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The null hypothesis indicates that there is no relationship between two population parameters, that is, between an independent variable and a dependent variable. If the result of the experiment showed a relationship between the two parameters, the result could be due to experimental or sampling error. On the other hand, if the null hypothesis is false, there is a relationship in the phenomenon being measured.
Uses of the null hypothesis
The null hypothesis is useful since it helps to conclude whether or not a relationship exists between two measured phenomena. The null hypothesis can indicate to the user if the results obtained are due to chance or to the manipulation of a phenomenon. The test of a hypothesis allows to reject or accept said hypothesis within a certain level of confidence.
Two approaches can be used for the statistical deduction of a null hypothesis: Ronald Fisher’s test of significance and Jerzy Neyman and Egon Pearson’s hypothesis test . Fisher’s test of significance approach states that a null hypothesis is rejected if the measured data is significantly improbable. That is, the null hypothesis is rejected if it is false. When the null hypothesis is false, it is not only rejected, but an alternative hypothesis is substituted.
If the observed result is consistent with the position held by the null hypothesis, the hypothesis is accepted. On the other hand, the Neyman and Pearson hypothesis test is compared with an alternative hypothesis to draw a conclusion about the observed data. The two hypotheses are differentiated based on the observed samples.
How the null hypothesis works
A null hypothesis is a theory based on insufficient evidence, and that requires further testing to prove whether the observed data is true or false. For example, a null hypothesis statement could be “plant growth rate is not affected by sunlight.” It can be checked by measuring the growth of plants in the presence of sunlight and comparing it with the growth of plants in the absence of sunlight.
The rejection of the null hypothesis opens the way to new experiments to verify the existence of a relationship between the two variables. The rejection of a null hypothesis does not necessarily mean that the experiment did not work, but rather it opens the door to new experiments.
To differentiate the null hypothesis from other forms of hypotheses, the null hypothesis is written H0, while the alternative hypothesis is written HA or H1. Significance tests are used to determine the truth of a null hypothesis and to establish whether or not the observed data is due to chance or manipulation of said data.
For example, the researchers test the hypothesis by examining a random sample of plants grown with or without sunlight. If the result shows a statistically significant change from the observed data, the null hypothesis is rejected.
Example of a null hypothesis
It is assumed that the annual return on the bonds of the company No Profit Limited is 7.5%. To test whether the hypothesis is true or false, we assume that the null hypothesis is “the average annual return on the Null Profit Limited bonds is not 7.5%.” To test the hypothesis, we first accept the null hypothesis.
Any information that is contrary to the stated null hypothesis is considered the alternative hypothesis for the purposes of hypothesis testing. In this case, the alternative hypothesis is “the average annual return of Profit Null Limited is 7.5%”.
We sample annual bond yields for the past five years to calculate the sample mean for the previous five years. The result is then compared to the assumed average annual return of 7.5% to test the null hypothesis.
It turns out that, surprisingly, the average annual return for the five-year period is 7.5%; being so, the null hypothesis is rejected. Therefore, the alternative hypothesis is accepted.
What is an alternative hypothesis?
An alternative hypothesis is the opposite of a null hypothesis. An alternative hypothesis and a null hypothesis are mutually exclusive, which means that only one of the two hypotheses can be true.
There is statistical significance between the two variables. That is, if the samples used to test the null hypothesis give false results, it means that the alternative hypothesis is true and that there is statistical significance between the two variables.
Objective of the hypothesis test
Hypothesis testing is a statistical process that consists of testing a hypothesis about a phenomenon or a population parameter. It is an essential part of the scientific method, which is a systematic approach to evaluating theories through observations and determining the probability that a statement is true or false.
A good theory allows accurate predictions to be made. For an analyst making predictions, hypothesis testing is a rigorous means of supporting the prediction with statistical analysis. Hypothesis testing also identifies sufficient statistical evidence to support a given hypothesis about the population parameter.
Sources
- Bookdowm. (nd). The Neyman-Pearson hypothesis test theory .
- Giron, J. (1998). RA Fisher : His contribution to Statistical Science.
- Leenen, I. (2012). The test of the null hypothesis and its alternatives . Department of Educational Evaluation, Faculty of Medicine, National Autonomous University of Mexico.
- Rodriguez, E. (2005). Statistics and psychology : historical analysis of statistical inference.
- https://support.minitab.com/es-mx/minitab/18/help-and-how-to/statistics/basic-statistics/supporting-topics/basics/null-and-alternative-hypotheses/
