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Module overview
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Reproducible analysis is strongly impacted by statistical analyses.
Reproducible research requires understanding the notions of sampling, testing, power, model selection.
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Statistical basis for neuroimaging analyses: the basics
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Be familiar with the concept of sampling
Know what we call a distribution, a p-value, a confidence interval
Have some knowledge of Bayesian statistics and model comparison
This is in line with our overall goal of making science (including scientific training) more open.
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Effect size and variation of effect sizes in brain imaging
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Effect sizes come in many forms
Significance is not relevance
Difference between the raw effect size and the cohen’s d effect size
How can the effect size vary? Why is it important to know about this?
Effect sizes are under reported, not well understood, and are crucial for our scientific understanding. Let’s fix this.
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P-values and their issues
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A p-value does not give you an idea of the importance of the result
A p-value should always be complemented by other information (effect size, confidence interval)
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Statistical power in neuroimaging and statistical reproducibility
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The lack of power is much more problematic that it seems at first sight. - It would usually lead to wasted resources - If an under powered study yields some significant effects, these are likely to be overestimated - If an under powered study yields some significant effects, these are less likely to replicate
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The positive Predictive Value
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A significant (say at the 0.05 level) may have a low chance of replication.
The PPV estimates the probability that the alternative hypothesis \(H_A\) is true given that the test is significant at some \(\alpha\) level.
This probability depends on several factors such as power \(\beta\), \(\alpha\) level, but also the prior chance that \(H_A\) is true.
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Cultural and psychological issues
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FIXME: more reference material.