Frequently Asked Questions

A curated summary of the top questions asked on our Slack community, often relating to implementation, functionality, and building better products generally.
Statsig FAQs

How are p-values of experiments calculated and is it always assumed that the underlying distribution is a normal distribution?

In the context of hypothesis testing, the p-value is the probability of observing an effect equal to or larger than the measured metric delta, assuming that the null hypothesis is true. A p-value lower than a pre-defined threshold is considered evidence of a true effect.

The calculation of the p-value depends on the number of degrees of freedom (ν). For most experiments, a two-sample z-test is appropriate. However, for smaller experiments with ν < 100, Welch's t-test is used. In both cases, the p-value is dependent on the metric mean and variance computed for the test and control groups.

The z-statistic of a two-sample z-test is calculated using the formula: Z = (Xt - Xc) / sqrt(var(Xt) + var(Xc)). The two-sided p-value is then obtained from the standard normal cumulative distribution function.

For smaller sample sizes, Welch's t-test is the preferred statistical test due to its lower false positive rates in cases of unequal sizes and variances. The t-statistic is computed in the same way as the two-sample z-test, and the degrees of freedom ν are computed using a specific formula.

While the normal distribution is often used in these calculations due to the central limit theorem, the specific distribution used can depend on the nature of the experiment and the data. For instance, in Bayesian experiments, the posterior probability distribution is calculated, which can involve different distributions depending on the prior beliefs and the likelihood.

It's important to note that it's typically assumed that the sample means are normally distributed. This is generally true for most metrics thanks to the central limit theorem, even if the distribution of the metric values themselves is not normal.

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