What are some common pitfalls to avoid when calculating and interpreting the margin of error between two numbers?

Common pitfalls include: Assuming that the samples are independent when they are not, using the wrong formula (e.g., using a formula for comparing means when comparing proportions), failing to account for small sample sizes (which may require alternative methods), and misinterpreting the margin of error as the maximum possible difference rather than a range of plausible differences.