## Monday, May 30, 2011

### Hypothesis Testing

As a scientist and a rational human being, learn to question everything and strive to find answers on your own through research. 'Doubt' is the most sacred thing for a scientist and an adherent of the scientific method. This doubt keeps you on focused when you feel like surrendering or believing in something at face value without adequate scientific research. As scientists, we constantly strive to create a rational and lucid picture of the world by piecing together one fact at a time, through theorising and experimentation (Pilgrim, 2011). A Hypothesis means to “Ask a Question of Nature”. In Science we often need to test our hypothesis. A hypothesis is an educated guess, based on observation. Usually, a hypothesis can be supported or refuted through experimentation or more observation. A hypothesis can be disproven, but cannot be proven to be true (Helmenstine, 2010). To test the hypothesis we create an experiment that will yield one of two answers: Yes or No or True or False. The classical way to make statistical comparisons is to prepare a statement about a fact for which it is possible to calculate its probability of occurrence. This statement is the null hypothesis and its counterpart is the alternative hypothesis (Fraser, 2011). The null hypothesis is traditionally written as H0 and the alternative hypothesis as H1 or Ha. A statistical test measures the experimental strength of evidence against the null hypothesis. A Null Hypothesis is a statement that the difference between two values can be explained by random error. It is retained if the test for significance does not fail (H0). A null hypothesis assumes that the numerical quantities being compared are the same. The probability of the observed differences appearing as a result of random error is then calculated from statistical theory. The alternative hypothesis is therefore a statement that the difference between two values is too great to be explained by random error. The alternate hypothesis is accepted if a test for significance shows that the null hypothesis should be rejected (Ha or H1). Typical tests for significance are the F ratio test and the t-test. If we reject the null hypothesis at say, a 95% confidence level, there is a 5% probability that the null hypothesis was incorrectly rejected. An example of hypothesis testing is:

Let μ1 and μ2 be the means of two samples; If one wants to investigate the likelihood that their means are the same, then the null hypothesis is:
H0: μ1 =μ2
and the alternative hypothesis is:
H1: μ1 ≠μ2
but it could also be:
H1: μ1 >μ2
The first example of H1 is said to be two-sided or two-tailed because includes both μ1 >μ2 and μ1 <μ2; The second is said to be one-sided or one-tailed. The number of sides has implications on how to formulate the test (Fraser 2011).

References:

Fraser A.W., (2011), “Statistical Method Validation for Analytical Methods – a practical approach”
Helmestine A.M., (2010) “Scientific Hypothesis, Theory, Law Definitions” http://chemistry.about.com/od/chemistry101/a/lawtheory.htm (accessed 25 May 2011)
Pilgrim G. (2011) “Hypothesis versus Theory” http://www.buzzle.com/articles/hypothesis-vs-theory.html (accessed 25 May 2011)