Abstract
In Chapter 10 we laid out the main ideas in assessing statistical significance. First, there is a null hypothesis; second, there is a statistic that defines some deviation away from a null model; third there is a \(p\)-value to judge the rarity of the observed deviation under the null hypothesis.
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- 1.
One idea is to find the “worst case” \(p\)-value (the largest) among all possible values of \(\omega \). However, this often remains intractable, except in large samples.
- 2.
Fisher also pointed out that with six cups there would be only 20 permutations and thus one would at best obtain \(p=.05\); he considered this \(p\)-value too large to be useful.
- 3.
Some care is required to state correctly the null hypothesis, but roughly speaking it corresponds to time intervals between post-synaptic currents being i.i.d., which they would not be if there were repeated patterns.
- 4.
This is important to the logic of the mirror neuron argument. See Dinstein (2008).
- 5.
We use the absolute value form \(|T_i| > c_{\alpha }\) for consistency with the two-sided tests emphasized in Chapter 10 but the logic is the same for all significance tests.
- 6.
The permutations were done in source space; see Xu et al. (2011).
- 7.
The null hypothesis was that for every brain source the theoretical mean activities in all movement directions were equal.
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Kass, R.E., Eden, U.T., Brown, E.N. (2014). General Methods for Testing Hypotheses. In: Analysis of Neural Data. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9602-1_11
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