Core Statistics Calculators
This page presents tools that summarise probability updates, quantify group differences and generate values for assessing statistical claims using numerical evidence.
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Bayes' Theorem Calculator
A relationship between prior beliefs and new observations shows how updated probabilities shift once fresh information is taken into account.
Example use: Estimating the chance that a light flicker in a room is caused by a loose bulb after noticing it happen once.
Inputs: prior probability, sensitivity, false positive rate
Outputs: posterior probability, probability of not-A given the observation, probability of A given the absence of the observation, probability of not-A given the absence of the observation, total probability of the observation
Visual: a set of bars comparing the updated probabilities after incorporating the new information
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Effect Size Calculator
A comparison of two groups shows how far apart their average values are once differences in spread and sample size are taken into account.
Example use: Comparing how many minutes two people usually spend brushing their teeth each morning.
Inputs: group 1 values, group 2 values, mean 1, mean 2, standard deviation 1, standard deviation 2, sample size 1, sample size 2
Outputs: standardised mean difference, unbiased effect size, effect size r, pooled standard deviation, interpretation
Visual: two overlapping bell-shaped curves showing how much the groups differ
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P-Value Calculator
A comparison between a test statistic and a reference distribution shows how unusual the observed result would be if the underlying assumption were true.
Example use: Checking how surprising a particular number of heads would be when flipping a coin several times.
Inputs: distribution type, score, degrees of freedom, degrees of freedom 2, hypothesis type
Outputs: degrees of freedom, tail type, p-value, identified distribution, test statistic, cumulative probability, tail adjustment
Visual: a smooth density curve with a vertical line marking the test statistic and the shaded tail region
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Sample Size Calculator
A relationship between confidence, margin of error, and population size determines how many observations are needed to estimate a proportion reliably.
Example use: Working out how many people to ask when checking how many neighbours prefer tea over coffee.
Inputs: confidence level, margin of error, proportion, population size
Outputs: recommended sample size, confidence level z-score, ideal sample size unadjusted
Visual: a curve showing how the required sample size changes as the confidence level increases
Core Statistics FAQs
Effect size quantifies how large a measured difference is, offering a scale that remains stable regardless of sample size.
Bayes' Theorem updates an initial probability by incorporating new evidence, producing a revised likelihood based on combined information.
Larger sample sizes reduce random variation, increasing the likelihood of detecting differences that genuinely exist within the population.