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Between Confidence and Credibility
Some researchers confuse frequentist confidence intervals and Bayesian credible intervals.
This article gives an overview of differences between these two intervals.
Frequentist and Bayesian
In the 2019 political science compendium book Sex, Lies and Politics, one academic states:
The grey of the graph represents the width of the confidence interval, indicating a 95 per cent probability that the true score lies within this area.
This is an incorrect interpretation of confidence intervals, based on a historical schism in statistical practice.
Broadly, there are two schools of thought about what a probability is: frequentist and Bayesians.
Frequentists, as the name suggests, interpret probabilities as the frequencies that events occur in the long run. A fair coin will, at its limit, show Tails half the time: hence, the probability is 1/2.
Bayesians believe probabilities are subjective, reflecting degrees of beliefs about events. Our prior belief is that the probability of a coin showing Tails is 1/2. We flip the coin, updating that belief using Bayes’ Theorem.
