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• Null and Alternative Hypotheses | Definitions & Examples

Null and Alternative Hypotheses | Definitions & Examples

Published on 5 October 2022 by Shaun Turney . Revised on 6 December 2022.

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 ): There’s an effect in the population.

The effect is usually the effect of the independent variable on the dependent variable .

Table of contents

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

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.” On the other hand, 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.

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.

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 ≤).

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.

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.

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

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.

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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Module 9: Hypothesis Testing With One Sample

Null and alternative hypotheses, learning outcomes.

• Describe hypothesis testing in general and in practice

The actual test begins by considering two  hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.

H 0 : The null hypothesis: It is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt.

H a : The alternative hypothesis : It is a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0 .

Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.

After you have determined which hypothesis the sample supports, you make adecision. There are two options for a  decision . They are “reject H 0 ” if the sample information favors the alternative hypothesis or “do not reject H 0 ” or “decline to reject H 0 ” if the sample information is insufficient to reject the null hypothesis.

Mathematical Symbols Used in  H 0 and H a :

H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers (including one of the co-authors in research work) use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.

H 0 : No more than 30% of the registered voters in Santa Clara County voted in the primary election. p ≤ 30

H a : More than 30% of the registered voters in Santa Clara County voted in the primary election. p > 30

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses.

H 0 : The drug reduces cholesterol by 25%. p = 0.25

H a : The drug does not reduce cholesterol by 25%. p ≠ 0.25

We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are:

H 0 : μ = 2.0

H a : μ ≠ 2.0

We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H 0 : μ __ 66 H a : μ __ 66

• H 0 : μ = 66
• H a : μ ≠ 66

We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:

H 0 : μ ≥ 5

H a : μ < 5

We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H 0 : μ __ 45 H a : μ __ 45

• H 0 : μ ≥ 45
• H a : μ < 45

In an issue of U.S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%. State the null and alternative hypotheses.

H 0 : p ≤ 0.066

H a : p > 0.066

On a state driver’s test, about 40% pass the test on the first try. We want to test if more than 40% pass on the first try. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses. H 0 : p __ 0.40 H a : p __ 0.40

• H 0 : p = 0.40
• H a : p > 0.40

Concept Review

In a  hypothesis test , sample data is evaluated in order to arrive at a decision about some type of claim. If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we: Evaluate the null hypothesis , typically denoted with H 0 . The null is not rejected unless the hypothesis test shows otherwise. The null statement must always contain some form of equality (=, ≤ or ≥) Always write the alternative hypothesis , typically denoted with H a or H 1 , using less than, greater than, or not equals symbols, i.e., (≠, >, or <). If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis. Never state that a claim is proven true or false. Keep in mind the underlying fact that hypothesis testing is based on probability laws; therefore, we can talk only in terms of non-absolute certainties.

Formula Review

H 0 and H a are contradictory.

• OpenStax, Statistics, Null and Alternative Hypotheses. Provided by : OpenStax. Located at : http://cnx.org/contents/[email protected]:58/Introductory_Statistics . License : CC BY: Attribution
• Introductory Statistics . Authored by : Barbara Illowski, Susan Dean. Provided by : Open Stax. Located at : http://cnx.org/contents/[email protected] . License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected]
• Simple hypothesis testing | Probability and Statistics | Khan Academy. Authored by : Khan Academy. Located at : https://youtu.be/5D1gV37bKXY . License : All Rights Reserved . License Terms : Standard YouTube License

Microbe Notes

Null hypothesis and alternative hypothesis with 9 differences

Table of Contents

Interesting Science Videos

Null hypothesis definition

The null hypothesis is a general statement that states that there is no relationship between two phenomenons under consideration or that there is no association between two groups.

• A hypothesis, in general, is an assumption that is yet to be proved with sufficient pieces of evidence. A null hypothesis thus is the hypothesis a researcher is trying to disprove.
• A null hypothesis is a hypothesis capable of being objectively verified, tested, and even rejected.
• If a study is to compare method A with method B about their relationship, and if the study is preceded on the assumption that both methods are equally good, then this assumption is termed as the null hypothesis.
• The null hypothesis should always be a specific hypothesis, i.e., it should not state about or approximately a certain value.

