Overview

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BiteSize Statistics for Business: Hypothesis Testing for Two Samples is the second course in the BiteSize Stats for Business specialization. It extends single-sample inference to the comparisons that drive most real business decisions: does group A differ from group B — in a mean, a proportion, a category, or across more than two groups at once? Across five modules, learners progress from two-sample Z- and t-tests for independent groups (including full A/B testing pipelines), through the paired t-test for before/after and matched designs, to the two-proportion Z-test, the chi-square test of independence with Cramér's V, and finally one-way ANOVA with Tukey's HSD post-hoc test. Every core lesson pairs a focused reading with a hands-on interactive notebook built around a realistic business scenario, and every module includes a fully worked demo case study and one or more ungraded practice projects applying the module's tools to a new scenario.

Syllabus

Two-Sample Z and T Tests
- Introduces the sampling distribution of the difference between two independent sample means and the conditions required for valid two-sample inference. Students run the two-sample Z-test when population standard deviations are known, the Welch two-sample t-test when they are not, and apply both within a complete A/B testing pipeline — including the pitfalls of peeking and multiple testing.
The Paired t-Test
- Distinguishes paired from independent sample designs and shows why pairing reduces noise and produces a more powerful test. Students calculate paired differences and the paired t-statistic, construct confidence intervals for the mean difference, and apply the CI-hypothesis test duality to before/after and matched business comparisons.
Two-Sample Proportion Tests
- Covers the two-proportion Z-test for comparing two independent proportions, including the pooled standard error used for testing and the unpooled standard error used for confidence intervals. Students apply proportion tests to ad-channel comparisons, send-time optimization, and defect-rate analysis, learning when a statistically significant difference is too small to matter.
The Chi-Square Test of Independence
- Builds a contingency table from two categorical variables and calculates expected frequencies under independence, then the chi-square test of independence for detecting association. Students calculate Cramér's V to measure association strength separately from statistical significance, applying both to customer churn and survey-association questions.
One-Way ANOVA
- Explains why running multiple pairwise t-tests inflates the Type I error rate and introduces one-way ANOVA as the corrective F-test comparing between-group and within-group variance. Students construct the ANOVA table, run Tukey's HSD post-hoc test to identify which specific group pairs differ, and calculate eta-squared as an effect size, applying the full pipeline to a real four-region sales comparison.