When carrying out an experiment, researchers develop a hypothesis to test. Often, they formulate an first or null hypothesis, along with a secondary hypothesis known as the alternative hypothesis. Understanding alternative hypotheses, including their significance, can be beneficial if you conduct research.

This article explains what an alternative hypothesis is, how it differs from a null hypothesis, and provides several examples for better understanding.

In statistical hypothesis testing, the alternative hypothesis is a crucial proposition. The objective of the hypothesis test is to show that, under the given conditions, there is enough evidence to support the credibility of the alternative hypothesis over the default assumption made by the null hypothesis.

Both hypotheses serve the same purpose of providing the researcher with a basic guideline. The researcher uses the statements from each hypothesis to direct their research. In statistics, the alternative hypothesis is often denoted as Ha or H1.

### What is a Hypothesis?

A hypothesis is a statement that describes a relationship between two or more variables. It serves as a working statement or theory, formulated on insufficient evidence, that researchers aim to test.

When conducting experiments, researchers often propose testable claims based on the relationships between variables. These claims seek to answer questions like “What causes what?” and “To what extent?” The validity of a hypothesis can be determined to be true or false based on complete evidence.

Among various types of hypotheses, the null and alternative hypotheses are commonly discussed. The null hypothesis, denoted as Ho, assumes that there is no relationship between the variables, and it is considered true until proven otherwise. Conversely, the alternative hypothesis, denoted as H1, suggests a relationship between the variables and provides evidence to reject the null hypothesis.

**Example of a Hypothesis:**

The mean age of all college students is 20.4 years. (simple hypothesis).

### Alternative Hypothesis

An alternative hypothesis in statistics is a proposed statement or argument in a hypothesis test that suggests a statistical relationship between variables. It usually aligns with the research hypothesis and is tested against the null hypothesis.

The alternative hypothesis is one of the two mutually exclusive statements in statistical hypothesis testing. It opposes the null hypothesis. In simple terms, if there is sufficient evidence to reject the null hypothesis, the alternative hypothesis is accepted as true.

In research, the alternative hypothesis indicates a connection between the dependent and independent variables under study. Conversely, the null hypothesis asserts that no such connection exists. An experimental hypothesis predicts changes in the dependent variable when the independent variable is altered. During hypothesis testing, either the null or the alternative hypothesis is accepted. If the alternative hypothesis is proved, the null hypothesis is rejected.

The concept of the alternative hypothesis is crucial in modern statistical hypothesis testing. Statisticians Jerzy Neyman and Egon Pearson developed this idea, which is employed in the Neyman-Pearson lemma technique to ensure that the hypothesis test has the greatest statistical power. The main types of alternative hypotheses include point, one-tailed directional, two-tailed directional, and non-directional.

Correctly forming an alternative hypothesis is essential in research and is widely applied across various fields such as statistics, medicine, psychology, science, and mathematics. While explanations for benefits are sometimes basic and vague, a well-formulated alternative hypothesis can address key issues and significant matters.

In decision-making under uncertainty, alternative theories or suggestions are often overlooked or given little consideration, depending on how they are presented. Representations that encourage further research, inspire hope, and enthusiasm, or lead to thorough evaluations can result in the acceptance of alternative hypotheses.

### Symbol

The symbols Ha or H1 denote the alternative hypothesis. Here are some representations interpreting different scenarios:

**Right-tailed**: The sample proportion (π) is greater than the specified value (π0): (H1 = π > π0)**Left-tailed**: The sample proportion (π) is less than the specified value (π0): (H1 = π < π0)**Two-tailed**: The sample proportion (π) is not equal to a specific value (π0): (H1 = π ≠ π0)

#### Example

Consider the following research question and hypotheses to understand the concept better:

**Research Question**: Does food C increase the risk of a heart attack?

**Ha**: Consumption of food C increases the risk of a heart attack (Alternative: aligns with the research question or hypothesis)**H0**: Consumption of food C does not increase the risk of a heart attack (Null hypothesis)

Here, Ha and H0 are contradictory statements. The null hypothesis (H0) is initially assumed to be true. If evidence proves the null hypothesis wrong, it is rejected, and the alternative hypothesis (Ha) is accepted.

### Examples of Alternative Hypotheses

Here are examples of alternative hypotheses:

### One-Tailed Example

**Example 1:**

- Research Question: Are candidates with experience likely to get a job?
- Null Hypothesis: Experience does not matter in getting a job.
- Alternative Hypothesis: Candidates with work experience are more likely to receive an interview.

**Example 2:**

- Research Question: Do home games affect a team’s performance?
- Null Hypothesis: Home games do not affect a team’s performance.
- Alternative Hypothesis: Teams with home advantage are more likely to win a match.

