Answer to Question 1
When people are similar to one another, they are less likely to differ in their scores on the DV. As such, a variable that has a small effect might be easier to spot People in a given group don't differ, so they have similar scores with no treatment. A small effect will be easier to see because differences will be due to the treatment rather than due to measurement error.
When people differ from one another, you often expect differences that don't mean anything. Thus, a small difference due to an IV is hidden by the naturally occurring differences between groups.
Thus, if your groups are heterogeneous (i.e., variable), producing a lot of difference even in the absence of the IV, you need a larger sample to be confident that the IV made a difference. On the other hand, if your groups are similar, you don't need such a large sample because small differences stand out more.
Answer to Question 2
Correlational studies are those whose methodology involves variables that are not manipulated; they are measured as they exist. Such studies can help detect relationships between variables but not cause. Correlational analysis involves different types of statistical approaches. The approaches are correlational, but if the methodology is such that it can legitimately lead to causal analysis, the correlational approach does not mean that the researcher can't invoke causal statements.
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