Thursday, October 16, 2008

Basic Statistics: Hypothesis Testing

Hypothesis is a tentative assumption about the population parameter.  Such a tentative statement is called Null hypothesis and the one opposite to such tentative statement is alternative hypothesis. Usually the research hypothesis is expressed as the alternative hypothesis.

Type I and Type II errors: As hypothesis tests are based on sample information there will be the possibility of errors.

Type I error: Rejecting the null hypothesis when it is true
Type II error: Accepting the null when it is not true or false

Level of significance: It is the probability of making a type I error when the null hypothesis is true. The applications of hypothesis testing that only control for the type I error are called as "significance tests".

Most of the hypothesis tests control for the probability of making type I error, they do not control for the probability of making type II error.  Hence, though we decide to accept null, we can't determine how confident we can be with that decision. Because of the uncertainity associated with making a Type II error, it is suggested that the use of the statement "do not reject null" instead of "accept Null".  In effect by not directly accepting null, one can avoid the risk of making Type II error.  

Whenever the probability of making Type II error is not controlled, the optimal conclusions should be 'do not reject the null' or 'reject the null'.

The constructive comments and additions are encouraged!!

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