Bayesian calculator for UX Research

Bayesian Calculator for UX Research

Optimize your analysis of binomial data—such as completion rates, agreement percentages, and theme occurrences—with this Bayesian beta-binomial calculator.

Bayesian analysis offers more intuitive and actionable insights than traditional frequentist statistics. Additionally, you can integrate informative priors based on expectations from past research, or from your own assumptions. To create intuition-based priors, try my Intuition-based Bayesian Priors Calculator .

Advantages of this approach:

Use Credible Intervals instead of Confidence Intervals for simpler, probability-based interpretations of uncertainty, providing a direct understanding of parameter ranges.

Use Probability of Direction instead of p-value to assess the likelihood that one option (A) outperforms another (B). This provides clearer and more actionable insights compared to null hypothesis significance testing, making it easier to communicate findings to stakeholders.

Inputs

Successes A

Trials A

Successes B

Trials B

Use Informative Prior

Alpha A (Prior)

Beta A (Prior)

Alpha B (Prior)

Beta B (Prior)

Posterior Distributions

Probability of Direction

Probability (\( P(p_A > p_B) \)):

Probability (\( P(p_B > p_A) \)):

For comparison, p-value from Fisher's Exact Test:

95% Credible Intervals

Group	Observed P	Best Estimate P	CI Lower Bound	CI Upper Bound
Group A
Group B

Additional Explanation

Posterior Distributions: These distributions represent the updated beliefs about the success probabilities of each treatment after observing the data. They combine the prior beliefs (if informative priors are used) with the observed data.

P-Direction Test: This test calculates the probability that the success probability of Treatment A is greater than Treatment B (\( P(p_A > p_B) \)) and vice versa. It provides a Bayesian interpretation of the evidence supporting one treatment over the other.

95% Credible Intervals: This section displays the observed proportions, the best estimates based on the posterior distributions, and the 95% credible intervals for each treatment. These estimates provide a summary of each group's 'success probability' \( p \) and the uncertainty around it.

Fisher's Exact Test: A frequentist statistical test used to determine if there are nonrandom associations between two categorical variables. In this context, it assesses whether the difference in success rates between the two treatments is statistically significant.

Mathematical Foundations:

Beta Distribution: The Beta distribution is a conjugate prior for the binomial distribution in Bayesian statistics. It is parameterized by alpha (\( \alpha \)) and beta (\( \beta \)) parameters, which can be adjusted to reflect prior beliefs about the success probabilities.

Credible Intervals: These intervals represent the range within which the true success probability lies with a certain level of confidence (e.g., 95%). They are derived from the posterior distributions.

Fisher's Exact Test: This test calculates the exact probability of obtaining a contingency table at least as extreme as the one observed, under the null hypothesis of no association between the variables.