### Two-Tailed Example

**Example 1:**

- Research Question: Does sleeping less lead to depression?
- Null Hypothesis: Sleeping less does not have an effect on depression.
- Alternative Hypothesis: Sleeping less has an effect on depression.

**Example 2:**

**Research Question:**Do home games affect a team’s performance?**Null Hypothesis:**Home games do not affect a team’s performance.**Alternative Hypothesis:**Home games have an effect on a team’s performance.

### Types of Alternative Hypotheses

There are several types of alternative hypotheses, each focusing on different aspects of the sampling distribution:

#### 1. **One-Tailed Test (H1)**

In a one-tailed directional test, the alternative hypothesis tests only one direction. For instance, the test can only determine if the differences are greater than or less than zero, but not both simultaneously. If the researcher suspects the difference is less than zero, the test is described as left-tailed. Conversely, if the researcher proposes the difference is greater than zero, the test is described as right-tailed.

This type of hypothesis focuses on only one region of rejection in the sampling distribution, which can be either upper or lower.

**Upper-Tailed Test (H1)**: The population characteristic is greater than the hypothesized value.**Lower-Tailed Test (H1)**: The population characteristic is less than the hypothesized value.

**One-tailed Example**

A company’s executives believe that candidates with at least four years of work experience are more likely to receive an interview. Their null hypothesis is that experience doesn’t impact interview invitations.

Their alternative hypothesis states that candidates without experience receive as many interview invitations as those with four years of experience. This is a one-tailed hypothesis as it predicts a trend in one direction.

#### 2. **Two-Tailed Test (H1)**

In a two-tailed or non-directional test, the alternative hypothesis asserts that its parameters are not equal to the null hypothesis value. This means that in a two-tailed directional test, it is stated that there are differences present that are both greater than and less than the null value. It’s crucial to note that this type of test only indicates the existence of a difference but does not specify the direction of the difference between the null and alternative hypotheses.

This hypothesis is concerned with both regions of rejection in the sampling distribution, testing for deviations in either direction from the hypothesized value.

**Two-tailed Example**

A school researcher claims that an advanced learning program will either significantly increase or decrease students’ test grades compared to the state average. The null hypothesis is that the program has no effect on grades, while the alternative hypothesis suggests a correlation between the program and test scores. This is a two-tailed hypothesis as it explores effects in both directions.

#### 3. **Non-Directional Test (H1)**

This hypothesis is not focused on a specific direction of rejection but rather on the idea that the null hypothesis is not true.

#### 4. **Point Test (H1)**

Point alternative hypotheses occur when the hypothesis test is framed so that the population distribution under the alternative hypothesis is fully defined, with no unknown parameters.

While these hypotheses are typically of no practical interest, they are crucial for theoretical considerations of statistical inference and form the basis of the Neyman–Pearson lemma.

## Developing an Alternative Hypothesis

Developing an alternative hypothesis involves identifying the relationships, effects, or conditions being studied and concluding that there is a different inference from the null hypothesis being considered.

Here’s a step-by-step guide:

- Understand the null hypothesis.
- Consider the alternative hypothesis.
- Choose the type of alternative hypothesis (one-tailed or two-tailed).
- Ensure the alternative hypothesis is true when the null hypothesis is false.

When identifying the information needed for the alternative hypothesis statement, look for phrases like:

- “Is it reasonable to conclude…”
- “Is there enough evidence to substantiate…”
- “Does the evidence suggest…”
- “Has there been a significant…”

Mathematically, alternative hypotheses always include an inequality symbol (usually ≠, but sometimes < or >). Ensure the alternative hypothesis does not include an “=” symbol.

Here are example sentences to help write hypotheses:

- Does the independent variable affect the dependent variable?
**Null Hypothesis (H0):**The independent variable does not affect the dependent variable.**Alternative Hypothesis (Ha):**The independent variable affects the dependent variable.

## Applications of the Alternative Hypothesis

Applications of the Alternative Hypothesis include:

### Rejecting the Null Hypothesis

Researchers conduct additional research to identify flaws in the null hypothesis. Using the alternative hypothesis as a guide, they determine if there is sufficient evidence to reject the null hypothesis.

### Guiding Research

Both the alternative and null hypotheses serve the purpose of providing researchers with a fundamental guideline. Researchers use these statements to guide their research and formulate hypotheses.

### Discovering New Theories

Alternative hypotheses can lead to the discovery of new theories. Researchers can use these alternative hypotheses to challenge and potentially disprove existing theories that lack substantial evidence.