Hypotesis Test

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Hypothesis Test

Setting up and testing hypotheses is an essential part of statisticalinference. In order to formulate such a test, usually some theory has beenput forward, either because it is believed to be true or because it is to be

used as a basis for argument, but has not been proved, for example,claiming that a new drug is better than the current drug for treatment ofthe same symptoms.

In each problem considered, the question of interest is simplified into twocompeting claims / hypotheses between which we have a choice; the nullhypothesis, denoted H0, against the alternative hypothesis, denoted H1.These two competing claims / hypotheses are not however treated on anequal basis: special consideration is given to the null hypothesis.

We have two common situations:

1. The experiment has been carried out in an attempt to disprove orreject a particular hypothesis, the null hypothesis, thus we give thatone priority so it cannot be rejected unless the evidence against it issufficiently strong. For example,H0: there is no difference in taste between coke and diet cokeagainstH1: there is a difference.

2. If one of the two hypotheses is 'simpler' we give it priority so that amore 'complicated' theory is not adopted unless there is sufficientevidence against the simpler one. For example, it is 'simpler' toclaim that there is no difference in flavour between coke and dietcoke than it is to say that there is a difference.

The hypotheses are often statements about population parameters likeexpected value and variance; for example H0might be that the expected

value of the height of ten year old boys in the Scottish population is notdifferent from that of ten year old girls. A hypothesis might also be astatement about the distributional form of a characteristic of interest, forexample that the height of ten year old boys is normally distributed withinthe Scottish population.


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Hypotesis Test

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