# 5: Two-Dimensional Data - Differences

- Page ID
- 3574

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All methods covered in this chapter based on the idea of statistical test and side-by-side comparison. If even there are methods which seemingly accept multiple samples (like ANOVA or analysis of tables), they internally do the same: compare two pooled variations, or expected and observed frequencies.

- 5.1: What is a statistical test?
- Philosophers postulated that science can never prove a theory, but only disprove it. If we collect 1000 facts that support a theory, it does not mean we have proved it—it is possible that the 1001st piece of evidence will disprove it. This is why in statistical testing we commonly use two hypotheses. The one we are trying to prove is called the alternative hypothesis (H₁). The other, default one, is called the null hypothesis (H₀).

- 5.2: Is there a difference? Comparing two samples
- Studying two samples, we use the same approach with two hypotheses. The typical null hypothesis is “there is no difference between these two samples”—in other words, they are both drawn from the same population. The alternative hypothesis is “there is a difference between these two samples”.