Null hypothesis symbol

• The symbol for the null hypothesis is H 0, and it is read as H-null, H-zero, or H-naught.
• The null hypothesis is usually associated with just ‘equals to’ sign as a null hypothesis can either be accepted or rejected.

Null hypothesis purpose

• The main purpose of a null hypothesis is to verify/ disprove the proposed statistical assumptions.
• Some scientific null hypothesis help to advance a theory.
• The null hypothesis is also used to verify the consistent results of multiple experiments. For e.g., the null hypothesis stating that there is no relation between some medication and age of the patients supports the general effectiveness conclusion, and allows recommendations.

Null hypothesis principle

• The principle of the null hypothesis is collecting the data and determining the chances of the collected data in the study of a random sample, proving that the null hypothesis is true.
• In situations or studies where the collected data doesn’t complete the expectation of the null hypothesis, it is concluded that the data doesn’t provide sufficient or reliable pieces of evidence to support the null hypothesis and thus, it is rejected.
• The data collected is tested through some statistical tool which is designed to measure the extent of departure of the date from the null hypothesis.
• The procedure decides whether the observed departure obtained from the statistical tool is larger than a defined value so that the probability of occurrence of a high departure value is very small under the null hypothesis.
• However, some data might not contradict the null hypothesis which explains that only a weak conclusion can be made and that the data doesn’t provide strong pieces of evidence against the null hypothesis and the null hypothesis might or might not be true.
• Under some other conditions, if the data collected is sufficient and is capable of providing enough evidence, the null hypothesis can be considered valid, indicating no relationship between the phenomena.

When to reject null hypothesis?

• When the p-value of the data is less than the significant level of the test, the null hypothesis is rejected, indicating the test results are significant.
• However, if the p-value is higher than the significant value, the null hypothesis is not rejected, and the results are considered not significant.
• The level of significance is an important concept while hypothesis testing as it determines the percentage risk of rejecting the null hypothesis when H 0 might happen to be true.
• In other words, if we take the level of significance at 5%, it means that the researcher is willing to take as much as a 5 percent risk of rejecting the null hypothesis when it (H 0 ) happens to be true.
• The null hypothesis cannot be accepted because the lack of evidence only means that the relationship is not proven. It doesn’t prove that something doesn’t exist, but it just means that there are not enough shreds of evidence and the study might have missed it.

Null hypothesis examples

The following are some examples of null hypothesis:

• If the hypothesis is that “the consumption of a particular medicine reduces the chances of heart arrest”, the null hypothesis will be “the consumption of the medicine doesn’t reduce the chances of heart arrest.”
• If the hypothesis is that, “If random test scores are collected from men and women, does the score of one group differ from the other?” a possible null hypothesis will be that the mean test score of men is the same as that of the women.

H 0 : µ 1 = µ 2

H 0 = null hypothesis µ 1 = mean score of men µ 2 = mean score of women

Alternative hypothesis definition

An alternative hypothesis is a statement that describes that there is a relationship between two selected variables in a study.

• An alternative hypothesis is usually used to state that a new theory is preferable to the old one (null hypothesis).
• This hypothesis can be simply termed as an alternative to the null hypothesis.
• The alternative hypothesis is the hypothesis that is to be proved that indicates that the results of a study are significant and that the sample observation is not results just from chance but from some non-random cause.
• If a study is to compare method A with method B about their relationship and we assume that the method A is superior or the method B is inferior, then such a statement is termed as an alternative hypothesis.
• Alternative hypotheses should be clearly stated, considering the nature of the research problem.

Alternative hypothesis symbol

• The symbol of the alternative hypothesis is either H 1 or H a while using less than, greater than or not equal signs.

