The Bayes calculator
If you are new to Bayesian statistics and want to know why you should use the Bayes Calculator, then read the information below. If you just want to use it, click here.
Bayesian stats are becoming more popular
Behavioural science is increasingly moving away from classical statistical results and interpretations to Bayesian inference. This was at one time seen as quite esoteric but is now becoming mainstream - and for a very good reason.
Classical statistical inference with its 'significance levels' (e.g., p<0.05) does not tell users what they want to know and leads to flawed conclusions and reasoning. Most commonly, when people see p-values greater than 0.05, they infer 'no difference' or 'no effect'. Since anyone studying statistics is told not to do this pretty much in the first week of their course, it is surprising that it is so common. Pick up any issue of a journal in behavioural, or social (or clinical or public health) science, and you will find numerous examples of papers where this is done.
What Bayesian statistics give you
What we actually want to know is as follows:
Given the data we have collected, under certain assumptions about the data and how it was collected, what is the likelihood that a hypothesis we have about it is correct?
Typical examples are:
What is the likelihood that intervention X resulted in a higher value on an outcome measure than comparison intervention Y?
What is the likelihood that variable X is positively correlated with variable Y?
Bayesian 'posterior likelihoods' give you the answers to those questions.
Better than that, they give you answers to what are often more meaningful questions about the likelihood that the difference is at least as large as some minimum value. For example:
What is the likelihood that Intervention X increased the value of an outcome compared with Y by more than Z?
Even better than that, Bayesian posterior likelihoods can take account of what you already found in previous studies. So if you had previously found that the likelihood of X being positively correlated with Y was 80%, and you collected some more data, you could use the 80% as your 'prior likelihood' (technically Bayesians refer to prior 'odds', which is slightly different), and update your posterior likelihood wth the new data. And you can do this as many times as you like.
What being a Bayesian means
Being a 'Bayesian' means using data efficiently and incrementally to form the best judgement about the likelihoods of things being true, and updating your judgements as new data come in. At some point, you might come to the view that for your purposes, the likelihood has reached a sufficiently high or low level that you can stop or suspend collecting data.
This might be when you are 95% confident, or 99% confident or 80% confident. Where you put the threshold will depend on the case in hand. But even if you stop collecting data, you are always reporting the likelihoods and willing to adjust them if new evidence comes in.
The Bayes calculator
I have worked with my ever-helpful and patient AI friend, Claude, to program a simple website that allows users to put in values from their favourite stats programs and calculate Bayesian posterior likelihoods. To try it out, click here. It works for mean differences, odds ratios and rate ratios.
Robert West
Unlocking Behaviour Change CIC and University College London