Introduction to hypothesis testing

TESTING OF THE HYPOTHESES

Life is a matter of choice as they say. There are many important decisions we have to make involve, a choices with lot of alternatives. Like the success rate in taking a degree, the chances of having same instructor for the semester, or even deciding to take a leave or not since some accreditation team would come to your workplace. The assumption such as these is referred as hypotheses

Statistical Hypothesis. Any assumptions or assertion made on distribution of a population which either true or false is called statistical hypothesis.

Hypothesis Testing. A statistical procedure in determining which hypothesis is more acceptable as true or which hypothesis is more likely to be false is known as hypothesis testing.

Five Basic Steps in Hypotesis Testing.

In hypothesis testing the following steps are suggested to be followed.

1.    Formulation of the null and alternative hypothesis. A null hypothesis (Ho) is a statement being tested. it is an assumed value as the true value of the parameter being tested and hoped to be rejected. A null hypothesis is usually stated with no difference: Example Ho Mean A =Mean B. If in case the null hypothesis is rejected, then an alternative is to be accepted. An alternative hypothesis is a set of possible values about the population parameter. There are three ways of stating the alternative hypothesis, That is, 

a.    Ha: ῦ≠ῦ

b.    Ha: ῦ >ῦ

c.    Ha: ῦ < ῦ

It is safer to state the first alternative hypothesis if the researcher has no idea about the true difference of the population parameters. However, If there are grounds to believe that the difference has definite direction.

One tailed test. A one –tailed test is a test which locates only one tail of the distribution as the rejection region, either to the left tail (Ha: ῦ < ῦ) or to the right tail (Ha: ῦ >ῦ) of the distribution of the test statistics with an associated area of the critical region.

2.    Choosing the statistical test and determining the sampling distribution. The selection of the statistical test depends on the manner in which the sample was drawn from the population. The nature of the population and the level of measurement used in the collection of the data. Once the test statistics is chosen, then the sampling distribution is determined so the probability statements about the occurrence or non-occurrence of the values can be obtained.

3.    Determination of the rejection region or critical region. The rejection region is the area in the sampling distribution of the test statistics which is usually located on the extreme tail(s) of the distribution where rare observations are expected to occur. The rejection region has an area equivalent to ∞, called the level of significance.

The level of significance is the probability of rejecting the null hypothesis given it is true. It is the percent risk of making a wrong decision. Setting up the level of significance means defining which is possible values that could occur under the null hypothesis which would be considered probable or improbable of occurring. Improbable values consist of those possible values which have negligible or zero probability of occurring when the hypothesis is true. Thus if one sets the level of significance to be .01, this means that the probability of getting an improbable value is to .01. Or there is one less chance in 100 that the difference could result when there is no difference in the population values.

The acceptance region is the region in the distribution of the test statistics where the true parameter lies. It is usually the middle area (for the two tailed test) in the distribution with an associated probability of 1-∞, which is also known as the level of confidence. The point that divides the rejection region and the acceptance region is called the critical point. A critical point is a value obtained in the sampling distribution of the test statistics at certain level of significance and degrees of freedom.

4.    Data generation and computation. At this stage it is assumed that the critical region and test statistics are completely determined. In the computation of the data, no alteration or data manipulation should be made to ensure and preserve the objectivity of the statistical tests of the hypotheses.

5.    Decision and conclusion. Using the results of the test, the researcher is now in a position to reject or to accept the null hypothesis. If the computed lies within the rejection area, then the null hypothesis is rejected. Otherwise accept. Then, conclusion may now be drawn the original problem.