P-value approach.

P-value approach.

p-value approach is one of the methods for testing of statistical hypothesis in which the decision is made by comparing the computed value and the table value of the applied test statistics for the given fixed α, AP- values conveys much information about the strength of evidence against H_o and allows on individual decision maker to draw a conclusion at any specified level α.

P-value needs no critical or table value. It can be tested simply comparing P- value with α level of significance . IT is the probability value or tail area under the curve of the test statistic used in the hypothesis to be obtained.

The p-value is the smallest level of significance at which H_o would be rejected when a specified test procedure is used on a given data set.

Hypothesis testing is done by using P- value approach as follows:

First H_o is set up

Then H₁ is chosen at α level of significance and test statistics are computed same as in rejected region method. The p-value is specified from the table of test statistics follow-

Let Z_c be the computed value of test statistic and the distribution of test statistical is N(0,1) then

For two-tailed test

$$P-value =2_p(Z>|Z_c|)$$

For right-tailed test

$$p-value =p\,(Z>Z_c)$$

for left-tailed test

$$p-value =P(Z<Z_c)$$

$$where Z- N(0,1)$$

Above probabilities can be obtained using a normal table.

The decision is made by comparing the p-value with the pre-fixed value ofα.

$$If\, p-value ≤ \,α, H_0\, is \,rejected \,at \,α\,level\, of \,significance.$$

$$If \,p-value > α\, , then\, H_0 \,is \,accepted.$$

For one-tailed test

$$If\, p-value \,i.e P_0\, ≤\,α\,H_0\, is\, rejected \,otherwise\, H_0 \,is\, accepted.$$

For two-tailed tests

$$If p-value\, i.e 2p_0≤\,α\, then H_0\, is\, rejected\, and \,otherwise\, H_0\, is \,accepted.$$

Analysis.

The tabulated data is now ready for analysis. There are different stages of analysis.

1. In the first stage, observed data are presented in terms of ratios, rates or proportions called indicators. Analysis of data by indicators is called descriptive analysis.
2. In the second stage, statistical descriptions of the frequency distribution of the quantitative variables in terms of their absolute values or positional values are described. The descriptions based on absolute values are mean, variance, skewness and kurtosis and the statistical descriptions based on positional values are median and different partition values. The analysis at this level is called statistical description.
3. At the third step, the hypotheses regarding the associations of different levels of the factors under study are tested. The analysis at this stage is called analytic study.

Statistical Descriptions.

Though the statistical description of the data is not possible in most of the cases related to attributes, statistical descriptions of the data related to the variables need to be computed according to the depth of the analysis desired. Statistical descriptions of data related to the variable are expressed either in terms of the positional values or in terms of absolute values.

If the interest of study is to find the positions of the observations in the order of data arranged (ranking of data), first of all, the partition values such as Quartiles, Deciles and percentiles are computed and then their derivations such as Quartile deviation are computed. Partitions valued are the values of the variable which divide the total number of observations into four equal parts. If the number of observations is divided into four equal parts, the positional value is called Quartiles, if into ten they are called Deciles and if 100 parts they are called as a percentile.

Quartiles are denoted by Q_i, i=1,2,3; Deciles by D_j, j=1,2,....9 and percentiles by p_k, k=1,2,....99. The middle of these partition values is the Median

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.