Editing Final Report/Thesis 2015 (section)

===P-Value Theorem Explanation===
The ''p-value'' is the probability of an effect equal to or greater than the one observed, presuming the null hypothesis of no effect is true. It is a measure of evidence against a null hypothesis <ref>B. David et al., “P Value and the Theory of Hypothesis Testing: An Explanation
for New Researchers,” Clinical Orthopaedics and Related Research®, Vol.468 (3),
pp.885-892 2010.</ref>.

In statistics, the ''p-value'' is used for testing a statistical hypothesis by observing
sample results. ''P-value'' testing is an effective method to presume whether the null
hypothesis of no effect is true. In this project, we will use ''p-values'' to do some
simple tests to determine whether English was the language in the original message
<ref>B. David et al., “P Value and the Theory of Hypothesis Testing: An Explanation
for New Researchers,” Clinical Orthopaedics and Related Research®, Vol.468 (3),
pp.885-892 2010.</ref>.

In this case, we make an assumption that English was not the language in the
original message. Thus we should get a larger ''p-value'' which is higher than 0.05 in
the simple test. This means the observed data point is in the range of “more likely
observation”, mentioned in Figure 1 below. Oppositely, if we get a smaller ''p-value''
which is lower than 0.05 in the simple test, this means the observed data point is in
the range of “very un-likely observations”. This indicates our assumption is wrong
and that English was the language in the original message <ref>G G. L et al., “What is the Value of a p Value?,” The Annals of Thoracic
Surgery, Vol.87(5), pp.1337-1343 2009.</ref>.

[[File: Technical_Background_P-value.png |thumb|700px|centre|'''Fig. 3:''' Example of a ''p-value'' computation <ref>No Author.p-value [online]. Available: http://en.wikipedia.org/wiki/P- value#cite_note-nature506-1</ref>]] 

As the graph in Figure 3 shows, the horizontal coordinate is the set of possible results, and the
vertical coordinate is the probability density. The ''p-value'' is in the right side of
observed data point, which is between the curve and horizontal coordinate <ref>No Author.p-value [online]. Available: http://en.wikipedia.org/wiki/Pvalue#
cite_note-nature506-1.</ref>.