Explain the difference between a one- and a two-tailed test of significance

October 29, 2019

Explain the difference between a one- and a two-tailed test of significance
A statistical hypothesis test in which the alternative hypothesis has only one end is known as the one-tailed test. A significance test in which the alternative hypothesis has two ends is called a two-tailed test. If there is a relationship between variables in a single direction.
When is a statistic more than just a statistic? When it is significant, of course! This lesson explains two-tailed tests, one kind of statistical significance test. See the formula to calculate the test statistic, an example, and how to interpret the result.
Difference Between One-tailed and Two-tailed Test

The two ways of carrying out statistical significance test of a characteristic, drawn from the population, concerning the test statistic, are a one-tailed test and two-tailed test. The one-tailed test refers to a test of the null hypothesis, in which the alternative hypothesis is articulated directionally. Here, the critical region lies only on one tail. However, if the alternative hypothesis is not exhibited directionally, then it is known as the two-tailed test of the null hypothesis., wherein the critical region is one both the tails.
Significance Tests
Tests of significance are statistical analyses designed to evaluate the probability of finding a particular value of a random variable as compared to all possible values for that same variable. Why would we want to do that? Let's go over an example: The residents of River Creek want to evaluate changes in the pH level of the water that runs behind their homes. For the last 32 years, the normal pH value for the creek has been 5.8, but since their small town has undergone so much new construction, has this affected the pH levels in their River Creek's water supply? The high school chemistry teacher decides to find out.

The mean is located at the highest point because this value and values closest to the mean are the most likely observations. As values spread out incrementally from the mean, the probability of obtaining those values decreases. The p-value is the probability associated with each observation such that the probability of obtaining a value equal to the mean is large, and the probability of obtaining a value much higher or much lower than the mean is small. The science teacher evaluates the pH level of the 50 samples and plots the values for each observation on a graph.
This graph is a visual representation of the frequencies each value is observed. The graph shows the data is normally distributed with a mean of 6.3 and a standard deviation of 0.04. He has met the third condition of significance testing and is ready to formulate the null and alternative hypotheses, which determine if one- or two-tailed significance tests are used. To test the hypothesis, test statistics is required, which follows a known distribution. 
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