Abstract
Classical null hypothesis significance testing is limited to the rejection of the point-null hypothesis; it does not allow the interpretation of non-significant results. This leads to a bias against the null hypothesis. Herein, we discuss statistical approaches to ‘null effect’ assessment focusing on the Bayesian parameter inference (BPI). Although Bayesian methods have been theoretically elaborated and implemented in common neuroimaging software packages, they are not widely used for ‘null effect’ assessment. BPI considers the posterior probability of finding the effect within or outside the region of practical equivalence to the null value. It can be used to find both ‘activated/deactivated’ and ‘not activated’ voxels or to indicate that the obtained data are not sufficient using a single decision rule. It also allows to evaluate the data as the sample size increases and decide to stop the experiment if the obtained data are sufficient to make a confident inference. To demonstrate the advantages of using BPI for fMRI data group analysis, we compare it with classical null hypothesis significance testing on empirical data. We also use simulated data to show how BPI performs under different effect sizes, noise levels, noise distributions and sample sizes. Finally, we consider the problem of defining the region of practical equivalence for BPI and discuss possible applications of BPI in fMRI studies. To facilitate ‘null effect’ assessment for fMRI practitioners, we provide Statistical Parametric Mapping 12 based toolbox for Bayesian inference.
Highlights
In the neuroimaging field, it is a common practice to identify statistically significant differences in local brain activity using the general linear model approach for mass-univariate null hypothesis significance testing (NHST) (Friston et al, 1994)
Bayesian methods have been described elsewhere, the distinguishing feature of this study is that we aim to demonstrate the practical implementation of Bayesian inference to the assessment of ‘null effects,’ and reemphasize its contributions over and above those of classical NHST
The ‘null effect’ was detected in all voxels beginning with a γ = 0.013% threshold using the ‘ROPE-only’ and ‘highest density interval (HDI)+ROPE’ decision rules
Summary
It is a common practice to identify statistically significant differences in local brain activity using the general linear model approach for mass-univariate null hypothesis significance testing (NHST) (Friston et al, 1994). NHST considers the probability of obtaining the observed data, or more extreme data, given that the null hypothesis of no difference is true. This probability, or p-value, of 0.01, means that, on average, in one out of 100 ‘hypothetical’ replications of the experiment, we find a difference no less than the one found under the null hypothesis. In the classical NHST framework, the question of interpreting non-significant results remains Using NHST, we can only state that we have ‘failed to reject the null.’ in the classical NHST framework, the question of interpreting non-significant results remains
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