2. Gaussian distribution

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Are your results empirically supported?
Or do they rely on your assumptions?
- Student's t-test (Gaussian, identical variance)
- Mann-Whitney U-test (identical shape and variance)

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Did you check if the assumptions were fulfilled?
- How did you do it?
- What was the result?
Describe it in the manuscript!

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3. Multiplicity
With more than one tested null hypothesis the real
significance level will differ from the nominal

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3. Multiplicity
- Multiplicity corrections correct the type-1 error rate
- Multiplicity corrections increase the type-2 error rate

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3. Multiplicity
- Bonferroni is not a good method, several better
exist, for example the methods developed
by Holm and Hochberg
- P-value corrections within endpoints do not solve
the problem of testing multiple endpoints

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3. Multiplicity
What is your strategy for dealing with multiplicity? Are
Bonferroni corrections necessary? Are all multiplicity
issues addressed?
Describe it in the manuscript!

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Summary
As an author of a scientific report your task is to
perform an adequate evaluation and presentation of
the uncertainty and limitations of your findings.
This involves more than just calculating a p-value.

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Summary
When a well-done trial or experiment or observational
study is fairly, honestly, and thoroughly reported, it will
have so many warts, footnotes, and exceptions that it
may be hard for the uninitiated to believe that the work
was of high quality.
Frederick Mosteller

24. Thank you for your attention!