Null And Alternative Hypothesis

In hypothesis testing there are two defining statements premised on the binomial concept.

One is the null hypothesis, which is that value considered correct within the given level of

significance. The other is the alternative hypothesis, which is that the hypothesized value

is not correct at the given level of significance. The alternative hypothesis as a value is

also known as the research hypothesis since it is a value that has been obtained from a

sampling experiment. For example, the hypothesis is that the average age of the population

in a certain country is 35. This value is the hypothesis. The alternative to the hypothesis

is that the average age of the population is not 35 but is some other value.

In hypothesis testing there are three possibilities. The first is that there is evidence

that the value is significantly different from the hypothesized value. The second is that

there is evidence that the value is significantly greater than the hypothesized value. The

third is that there is evidence that the value is significantly less than the hypothesized

value. Note, that in these sentences we say there is evidence because as always in

statistics there is no guarantee of the result but we are basing our analysis of the

population based only on sampling and of course our sample experiment may not yield the

correct result. These three possibilities lead to using a two-tail hypothesis test, a

right-tail hypothesis test, and a left-tail hypothesis test as explained in the next

section.

Power of a test

In any analytical work we would like the probability of making an error to be small. Thus,

in hypothesis testing we would like the probability of making a Type I error, α, or the

probability of making a Type II error β to be small. Thus, if a hypothesis is false then we

would like the hypothesis test to reject this conclusion every time. However, hypothesis

tests are not perfect and when a null hypothesis is false, a test may not reject it and

consequently a Type II error, β, is made or that is accepting a hypothesis when it is false.

When the null hypothesis is false this implies that the true population value, does not

equal the hypothesized population value but instead equals some other value. For each

possible value for which the alternative hypothesis is true, or the hypothesis is false,

there is a different probability, β of accepting the null hypothesis when it is false. We

would like this value of β to be as small as possible. Alternatively, we would like (1 - β)

the probability of rejecting a hypothesis when it is false, to be as large as possible.

Rejecting a null hypothesis when it is false is exactly what a good hypothesis test ought to

do.
A high value of (1 - β) approaching 1.0 means that the test is working well. Alternatively,

a low value of (1 - β) approaching zero means that the test is not working well and the test

is not rejecting the hypothesis when it is false. The value of (1 - β), the measure of how

well the test is doing, is called the power of the test.

ASHIF KHAN
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