Alternative hypothesis purpose

• An alternative hypothesis provides the researchers with some specific restatements and clarifications of the research problem.
• An alternative hypothesis provides a direction to the study, which then can be utilized by the researcher to obtain the desired results.
• Since the alternative hypothesis is selected before conducting the study, it allows the test to prove that the study is supported by evidence, separating it from the researchers’ desires and values.
• An alternative hypothesis provides a chance of discovering new theories that can disprove an existing one that might not be supported by evidence.
• The alternative hypothesis is important as they prove that a relationship exists between two variables selected and that the results of the study conducted are relevant and significant.

Alternative hypothesis principle

• The principle behind the alternative hypothesis is similar to that of the null hypothesis.
• The alternative hypothesis is based on the concept that when sufficient evidence is collected from the data of random sample, it provides a basis for proving the assumption made by the researcher regarding the study.
• Like in the null hypothesis, the data collected from a random sample is passed through a statistical tool that measures the extent of departure of the data from the null hypothesis.
• If the departure is small under the selected level of significance, the alternative hypothesis is accepted, and the null hypothesis is rejected.
• If the data collected don’t have chances of being in the study of the random sample and are instead decided by the relationship within the sample of the study, an alternative hypothesis stands true.

Alternative hypothesis examples

The following are some examples of alternative hypothesis:

1. If a researcher is assuming that the bearing capacity of a bridge is more than 10 tons, then the hypothesis under this study will be:

Null hypothesis H 0 : µ= 10 tons Alternative hypothesis H a : µ>10 tons

2. Under another study that is trying to test whether there is a significant difference between the effectiveness of medicine against heart arrest, the alternative hypothesis will be that there is a relationship between the medicine and chances of heart arrest.

Null hypothesis vs Alternative hypothesis

• R. Kothari (1990) Research Methodology. Vishwa Prakasan. India.
• https://www.statisticssolutions.com/null-hypothesis-and-alternative-hypothesis/
• https://byjus.com/maths/null-hypothesis/
• https://en.wikipedia.org/wiki/Null_hypothesis
• https://keydifferences.com/difference-between-null-and-alternative-hypothesis.html
• 5% – https://en.wikipedia.org/wiki/Null_hypothesis
• 3% – https://keydifferences.com/difference-between-null-and-alternative-hypothesis.html
• 2% – https://byjus.com/maths/null-hypothesis/
• 1% – https://www.wisdomjobs.com/e-university/research-methodology-tutorial-355/procedure-for-hypothesis-testing-11525.html
• 1% – https://www.thoughtco.com/definition-of-null-hypothesis-and-examples-605436
• 1% – https://www.quora.com/What-are-the-different-types-of-hypothesis-and-what-are-some-examples-of-them
• 1% – https://www.dummies.com/education/math/statistics/what-a-p-value-tells-you-about-statistical-data/
• 1% – https://www.coursehero.com/file/p7jfbal5/These-are-hypotheses-capable-of-being-objectively-verified-and-tested-Thus-we/
• 1% – https://support.minitab.com/en-us/minitab/18/help-and-how-to/modeling-statistics/anova/how-to/one-way-anova/interpret-the-results/all-statistics-and-graphs/methods/
• 1% – https://stats.stackexchange.com/questions/105319/test-whether-there-is-a-significant-difference-between-two-groups
• 1% – https://statisticsbyjim.com/hypothesis-testing/failing-reject-null-hypothesis/
• 1% – https://quizlet.com/45299306/statistics-flash-cards/
• <1% – https://www.thoughtco.com/significance-level-in-hypothesis-testing-1147177
• <1% – https://www.thoughtco.com/null-hypothesis-vs-alternative-hypothesis-3126413
• <1% – https://www.sagepub.com/sites/default/files/upm-binaries/40007_Chapter8.pdf
• <1% – https://www.differencebetween.com/difference-between-hypothesis-and-vs-assumption/
• <1% – https://www.coursehero.com/file/18076181/introduction-to-hypothesis/
• <1% – https://statisticsbyjim.com/glossary/significance-level/
• <1% – https://quizlet.com/164755799/research-methods-midterm-2-flash-cards/
• <1% – https://online.stat.psu.edu/statprogram/reviews/statistical-concepts/hypothesis-testing/p-value-approach

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10.1 - setting the hypotheses: examples.

