• Math Article ## 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 H a or H 1 . 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

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 π 0 , such that;

H 1 : π < π 0

Right-Tailed: It represents that the sample proportion (π) is greater than some value, denoted by π 0 .

H 1 : π > π 0

Two-Tailed: According to this hypothesis, the sample proportion (denoted by π) is not equal to a specific value which is represented by π 0 .

H 1 : π ≠ π 0

Note: The null hypothesis for all the three alternative hypotheses, would be H 1 : π = π 0 . • Share Share

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## Alternative Hypothesis ## What is Hypothesis?

Hypothesis is a working statement or a theory that is based on insufficient evidence. As a result, it gives way to further testing and experimentations. The outcome of the experiment could either be true or false. The two groups being compared are the independent variable. Before testing a hypothesis, one thing should be clear in our head, “Is there something causing something else?” if you think the answer is yes then think about “what is causing what”. Let's take an example to understand this better. Teachers who are given higher pay are expected to have positive attitudes towards the children while the teachers with lower pay are expected to have poor attitudes towards the children. The first thing that needs to be questioned is “are two or more groups being compared?”. If the answer is a yes then we come to the next question i.e., what groups are being compared? It is between teachers who get higher pay vs teachers who get lower pay. Thus the independent variable is teachers pay while the dependent variable is attitudes towards children.

## Types of Hypothesis

There are two types of statistical hypothesis.

Null Hypothesis: A null hypothesis can be defined as a hypothesis where there is no statistical significance between the two variables in the hypothesis. The researcher tries to disprove the hypothesis. It is denoted by H0.

Alternative Hypothesis: An alternative hypothesis, on the other hand, states that there is statistical significance between two variables. It is denoted by H1 or Ha.

Let’s take another example, you desire to see whether a coin will be fair and balanced. A null hypothesis might support that half of the total flips would result in Heads and half in Tails. The alternative hypothesis, on the other hand, might support that the number of Heads and Tails would be very different. Symbolically, these hypotheses would be expressed as:

H0: p = 0.5

Ha: p <> 0.5

Suppose the coin was flipped 50 times, resulting in 40 Heads and 10 Tails. Given this result, we would be inclined to reject the null hypothesis as the coin was probably not fair and balanced.

The alternative hypothesis can be defined as one in which a difference between two or more variables is anticipated by the researchers. In other words, the observed pattern of the data is not due to a chance occurrence. The concept of the alternative hypothesis is a central part of formal hypothesis testing.

For example, in the development of medicine, a hypothesis can be formulated that a new treatment for a disease is better than the existing one. Therefore, this hypothesis would be called an alternative hypothesis. But if the new treatment fails to be proved correct, it will be called as a null hypothesis. To summarize, a null hypothesis is further examined to see if it's true or false. If the null hypothesis stands rejected, the alternative hypothesis will be accepted.

Basically, the alternative hypothesis and null hypothesis are just opposite to each other. If your null hypothesis is “ there is more water in glass A than B'' then your alternative hypothesis will be “there is more water in glass B than A”. The alternative hypothesis is usually a statement that a researcher thinks is true which ultimately leads you to reject the null hypothesis and replace it with the alternate hypothesis.

## Examples of Alternative Hypothesis

Example 1: Ethanol’s boiling point is 173.1°F.

Solution 1:  There is a theory that states ethanol actually has a different boiling point, of over 174°F. The accepted fact that “ethanol boils at 173.1°F” is the null hypothesis while the theory “ethanol boils at temperatures of 174°F” is the alternate hypothesis.

Example 2: Elementary school students are performing at lower than average levels on standardized tests.

Solution 2: It would be a general thought that low test scores are due to poor teacher performance. However, you have a theory that the reason behind students performing poorly is because their classroom is not as well ventilated as the other classrooms in the school. Therefore, the accepted theory that the “low test scores are due to poor teacher performance” will be the null hypothesis while the theory that states “low test scores are due to inadequate ventilation in the classroom” stands as the alternative hypothesis.

## Difference Between The Null Hypothesis And Alternative Hypothesis

The difference between a null hypothesis and an alternative hypothesis is stated as follows:

The null hypothesis is often denoted as H0 while the alternative hypothesis is normally denoted as H1.

A null hypothesis states the exact opposite of what an investigator predicts or expects whereas an alternative hypothesis makes a statement that suggests or advises a potential result or an outcome that an investigator may expect.

A null hypothesis basically states that there is no exact or actual relationship between the variables. An alternative hypothesis contradicts it. ## FAQs on Alternative Hypothesis

Question 1: How is the Directional Alternative Hypothesis Different From the Non-Directional Alternative Hypothesis?

Solution 1:   Directional alternative hypothesis is a kind that explains the direction of the expected findings. It uniquely examines the relationship among the variables instead of comparing between the groups.

Nondirectional hypothesis, on the other hand, is a kind that has no definite direction of the expected findings.

Question 2: What is the Difference Between a Hypothesis and a Theory?

Solution 2: the difference between a hypothesis and a theory can easily be drawn. A hypothesis is merely a potential explanation or guess. A theory is a tool used to explain an idea or a principle. A hypothesis is subjective while a theory is an objective. Theories originate from hypothesis after it is found to be valid. A hypothesis is then generalized and formulated into principles and equations which then is applied to solve problems. It thus takes the name of theories. The distinction between theories and hypothesis was once (or maybe still) confusing because in everyday language they used to mean the same. It might be easy for a non-scientist to mute the distinction as they are not in the field of developing theories but for scientist who values the distinction between them will never use the word theory to denote their guesswork

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• Null and Alternative Hypotheses | Definitions & Examples ## Null & Alternative Hypotheses | Definitions, Templates & Examples

Published on May 6, 2022 by Shaun Turney . Revised on June 22, 2023.

