Have you ever tossed a coin waiting for the coin to land on either heads' or tails'? After you won (success) or lost (failure), it was known that the selection was fair or unbiase, right?! In statistical terms, this is known as a simple random bernoulli experiment.
Is one coin toss enough? If you are competitive, you may want the coin tossed more than once. The process of tossing the coin more than once, is known as a binomial experiment. You can see that bernoulli and binomial experiments are from a "kindred family".
How many coin tosses (trails) should you do? Another way of stating this, is what is the appropriate sample size determination. For such a simple experiment as this, fifty tosses would be close to normal.
What if the same person is tossing the coin for each trail? Is it still considered an unbiase experiment? The person that you are competing with, are your reflexes the same and are you the same age? The point that I'm making is, for any experiment the experimental unit should come from the same population to ensure randomness.
Let us say, that the two people competing are from the same population and both toss individual coins fifty times. You then count the number of heads' and tails' to determine the winner. Would you then believe that the game of chance was unbiase?
Are there other factors that could affect the experiment? Are you tossing the coin outside while the wind is blowing? How high should the coin be tossed? These factors are known as potential predictive variables to help explain the probability of success.
I've turned a fun game of chance into a statistical experiment. This is why we statistical consultants love what we do. We have to break down every aspect of the task into a scientific approach known as mathematical science or statistics. Being a statistical consultant is both challenging and rewarding. Of course, the coin-toss game is very simple as I wanted a non-technical person to follow along.
However, every day pharmaceutical companies have clinical trail studies, studying the efficacy of a new or existing drug. Telecommunication companies have to ensure not to many drop calls and that their product is competitive.
What if, for the clinical trail study, mortality occurred? It's safe to say, the mortality should be related to the health of the participant and not the new or existing drug. What if there was an earthquake and the telecommuication company had more drop calls than expected? Can these factors be included in the study? Only if you have historical data or in the cause of a catastrophe, a radar warning that it's coming, which of course would be to late to incorporate this information in a statistical model.
You see it could be very challenging to be a statistical consultant. The reward for being a statistical consultant to me, is a successful model that predicts what will happen within a reasonable level of assurance, and you help play a part in the success of others.
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