A significance test examines whether the null hypothesis provides a plausible explanation of the data. The null hypothesis itself does not involve the data. It is a statement about a parameter (a numerical characteristic of the population). These population values might be proportions or means or differences between means or proportions or correlations or odds ratios or any other numerical summary of the population. The alternative hypothesis is typically the research hypothesis of interest. Here are some examples.

Example 10.2: Hypotheses with One Sample of One Categorical Variable Section  

About 10% of the human population is left-handed. Suppose a researcher at Penn State speculates that students in the College of Arts and Architecture are more likely to be left-handed than people found in the general population. We only have one sample since we will be comparing a population proportion based on a sample value to a known population value.

• Research Question : Are artists more likely to be left-handed than people found in the general population?
• Response Variable : Classification of the student as either right-handed or left-handed

State Null and Alternative Hypotheses

• Null Hypothesis : Students in the College of Arts and Architecture are no more likely to be left-handed than people in the general population (population percent of left-handed students in the College of Art and Architecture = 10% or p = .10).
• Alternative Hypothesis : Students in the College of Arts and Architecture are more likely to be left-handed than people in the general population (population percent of left-handed students in the College of Arts and Architecture > 10% or p > .10). This is a one-sided alternative hypothesis.

Example 10.3: Hypotheses with One Sample of One Measurement Variable Section  

A generic brand of the anti-histamine Diphenhydramine markets a capsule with a 50 milligram dose. The manufacturer is worried that the machine that fills the capsules has come out of calibration and is no longer creating capsules with the appropriate dosage.

• Research Question : Does the data suggest that the population mean dosage of this brand is different than 50 mg?
• Response Variable : dosage of the active ingredient found by a chemical assay.
• Null Hypothesis : On the average, the dosage sold under this brand is 50 mg (population mean dosage = 50 mg).
• Alternative Hypothesis : On the average, the dosage sold under this brand is not 50 mg (population mean dosage ≠ 50 mg). This is a two-sided alternative hypothesis.

Example 10.4: Hypotheses with Two Samples of One Categorical Variable Section  

Many people are starting to prefer vegetarian meals on a regular basis. Specifically, a researcher believes that females are more likely than males to eat vegetarian meals on a regular basis.

• Research Question : Does the data suggest that females are more likely than males to eat vegetarian meals on a regular basis?
• Response Variable : Classification of whether or not a person eats vegetarian meals on a regular basis
• Explanatory (Grouping) Variable: Sex
• Null Hypothesis : There is no sex effect regarding those who eat vegetarian meals on a regular basis (population percent of females who eat vegetarian meals on a regular basis = population percent of males who eat vegetarian meals on a regular basis or p females = p males ).
• Alternative Hypothesis : Females are more likely than males to eat vegetarian meals on a regular basis (population percent of females who eat vegetarian meals on a regular basis > population percent of males who eat vegetarian meals on a regular basis or p females > p males ). This is a one-sided alternative hypothesis.

Example 10.5: Hypotheses with Two Samples of One Measurement Variable Section  

Obesity is a major health problem today. Research is starting to show that people may be able to lose more weight on a low carbohydrate diet than on a low fat diet.

• Research Question : Does the data suggest that, on the average, people are able to lose more weight on a low carbohydrate diet than on a low fat diet?
• Response Variable : Weight loss (pounds)
• Explanatory (Grouping) Variable : Type of diet
• Null Hypothesis : There is no difference in the mean amount of weight loss when comparing a low carbohydrate diet with a low fat diet (population mean weight loss on a low carbohydrate diet = population mean weight loss on a low fat diet).
• Alternative Hypothesis : The mean weight loss should be greater for those on a low carbohydrate diet when compared with those on a low fat diet (population mean weight loss on a low carbohydrate diet > population mean weight loss on a low fat diet). This is a one-sided alternative hypothesis.

