A slide deck from a lab workshop presented on the 19th of May, 2016.

1. Using Bayes factors in
biobehavioral research
Daniel S. Quintana
NORMENT, KB Jebsen Centre for Psychosis Research
Oslo University Hospital & Institute of Clinical Medicine
University of Oslo

2. Our field has
a problem
with p-values

3. 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

4. Bayes factors (B) indicate the
relative strength of evidence
for two theories - the null and
alternative hypotheses

5. Bayes factors vary between 0
and infinity, where 1 indicates
that the data do not favour
any theory

6. Bayes factors (B) only
consider the observed data,
and how they relate to the
alternative and null
hypotheses

7. 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)

8. Most null
results are
never written
up.

9. 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

10. Common language rules-of-
thumb
Jarosz & Wiley (2014), Journal of Problem Solving, 7

11. A comparison of 855 p-values and corresponding B’s
Wetzels et al. (2011) Perspectives on Psychological Science, 6

12. 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

13. Bayes factors (B) not affected
by stopping rules

14. Bayes factors (B) are ratios of
probabilities so two B’s of
equal value provide
equivalent evidence

15. 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

16. 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

17. In JASP you can perform
common analyses using NHST
and Bayes - if you can’t find
your analysis, it’s possible
using R scripting

18. Example: Personality dataset
• Run a full correlation matrix with plots
• Are not significant correlations due to data
insensitivity?

19. Example: t-tests
• Compare sexes on full NEO and first 3 questions

20. Example: t-tests

21. Example: t-tests

23. The average effect size (d) in
social psych is .36, so let’s shift
the cauchy prior to .36

24. Example: t-tests

25. Example: t-tests

26. Example: t-tests

27. Example: Repeated measures
ANOVA
• Compare repeated measures factors

28. Questions?
Bayes theorem
Bae’s theorem