Question

Which of the following statements regarding hypothesis testing is correct?

1) All else being equal, a significant difference between experimental and control group results in two identical distributions with the same mean.
2) All else being equal, a significant difference between experimental and control group results in two identical distributions with different means.
3) All else being equal, a significant difference between experimental and control group results in two different distributions with different means.
4) All else being equal, a significant difference between experimental and control group results in two different distributions with the same mean.

Answer 1

Option 3 is correct: a significant difference in hypothesis testing indicates two different distributions with different means. The control group should match the test group except for the independent variable to validate results.

Step-by-step explanation:

Regarding the correct statement about hypothesis testing, option 3 is correct, which asserts that all else being equal, a significant difference between experimental and control group results in two different distributions with different means. This circumstance arises because if the null hypothesis of equal group population means is rejected, it is often the case that the experimental condition has caused a shift in the distribution, leading to dissimilar distributions as well as dissimilar means.

The control group should ideally be identical to the experimental group except for the manipulation of the independent variable to ensure that any observed effects can be attributed to the intervention and not to other factors. Controls are critical as they allow for comparison between groups that are different in only the independent variable being tested, thus enhancing the validity of the experimental results.