Example 10.6: Hypotheses about the relationship between Two Categorical Variables Section  

• Research Question : Do the odds of having a stroke increase if you inhale second hand smoke ? A case-control study of non-smoking stroke patients and controls of the same age and occupation are asked if someone in their household smokes.
• Variables : There are two different categorical variables (Stroke patient vs control and whether the subject lives in the same household as a smoker). Living with a smoker (or not) is the natural explanatory variable and having a stroke (or not) is the natural response variable in this situation.
• Null Hypothesis : There is no relationship between whether or not a person has a stroke and whether or not a person lives with a smoker (odds ratio between stroke and second-hand smoke situation is = 1).
• Alternative Hypothesis : There is a relationship between whether or not a person has a stroke and whether or not a person lives with a smoker (odds ratio between stroke and second-hand smoke situation is > 1). This is a one-tailed alternative.

This research question might also be addressed like example 11.4 by making the hypotheses about comparing the proportion of stroke patients that live with smokers to the proportion of controls that live with smokers.

Example 10.7: Hypotheses about the relationship between Two Measurement Variables Section  

• Research Question : A financial analyst believes there might be a positive association between the change in a stock's price and the amount of the stock purchased by non-management employees the previous day (stock trading by management being under "insider-trading" regulatory restrictions).
• Variables : Daily price change information (the response variable) and previous day stock purchases by non-management employees (explanatory variable). These are two different measurement variables.
• Null Hypothesis : The correlation between the daily stock price change (\$) and the daily stock purchases by non-management employees (\$) = 0.
• Alternative Hypothesis : The correlation between the daily stock price change (\$) and the daily stock purchases by non-management employees (\$) > 0. This is a one-sided alternative hypothesis.

Example 10.8: Hypotheses about comparing the relationship between Two Measurement Variables in Two Samples Section  

• Research Question : Is there a linear relationship between the amount of the bill (\$) at a restaurant and the tip (\$) that was left. Is the strength of this association different for family restaurants than for fine dining restaurants?
• Variables : There are two different measurement variables. The size of the tip would depend on the size of the bill so the amount of the bill would be the explanatory variable and the size of the tip would be the response variable.
• Null Hypothesis : The correlation between the amount of the bill (\$) at a restaurant and the tip (\$) that was left is the same at family restaurants as it is at fine dining restaurants.
• Alternative Hypothesis : The correlation between the amount of the bill (\$) at a restaurant and the tip (\$) that was left is the difference at family restaurants then it is at fine dining restaurants. This is a two-sided alternative hypothesis.

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• Knowledge Base

Methodology

• How to Write a Strong Hypothesis | Steps & Examples

How to Write a Strong Hypothesis | Steps & Examples

Published on May 6, 2022 by Shona McCombes . Revised on November 20, 2023.

A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection .

Example: Hypothesis

Daily apple consumption leads to fewer doctor’s visits.

Table of contents

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, other interesting articles, frequently asked questions about writing hypotheses.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess – it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Variables in hypotheses

Hypotheses propose a relationship between two or more types of variables .

• An independent variable is something the researcher changes or controls.
• A dependent variable is something the researcher observes and measures.

If there are any control variables , extraneous variables , or confounding variables , be sure to jot those down as you go to minimize the chances that research bias  will affect your results.

In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .

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Step 1. Ask a question

Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.

Step 2. Do some preliminary research

Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find.

At this stage, you might construct a conceptual framework to ensure that you’re embarking on a relevant topic . This can also help you identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalize more complex constructs.

Step 3. Formulate your hypothesis

Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.

4. Refine your hypothesis

You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain:

• The relevant variables
• The specific group being studied
• The predicted outcome of the experiment or analysis

5. Phrase your hypothesis in three ways

To identify the variables, you can write a simple prediction in  if…then form. The first part of the sentence states the independent variable and the second part states the dependent variable.

In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.

If you are comparing two groups, the hypothesis can state what difference you expect to find between them.

