Selecting the right statistical test is essential for drawing valid conclusions in hypothesis testing and A/B testing. Your choice depends on several factors: the type of data you have, the sample size, and the nature of your hypothesis. Begin by identifying whether your data is categorical or numerical. Categorical data is divided into groups, such as user gender or device type, while numerical data consists of measurable quantities, like revenue or time spent on a site.

Next, consider whether you are comparing means, proportions, or distributions:

• If you are comparing the average of two independent groups with numerical data and your sample size is sufficiently large; a two-sample t-test is often appropriate;
• For smaller samples or when population variance is unknown; the t-test is preferred over the z-test;
• When comparing proportions, such as conversion rates between two groups; a z-test for proportions is suitable if sample sizes are large enough to meet normality assumptions;
• For categorical data with more than two groups or categories; the chi-square test is commonly used to determine if distributions differ from expected frequencies;
• If you have paired or matched samples, such as before-and-after measurements on the same subjects; use a paired t-test.

Always check the assumptions of your chosen test, such as normality for t-tests and sufficient sample size for z-tests and chi-square tests. The hypothesis you are testing—whether it is about means, proportions, or distributions—guides your selection further. By carefully considering these aspects, you can select the most appropriate statistical test and ensure your experimental results are robust and meaningful.