Tuesday, September 23, 2014

The Fact and the Hypothesis

A good fact to submit is that we can't easily know the exact truth values/parameters of a population. Mostly, population parameters also change slightly by time and/or affected by different surrounding factors.


Example: a production line for the 500 ml bottles is assumed to produce a population of bottles such that mean value of bottles capacity is exactly 500 ml.

Nice, but what happens in realty?

In realty, several factors will mostly affect the production: human factors, machine factors, environment temperature...etc. Also, each new bottle will contribute in the population mean value. This means a continuous slight change, either up or down, of the mean capacity.

Here comes the hypothesis!

As you see, the ground truth value for population mean is difficult to be exactly determined. However, we have general assumptions/expectations.
OK, constructing a hypothesis should always be driven by our initial knowledge and expectations about the population.
Testing the hypothesis is statistical checking methods to judge these beliefs. Test results should conclude/push more beliefs into either:
  • Failure to say the parameter (eg mean value) has changed. Example: the 500 ml bottles capacity should be considered stable/no change at 500 ml. This conclusion is known as (failing to reject the null hypothesis).
  • Rejecting this initial assumption (we call it later the null hypothesis). This means that some factors affected the production and the mean value has changed to different values (up or down). Then, further monitoring/improvements should be decided to solve the issue. This conclusion is known as (rejecting the null hypothesis).
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