6. Write a null hypothesis

If your research involves statistical hypothesis testing , you will also have to write a null hypothesis . The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .

• H 0 : The number of lectures attended by first-year students has no effect on their final exam scores.
• H 1 : The number of lectures attended by first-year students has a positive effect on their final exam scores.

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

• Sampling methods
• Simple random sampling
• Stratified sampling
• Cluster sampling
• Likert scales
• Reproducibility

 Statistics

• Null hypothesis
• Statistical power
• Probability distribution
• Effect size
• Poisson distribution

Research bias

• Optimism bias
• Cognitive bias
• Implicit bias
• Hawthorne effect
• Anchoring bias
• Explicit bias

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A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

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.

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.

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About the null and alternative hypotheses

The null and alternative hypotheses are two mutually exclusive statements about a population. A hypothesis test uses sample data to determine whether to reject the null hypothesis.

One-sided and two-sided hypotheses

Examples of two-sided and one-sided hypotheses.

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Alternative Hypothesis

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Diving deep into the realm of scientific research, the alternative hypothesis plays a pivotal role in steering investigations. It stands contrary to the null hypothesis , providing a different perspective or direction. This essential component often sets the foundation for groundbreaking discoveries. If you’re keen on understanding this concept further, our collection of alternative hypothesis statement examples, combined with a thorough writing guide and insightful tips, will serve as your comprehensive roadmap.

What is an Alternative hypothesis?

An alternative hypothesis is a statement used in statistical testing that indicates the presence of an effect, relationship, or difference. It stands in direct contrast to the null hypothesis, which posits that there is no effect or relationship. The alternative causual hypothesis provides a specific direction to the research and can be directional (e.g., one value is greater than another) or non-directional (e.g., two values are not equal).

What is an example of an Alternative hypothesis statement?

If a researcher is studying the effect of a new teaching method on student performance, the null hypothesis might be: “The new teaching method has no effect on student performance.” An example of an alternative hypothesis could be:

Directional: “Students exposed to the new teaching method will perform better than those who were not.” Non-directional: “Student performance will be different for those exposed to the new teaching method compared to those who were not.”

100 Alternative Hypothesis Statement Examples

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The alternative hypothesis symbolizes a statement of what a statistical hypothesis test is set to establish. Often contrasted with a null hypothesis, it indicates the expected direction of the tested relation. Dive into these varied thesis statement examples showcasing the core essence of alternative hypotheses.

