Why is it important that two samples be independent? Explain.
First of all, you should be aware that there are plenty of situations where it is NOT important that two samples are independent, and in fact where having dependent samples can be a benefit. That being said, if we are using statistical tests that assume independent samples, it is important to actually meet that assumption. The easiest way to understand this is through an example.
Imagine that you’ve developed a new weight loss program and you’re interested in measuring whether it works. You put some notices in the local paper asking people to participate in a weight loss study and you offer to pay them a bit for their participation. As people contact you, you randomly assign them to one of two conditions (1. weight loss program or 2. no treatment control). Everyone is weighed at the beginning of the study and asked to either follow the weight loss program (Group 1) or just continue their normal …
This solution goes through statistical concept of independence with regards to two samples.