Date post: | 14-Apr-2017 |
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Using Bayes factors in biobehavioral research
Daniel S. QuintanaNORMENT, KB Jebsen Centre for Psychosis Research Oslo University Hospital & Institute of Clinical Medicine University of Oslo
Our field has a problem with p-values
The main problems with p-values (or NHSTs)
• Running more participants will get you a
significant result (eventually)
• Can’t ‘compare’ p-values between studies
• A p-value cannot provide evidence for the null,
no matter how ‘significant’ the p-value is
Bayes factors (B) indicate the relative strength of evidence for two theories - the null and alternative hypotheses
Bayes factors vary between 0 and infinity, where 1 indicates that the data do not favour any theory
Bayes factors (B) only consider the observed data, and how they relate to the alternative and null hypotheses
Bayes factors provide 3 conclusions
• Evidence for the null (B < 0.33)
• Evidence for the alternative hypothesis (B > 3)
• Evidence is not sensitive (B is between .33 & 3)
Most null results are never written up.
Bayes factors (B) can provide evidence of whether a non-significant result was due to insensitive data (i.e. underpowered) or the data favours the null
Common language rules-of-thumb
Jarosz & Wiley (2014), Journal of Problem Solving, 7
A comparison of 855 p-values and corresponding B’s
Wetzels et al. (2011) Perspectives on Psychological Science, 6
A comparison of 855 p-values and corresponding B’s
Wetzels et al. (2011) Perspectives on Psychological Science, 6
• The corresponding B of 18% of p-values only provide anecdotal evidence for the alternative hypothesis
• The corresponding B values of 14% of p-values suggest the data were simply insensitive
Bayes factors (B) not affected by stopping rules
Bayes factors (B) are ratios of probabilities so two B’s of equal value provide equivalent evidence
Example: HRV in psychosis spectrum disorders
• When comparing HRV between schizophrenia
group and clinical group, p = 0.001
• B = 133.5, providing support for the null
hypothesis. In other words, given the data, the
alternative hypothesis is 133 times more likely
than the null
Quintana et al. (2016) Acta Psychiatrica Scandinavica, 133
Example: HRV in psychosis spectrum disorders• When comparing HRV between Bipolar Disorders
and schizophrenia, p = 0.99
• This is a ‘large’ p-value, but still can’t use this to
support null hypothesis
• B = 0.21, providing support for the null hypothesis
• Although this was ‘highly significant’, the null
was only 5 times more likely under the null
In JASP you can perform common analyses using NHST and Bayes - if you can’t find your analysis, it’s possible using R scripting
Example: Personality dataset
• Run a full correlation matrix with plots
• Are not significant correlations due to data
insensitivity?
Example: t-tests
• Compare sexes on full NEO and first 3 questions
Example: t-tests
Example: t-tests
The average effect size (d) in social psych is .36, so let’s shift the cauchy prior to .36
Example: t-tests
Example: t-tests
Example: t-tests
Example: Repeated measures ANOVA
• Compare repeated measures factors
Questions?
Bayes theorem
Bae’s theorem