Null vs. Alternative Hypothesis

The null and alternative hypothesis represents two opposing suppositions or statements used in statistical tests. The key difference is that the null hypothesis disapproves of the phenomenon or event put forth by the alternative hypothesis or research hypothesis. So, the statement defining the null hypothesis is tested in a statistical test like a t-test and linear regression. The statement explaining the alternative hypothesis is tested against the null hypothesis. Proving the null hypothesis points to the rejection of the alternative hypothesis.

• In null vs. alternative hypotheses, the two hypotheses exemplify the opposing statements in a statistical test. The null hypothesis is a "no effect" statement, and the alternative hypothesis is a statement defining the "effect."
• Null vs. alternative hypothesis symbols: Null hypothesis is denoted by the symbol H₀, and H₁ or H_a denotes the alternative hypothesis. 
• The alternative hypothesis can be one-sided (directional) or two-sided (non-directional). The main types of null hypotheses are simple, composite, exact, and inexact hypotheses.
• The null hypothesis is favored if the p-value is higher than the statistical significance level. In contrast, the alternate hypothesis is favored if the p-value is lower than the statistical significance level.

The null hypothesis is denoted by the symbol H₀. It implies that there is no effect on the population and that is dependent variable is not influenced by the independent variable in the study. According to the null hypothesis, the result or effect is caused by chance and establishes no relation between the two variables. The null hypothesis is generally based on a previous analysis or specialized knowledge. The main types of null hypotheses are simple, composite, exact, and inexact hypotheses.

To justify the research hypothesis or the argument coined by the researcher, the null hypothesis constructed against the alternative hypothesis must be proved wrong. It can only turn out in two ways, either getting rejected or accepted, depending upon the experimental data and nature of the scenario taken for observation. The null hypothesis is accepted if the statistical test provides no satisfactory evidence proving the anticipated effect on the population. Furthermore, incorrectly rejecting the null hypothesis points to type I error  (false positive conclusion), and incorrectly failing to reject the null hypothesis results in type II error (false negative conclusion).

The symbol H₁ or H_a denotes the alternative hypothesis. It can be based on limited evidence or belief. It implies the effect on the population; the independent variable influences the dependent variable in the study. The alternative hypothesis can be one-sided (directional) or two (non-directional). 

The alternative hypothesis defines a statistically substantial relationship between the two variables. It can be based on limited evidence or belief. From the researcher's perspective, this statement stands correct and thus works to reject the contrasting null hypothesis to replace it with the new or improved theory. The researcher predicts the distinguishing factors between the two variables, ensuring that the data observed is not due to chance.

Null vs. alternative hypothesis example statistics:

• Research question: Does following a healthy diet ensure weight loss?
• Null hypothesis: Healthy diet has no effect on weight loss
• Alternative hypothesis: Healthy diet has an effect on weight loss
• Statistical test output: Consider applying linear regression. If the beta value is equal to zero, then there exists no relationship, and if the beta value is not equal to zero implies the relationship between variables.

• Both null and alternative hypotheses are statements used in statistical hypothesis testing.
• Both can be applied to a single scenario; however, the result and agendas are poles apart.
• Both the hypotheses used the same route to a conclusion, following the same steps: defining the hypothesis, setting up the criteria, calculating the statistics, and finally arriving at a decision.

This has been a Guide to What is Null vs. Alternative Hypothesis. We explain the statements, differences, infographics, and examples. You can learn more about them from the following articles –

• Inferential Statistics
• Statistical Analysis
• Econometrics