# What is an Alternative Hypothesis? Definition, Types, and Examples

The alternative hypothesis is a way to propose a contrasting view on a proposed theory by a researcher. It tries to prove the original statement provided by the null statement false.

Let us discuss what an alternative hypothesis is, how it is different from the null hypothesis, its types, and some examples in our article.

## What is an Alternative Hypothesis?

An alternative hypothesis is a contradictory theory to that taken by a Null Hypothesis about a specified research parameter.

As the name suggests, the alternative hypothesis proposes an alternative theory and rejects the null hypothesis statement for a research parameter.

The value of research can be greater than, not equal to, or less than the value of a null hypothesis result but cannot be equal to that.

The null hypothesis proposes that there is no relation between the independent and dependent variables in a population parameter. If the null hypothesis is true, then these variables do not change mutually.

If the null hypothesis is false, then there exists a relationship between the two variables. This scenario further leads to the alternative hypothesis that defines the value of the result as greater than, less than, or simply not equal to the value received in the null hypothesis.

## Symbols

• The null hypothesis is denoted by Ho.
• The Alternative hypothesis is denoted by Ha or H1.
• The sample population is denoted by (π).
• The left-tailed, right-tailed, and two-tailed hypotheses can then be denoted by a combination of Ho, Ha, and (π).

## Understanding Alternative Hypothesis

The base of the alternative hypothesis comes from two approaches undertaken to verify the statements in a null hypothesis.

Fisher’s Significance Testing method is one way to determine whether the statement in the Null Hypothesis is false. If the statement is false, it should be rejected and replaced with an alternative statement.

Similarly, hypothesis testing directly compares the observed data in a defined population data set with the Null hypothesis results.

Essentially, both these methods verify the null statements and provide the basis for the formation of an alternative hypothesis if possible.

It should be noted that the rejection of the null hypothesis does not mean the statement is proven false. It only provides an opportunity to test an alternative theory.

Researchers consider only a sample size from the total data population set. Therefore, to completely reject a theory, all results must prove the statement false which can be a lengthy exercise.

## Types of Alternative Hypothesis

There are two main types of alternative hypotheses.

One-Tailed or Directional Hypothesis

In this type of alternative hypothesis, the results are one-tailed or directional. These results can be greater than or less than the values of the null statement.

If the alternative hypothesis results are less than the value of null, then it is called the left-tailed hypothesis. Contrarily, when the value of the results is greater than the null statement, it’s called right-tailed.

Two-Tailed or Non-Directional Hypothesis

This type of alternative theory only states a difference from the null theory. It simply contradicts the original statement in the null hypothesis but does not measure the value.

In other words, the value of the alternative theory can be either less than or greater than the value of the null statement.

## Examples of Alternative Hypothesis

Example 1

Suppose a high school proposes that providing a laptop to all students during classes will improve their grades among other students in the school.

They create a null hypothesis by stating:

“Students with a personal laptop in the classes will score more than 10% on average from those without a laptop in the school”.

The research can validate the hypothesis or reject it by examining the results of the students with laptops.

At the same time, the school can propose an alternative hypothesis stating:

“Providing laptops to students in the classrooms will not improve their grades as compared to other students without laptops”.

This is an example of a non-directional alternative hypothesis that can provide different results in any direction.

Example 2

An investment firm wants to set up an index fund following the S&P500 index. The null hypothesis states an index fund generates a 10% rate of return when followed the same way as S&P500.

An alternative hypothesis states that actively managing the fund and changing it continuously will produce more than a 10% rate of return as compared to S&P500.

Both these hypotheses can prove true or false depending on the data samples, duration of the investment period, and several other factors.

## Null Hypothesis Vs. Alternative Hypothesis – Key Differences

The null and alternative hypotheses are often contradictory in nature. In practice, an alternative hypothesis is created to prove the null theory false.

Here are some key points to remember when discussing both these sets of theories.

Statements

Both hypothesis forms use symbols to denote their respective theories. The null hypothesis uses Ho and the alternative hypothesis uses H1 or Ha.

Both statements can be directional or non-directional. It means both these theories can state a fact with less than or greater than a particular value set as a test benchmark.

Assumptions for Hypothesis

A null hypothesis generally proposes something as a theory. It means it says something is true. For example, a null hypothesis says faster internet speeds increase the number of internet users in a community.

An alternative hypothesis assumes the null statement is wrong. It means it discredits the original statements or tries to prove that statement false.

In this example, an alternative hypothesis will say faster internet does not increase or has no impact on the number of internet users in a community.

Purposes

The basic purpose of types of hypotheses is to present a theory. The way these statements are presented differentiates both types.

A null hypothesis proposes one theory and an alternative hypothesis proposes a contradictory theory to that one.

Hypothesis Tests

Since both these sets of theories can be directional or non-directional, there are different types of tests to confirm their validity.

Researchers can set a parameter in either direction, take a set of data points and run a test to verify either the null or alternative theories.

Result Interpretations (implication)

A rejection of the null hypothesis does not mean the original statement is false. Thus, the proposal of an alternative hypothesis requires further research and proof to reject the null statement completely.

Similarly, the alternative hypothesis can be right or wrong. Further research can propose another point of view and another alternative theory.

Thus, the research continues until a theory becomes a fact or law.