In this paper, the definition of a statistical hypothesis is discussed, and the considerations which need to be addressed when testing a hypothesis. In particular, the p-value, significance level, and power of a test are reviewed. Finally, the often quoted confidence interval is given a brief introduction.

The extraordinary success of physicists to find simple laws that explain many phenomena is beguiling. With the exception of quantum mechanics, it suggests a deterministic world in which theories are right or wrong, and the world is simple. However, attempts to apply such thinking to other phenomena have not been so successful. Individually and collectively we face many situations dominated by u...

OBJECTIVE — Previous reports have predicted greater risk of type 1 diabetes among people who were heavier as young children. The Accelerator Hypothesis predicts earlier onset in heavier people, without necessarily a change in risk, and views type 1 and type 2 diabetes as the same disorder of insulin resistance, set against different genetic backgrounds. Insulin resistance is a function of fat m...

E-learning has become an efficient and widespread means of education at all levels of human activities. Statistics is no exception. Unfortunately the main focus in statistics teaching is usually paid to the substitution in formulas. Suitable websites can simplify and automate calculations and provide more attention and time to the basic principles of statistics, mathematization of real-life sit...

Consider a decision maker who is responsible to dynamically collect observations so as to enhance his information about an underlying phenomena of interest in a speedy manner while accounting for the penalty of wrong declaration. Due to the sequential nature of the problem, the decision maker relies on his current information state to adaptively select the most “informative” sensing action amon...

The underlying hypothesis of this field is that due to constraints that limit the degrees of freedom of the generative process, data tend to lie near a low dimensional submanifold. This has been empirically observed to be the case, for example, in speech and video data. Although there are many widely used algorithms motivated by this hypothesis, the basic question of testing this hypothesis is ...

It is often the case that we want to infer information using collected data, such as whether two samples can be considered to be from the same population, whether one sample has systematically larger values than another, or whether samples can be considered to be correlated. Such hypotheses may be formally tested using inferential statistics, allowing conclusions to be drawn, allowing the poten...