Classical statistics experiment design

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I will begin this discussion talking about the classical experimental design

In this design, we basically want to see if a certain element has any effect on specific outcomes.

What does this mean?

I will provide an example first off, and then break it down for you. - I will bold key elements and come to explore them further.

Imagine a professor wants to try to create the best environment scenario for his students to study in. The professor has a hunch that if students listen to music while studying, they might study more efficiently, and score higher on his exam.

The professor then decided to conduct an experiment with his students. His class has 300 students in it.

He then split the students in half randomly - he asked half the students to study in a quiet environment, and then he asked the other group of students to study with soft classical music playing in the background.

On the day of the test, he asked students to either mark and "1" or a "2" on their exam - "1" if they studied in the quiet, and "2" if they listened to music.

The professor then graded the exams, and then grouped together the "1" and the "2". He then averaged out the grades from group 1 and group 2.

After he got the average, he conducted statistical tests to see if differences existed between the two groups.

The professor saw that Group 1 - i.e the students who studied in an quiet environment scored the same as students who studied with music on - thus, his hutch was disproved, and he was able to conclude that there is no difference in the environments in which students study in.

So what are some of the key elements?

1) The professor had a hutch - in scientific terms, this means he has a hypothesis. His hypothesis could be about anything - i.e boys weight more then girls, car a uses more gas then car b... All research problems actually begin with ...