IS THE DIFFERENCE REAL?

So now the question is, "Is the difference real?" Usually when you conduct a study, you have some ideas that you want to explore. These ideas, often called hypotheses, typically involve comparisons of several groups, such as "Do men and women find life equally exciting?" "Does income differ between people who find life exciting and those who do not?" "Is a new machine making a real difference?"

Chances are if you compare two or more things, you are going to find some differences. After all, no two things are exactly the same. The question is not so much if things are different but rather, what can you make of the difference?

So far we have seen that different samples from the same population give different results. The real issue is, how much will they differ? How can you decide whether a difference in sample means can be attributed to their natural variability or to a real difference between groups in the population?