202602270818
Status: #reference
Tags:
State: #nascient

Experiment

An experiment is a concrete realization of a given sample space. It is similar to the concept of event in the sense that they are both drawn from a sample space.

While an event is a description of a specific outcome or set of outcomes that can originate from a sample space, an experiment is a draw that aim to answer some research question.

The research question informs the way the experiment is conduced (the way samples are drawn from the sample space), and then based on the statistics pertaining to the drawn observations and their distributions, we can then use some inference engine to gain insight out of them.

Since an ill-done experiment doesn't tell us anything substantial, we need the theory of Design and Analysis of Experiments Assignment 1 to inform us of how a given experiment should be designed, informing things like:

• How many samples should be drawn?
• What kind of analysis we can do based on the theoretically justifiable assumptions?
• What kind of inherent variability we have to account for in the way we administrate a treatment?
• Etc.

Failure to account for these things will greatly increase the Type I Error - Rejecting a True Null Hypothesis or the Type II Error - Failing to reject a False Null Hypothesis, as we have different individuals with different skills, and we fail to account for the interpersonal variability when testing the improvement to their math skills after a tutoring session, we might fail to realize the genius of our tutoring technique because the positive change brought by the treatment is overawed by the interpersonal variability of some people just being Terrence Tao, and others being bad.

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