Level of significance and testing of hypothesis.

The level of significance.

The probability of rejecting null hypothesis H₀ when it is true is called the level of significance. It is the probability of type I error or the size of the critical region. That is the level of significance is the conditional probability that a sample point falls in rejecting region under the condition that the parametric value is a usually specified in the null hypothesis H0. It is the therefore denoted by (α).

Generally, the level of significance employed in a test is 5% and 1%. If it is fixed at 5 %, we are ready to take 5% risk of rejecting the true null hypothesis. IUn other words, if we fix (α) at 5% it implies that we are (1-α)=95% confident that our decision of rejecting H0 is correct. Higher the level of significance (α) higher the probability of type I error and lower the (1-α) level of confidence. So, we fix (α) at 1% we are reducing the (α) from 5% higher level, and we are increasing the 1-α level of confidence or probability of accepting H₀ When it is true.

Procedure for hypothesis testing.

Procedure for hypothesis refers to all those steps that are undertaken for making a choice between the two actions Ie rejection and acceptance of a null hypothesis. The various steps involved in hypothesis testing are stated below.

1. The setting of the hypothesis.
2. Selecting a significance level.
3. Test statistic.
4. Critical value.
5. Decision

1. The setting of the hypothesis.

1. Set up the null hypothesis (H₀).
2. Set up the alternate hypothesis (H₁).

In alternate hypothesis, we have to use either one-tailed (right or left tailed) test or two-tailed test.

2. Selecting a significance level.

The hypothesis is tested on a pre-determined level of significance. Usually, either 5% level or 1% level is adopted for the purpose. The factors that affect the level of significance are.

1. The magnitude of the difference between the sample means.
2. The variability of measurements within samples.
3. Whether the hypothesis is directed or non-directional.

3. Test statistic.

At this step, a test statistic is defined. The value of test statistic is obtained using the sample observations selected by the researcher and the hypothetical parameter values stated under the null hypothesis.

4. Critical value.

Using the distribution of test statistic, the level of significance (), and the type of test (two-tailed right or left tailed), the critical value is obtained.

5. Decision.

Decisions are made about rejecting the null hypothesis comparing the value of test statistic and critical value.

The null hypothesis is rejected when.

1. The value of test statistic < lower critical value.

The value of test statistic>upper critical value.

The value in case of a two –tailed test.

2. Values of test statistic > critical value, in the case of a right-tailed test.
3. Values of test statistic < critical value, in a case of a lest-tailed test.

Otherwise, the null hypothesis can not be rejected due to lack of enough statistical evidence against it.

Main stages of a hypothesis can be summarised as follows.

Generalisation.

Generalisation is the process of drawing a conclusion from the field or from any research work.It is considered as one of the most important parts and more experiment is necessary for generalisation. It can be done by the two steps.

Mainly by the

1. Statistical or Mathematical method.
2. Logical method.

Comparing these two methods of generalisation statical or mathematical method is easier .In this case, this is because in this method different mathematical morals help to draw the conclusion. In the case of the logical methods, there is the absence of the logical morals due to this reason it is difficult than statical method.

[II] Statical method or mathematical methods.

In this method, the drawing inference is mathematical in nature. In a statical method not only the causal connection of the factor is stated but also the degree of connection is given by mathematical relationships.

In this case, the causal connection between X and Y expressed as

The first equation shows that X and Y are linearly connected. The second equation shows that the nature of the relationship is parabolic and the third equation shows that the X and Y are exponentially connected.

[II]The logical method of generalisation.

a. The method of Agreement.

In this method, if a factor is common in all situation to produce certain effect then that common factor can be considered as the cause for the effect.For example.

A+B+C produce X and C+D+E produce Y then C is considered as the cause of the production of Y. Above method is called a positive method. The positive word is used to denote the presence of C. The method may be negative for instance.

If A+B+\(\overline{C}\) produce\(\overline{X}\)and\(\overline{C}\)+D+E produce \(\overline{X}\), and then \(\overline{C}\)produce\(\overline{X}\) .Note C produce none X implying C produce X.

b. Method of difference.

This method is the combination of Positive and Negative methods. In this methods if A+B+C produce X and If A+B+\(\overline{C}\)produce\(\overline{X}\). Then C produce X.

c. Joint variance.

This is a combination of the methods and difference.

Thus, if A+B+C produce X, A+P+Q produce \(\overline{X}\) ; \(\overline{A}\)+B+C produce \(\overline{X}\) then A and X are said to be causally connected.

d. The method of Residues.

In this method, if a phenomenon occurs under certain circumstance and it is known on the basis of previous knowledge that a part of the phenomenon is causally connected with some of the circumstances then it is assumed that remaining phenomenon is also causally connected.

e. The method of concomitant variation.

This method is also known as quantitative induction. In this method, the positive correlation between two factors is connected as a basis for drawing an inference that they are causally connected.

Reference.

Kerlinger, F.N. Foundation of Behavioural Research. New Delhi: Surjeet Publication, 2000.

Kothari, C.R. Research Methodology. India: Vishwa Prakashan, 1990.

Singh, M.L. and J.M Singh. Understanding Research Methodology. 1998.

Singh, Mrigendra Lal. Understanding Research Methodology. Nepal: National Book centre, 2013.