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# Tow Sided p-value

Tow Sided p-value

In statistics, the two sided p-value is applied in carrying out two-tailed tests. This is a method applied where the critical area of distribution has two sides. The tests investigates whether the sample size is greater or smaller than a certain range of value. This is done by comparing the calculated value and the two-sided p-value. It is applied in Null hypothesis testing and testing for the statistical significance. In case the sample being tested is in the critical/shaded  areas (rejection region), the null hypothesis is rejected and the alternative hypothesis is accepted. The two sided p-value derives its name from the testing the area under the two tails of a normal distribution. The graph below shows how the it looks like

Two sided p-value and significance level

The p-value dependents on the selected significance level. For instance, if the data uses a significance level of 0.05, the two tailed test allots half of the significance level to the left and the other half to the right. This means that each tail will have 0.025 on each side of the distribution of test statistic. Regardless of the direction indicated in the hypothesis testing, the two sided tests the possibility of relationship on both sides of direction. For instance, a researcher may be investigating whether the sample mean given is greater than x using a t-test. In this case, the two-tailed test would be whether the mean is greater of less than x.  the test statistic would be top 2.5% and bottom 2.5% of its probability distribution.

How two-sided p-value works

The p-value, also referred critical p-value is used in the hypothesis testing, to determine whether the claim is true or not. To test the claim, the z-value is calculated using the given statistics and the corresponding p-value obtained from the tables. the calculated z-value is then compared with the tabulated p-value to determine whether to reject of accept the null hypothesis. This test is programmed to show whether the mean of the given sample is greater or less than the population mean.

The two test p-value is designed in manner that it represents the both sides of the data ranges according to the involved probability distribution. The probability distribution is considered as the likelihood of occurrence of a particular outcome on the basis of the predetermined standards.  If there is data which is above the upper limit, or below the set lower limit is considered outside the acceptance range, also referred to as the rejection region. Therefore, if the calculated value falls in the rejection region, the cull hypothesis is rejected and vice versa.