Alternative Hypothesis

Alternative hypothesis defines there is a statistically important relationship between two variables. Whereas null hypothesis states there is no statistical relationship between the two variables. In statistics, we usually come across various kinds of hypotheses. A statistical hypothesis is supposed to be a working statement which is assumed to be logical with given data. It should be noticed that a hypothesis is neither considered true nor false.


The alternative hypothesis is a statement used in statistical inference experiment. It is contradictory to the null hypothesis and denoted by Ha or H1. We can also say that it is simply an alternative to the null. In hypothesis testing, an alternative theory is a statement which a researcher is testing. This statement is true from the researcher’s point of view and ultimately proves to reject the null to replace it with an alternative assumption. In this hypothesis, the difference between two or more variables is predicted by the researchers, such that the pattern of data observed in the test is not due to chance.


To check the water quality of a river for one year, the researchers are doing the observation. As per the null hypothesis, there is no change in water quality in the first half of the year as compared to the second half. But in the alternative hypothesis, the quality of water is poor in the second half when observed.

Difference Between Null and Alternative Hypothesis

Null Hypothesis

Alternative Hypothesis

It denotes there is no relationship between two measured phenomena.

It’s a hypothesis that a random cause may influence the observed data or sample.

It is represented by H0

It is represented by Ha or H1

Example: Rohan will win at least Rs.100000 in lucky draw.

Example: Rohan will win less than Rs.100000 in lucky draw.


Basically, there are three types of the alternative hypothesis, they are;

Left-Tailed: Here, it is expected that the sample proportion (π) is less than a specified value which is denoted by π0, such that;

H1 : π < π0

Right-Tailed: It represents that the sample proportion (π) is greater than some value, denoted by π0.

H1 : π > π0

Two-Tailed: According to this hypothesis, the sample proportion (denoted by π) is not equal to a specific value which is represented by π0.

H1 : π ≠ π0

Note: The null hypothesis for all the three alternative hypotheses, would be H1 : π = π0.