The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test :

• Null hypothesis ( H 0 ): There’s no effect in the population .
• Alternative hypothesis ( H a or H 1 ) : There’s an effect in the population.

Answering your research question with hypotheses, what is a null hypothesis, what is an alternative hypothesis, similarities and differences between null and alternative hypotheses, how to write null and alternative hypotheses, other interesting articles, frequently asked questions.

The null and alternative hypotheses offer competing answers to your research question . When the research question asks “Does the independent variable affect the dependent variable?”:

• The null hypothesis ( H 0 ) answers “No, there’s no effect in the population.”
• The alternative hypothesis ( H a ) answers “Yes, there is an effect in the population.”

The null and alternative are always claims about the population. That’s because the goal of hypothesis testing is to make inferences about a population based on a sample . Often, we infer whether there’s an effect in the population by looking at differences between groups or relationships between variables in the sample. It’s critical for your research to write strong hypotheses .

You can use a statistical test to decide whether the evidence favors the null or alternative hypothesis. Each type of statistical test comes with a specific way of phrasing the null and alternative hypothesis. However, the hypotheses can also be phrased in a general way that applies to any test.

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The null hypothesis is the claim that there’s no effect in the population.

If the sample provides enough evidence against the claim that there’s no effect in the population ( p ≤ α), then we can reject the null hypothesis . Otherwise, we fail to reject the null hypothesis.

Although “fail to reject” may sound awkward, it’s the only wording that statisticians accept . Be careful not to say you “prove” or “accept” the null hypothesis.

Null hypotheses often include phrases such as “no effect,” “no difference,” or “no relationship.” When written in mathematical terms, they always include an equality (usually =, but sometimes ≥ or ≤).

You can never know with complete certainty whether there is an effect in the population. Some percentage of the time, your inference about the population will be incorrect. When you incorrectly reject the null hypothesis, it’s called a type I error . When you incorrectly fail to reject it, it’s a type II error.

## Examples of null hypotheses

The table below gives examples of research questions and null hypotheses. There’s always more than one way to answer a research question, but these null hypotheses can help you get started.

*Note that some researchers prefer to always write the null hypothesis in terms of “no effect” and “=”. It would be fine to say that daily meditation has no effect on the incidence of depression and p 1 = p 2 .

The alternative hypothesis ( H a ) is the other answer to your research question . It claims that there’s an effect in the population.

Often, your alternative hypothesis is the same as your research hypothesis. In other words, it’s the claim that you expect or hope will be true.

The alternative hypothesis is the complement to the null hypothesis. Null and alternative hypotheses are exhaustive, meaning that together they cover every possible outcome. They are also mutually exclusive, meaning that only one can be true at a time.

Alternative hypotheses often include phrases such as “an effect,” “a difference,” or “a relationship.” When alternative hypotheses are written in mathematical terms, they always include an inequality (usually ≠, but sometimes < or >). As with null hypotheses, there are many acceptable ways to phrase an alternative hypothesis.

## Examples of alternative hypotheses

The table below gives examples of research questions and alternative hypotheses to help you get started with formulating your own.

Null and alternative hypotheses are similar in some ways:

• They’re both answers to the research question.
• They both make claims about the population.
• They’re both evaluated by statistical tests.

However, there are important differences between the two types of hypotheses, summarized in the following table.

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To help you write your hypotheses, you can use the template sentences below. If you know which statistical test you’re going to use, you can use the test-specific template sentences. Otherwise, you can use the general template sentences.

## General template sentences

The only thing you need to know to use these general template sentences are your dependent and independent variables. To write your research question, null hypothesis, and alternative hypothesis, fill in the following sentences with your variables:

Does independent variable affect dependent variable ?

• Null hypothesis ( H 0 ): Independent variable does not affect dependent variable.
• Alternative hypothesis ( H a ): Independent variable affects dependent variable.

## Test-specific template sentences

Once you know the statistical test you’ll be using, you can write your hypotheses in a more precise and mathematical way specific to the test you chose. The table below provides template sentences for common statistical tests.

Note: The template sentences above assume that you’re performing one-tailed tests . One-tailed tests are appropriate for most studies.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Normal distribution
• Descriptive statistics
• Measures of central tendency
• Correlation coefficient

Methodology

• Cluster sampling
• Stratified sampling
• Types of interviews
• Cohort study
• Thematic analysis

Research bias

• Implicit bias
• Cognitive bias
• Survivorship bias
• Availability heuristic
• Nonresponse bias
• Regression to the mean

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

The null hypothesis is often abbreviated as H 0 . When the null hypothesis is written using mathematical symbols, it always includes an equality symbol (usually =, but sometimes ≥ or ≤).

The alternative hypothesis is often abbreviated as H a or H 1 . When the alternative hypothesis is written using mathematical symbols, it always includes an inequality symbol (usually ≠, but sometimes < or >).

A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation (“ x affects y because …”).

A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses . In a well-designed study , the statistical hypotheses correspond logically to the research hypothesis.

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