• Smoking and Cancer : Smoking is positively related to lung cancer incidence.
• Diet and Weight Loss : The Atkins diet results in more weight loss than a conventional diet.
• Medication Efficiency : Drug A is more effective than Drug B in treating migraines.
• Exercise Duration : Engaging in physical activity for more than 30 minutes daily reduces depression symptoms.
• Class Size and Learning : Smaller class sizes lead to higher student test scores.
• Sugar Intake : Consuming more than 50 grams of sugar daily increases the risk of diabetes.
• Vitamin C and Cold : Vitamin C intake reduces the duration of the common cold.
• Sleep Duration : Sleeping less than 6 hours results in decreased cognitive function.
• Training Methods : Method X training increases employee productivity more than Method Y.
• Pollution Levels : Higher levels of industrial activity correlate with increased air pollution.
• Stress and Disease : Chronic stress has a positive relationship with heart diseases.
• Alcohol and Reaction Time : Alcohol consumption slows down reaction time.
• Meditation and Blood Pressure : Regular meditation lowers blood pressure.
• Organic Food : Consuming organic food leads to better gut health.
• Advertising : Increased advertising results in higher sales figures.
• Salary and Job Satisfaction : A higher salary correlates with job satisfaction.
• Age and Memory : As age increases, short-term memory retention decreases.
• Temperature and Aggression : Higher temperatures are associated with increased aggressive behavior.
• Social Media : Spending more than 2 hours on social media daily increases feelings of loneliness.
• Music and Concentration : Listening to classical music improves concentration during studies. …
• Recycling Habits : Communities with mandatory recycling policies have higher recycling rates.
• Urban Areas : Living in urban areas increases the likelihood of asthma.
• Pets and Loneliness : Owning a pet decreases feelings of loneliness.
• Reading Habits : Reading more than 3 books a month correlates with increased empathy.
• Green Spaces : Having access to green spaces reduces stress levels.
• Vaccination : Vaccination reduces the incidence of specific diseases.
• Chocolate and Mood : Consuming chocolate elevates mood.
• Remote Work : Working remotely improves overall work satisfaction.
• Financial Literacy : Financial literacy education reduces personal debt.
• Mindfulness and Anxiety : Practicing mindfulness decreases symptoms of anxiety. …
• Dietary Fiber : Higher dietary fiber intake is associated with lower risks of bowel cancer.
• Travel and Creativity : People who travel frequently are more creative.
• Education Level and Income : Individuals with higher education levels earn more income.
• Technology Adoption : People who receive technology training adapt to new devices faster.
• Parental Involvement and Academic Performance : Increased parental involvement enhances students’ academic performance.
• Exercise Frequency and Heart Health : Exercising at least five times a week improves heart health.
• Gender and Leadership Roles : Men are more likely to hold leadership positions in corporate settings.
• Social Support and Mental Health : Strong social support networks reduce the risk of depression.
• Quality of Sleep and Productivity : Better sleep quality leads to higher productivity levels.
• High-Fat Diet and Cholesterol Levels : A high-fat diet increases cholesterol levels.
• Caffeine Intake and Alertness : Higher caffeine intake enhances alertness and cognitive function.
• Online Shopping Habits : People who frequently shop online spend more money than in-store shoppers. …
• Education and Political Views : Higher education levels are associated with more liberal political views.
• Gender and Risk-Taking Behavior : Men are more likely to engage in risky behaviors.
• Temperature and Ice Cream Sales : Higher temperatures increase ice cream sales.
• Artificial Sweeteners and Weight Loss : Consuming products with artificial sweeteners aids in weight loss.
• Exercise and Stress Reduction : Regular exercise reduces stress levels.
• Music Genres and Mood : Listening to upbeat music improves mood.
• Online Learning and Engagement : Online learners are more engaged in virtual classroom discussions.
• Personality Traits and Job Performance : Extroverted individuals perform better in sales roles.
• Environmental Awareness and Recycling : Higher environmental awareness leads to more recycling practices.
• Social Media Usage and Self-Esteem : Excessive social media usage correlates with lower self-esteem. …
• Sleep Deprivation and Reaction Time : Sleep-deprived individuals have slower reaction times.
• Breakfast Consumption and Metabolism : Eating breakfast kickstarts metabolism for the day.
• Leadership Style and Employee Satisfaction : Transformational leadership style increases employee job satisfaction.
• Bilingualism and Cognitive Abilities : Bilingual individuals possess enhanced cognitive abilities.
• Video Game Playing and Aggression : Playing violent video games increases aggressive behavior.
• Hydration and Cognitive Function : Staying hydrated improves cognitive function.
• Parental Support and Academic Achievement : Supportive parenting leads to higher academic achievement.
• Workplace Flexibility and Work-Life Balance : Jobs with flexible schedules enhance work-life balance.
• Digital Learning and Knowledge Retention : Digital learning methods improve long-term knowledge retention.
• Art Exposure and Creativity : Exposure to various forms of art fosters creative thinking.
• Solar Energy Adoption and Utility Bills : Homes with solar energy systems experience lower utility bills.
• Parental Involvement and Student Behavior : Increased parental involvement reduces student behavioral issues.
• Team Diversity and Creativity : Diverse teams generate more creative solutions.
• Social Media Marketing and Brand Awareness : Social media marketing boosts brand awareness more than traditional methods.
• Morning Routine and Productivity : Following a structured morning routine enhances overall productivity.
• Music Training and Cognitive Development : Music training improves cognitive abilities in children.
• Employee Training and Job Satisfaction : Comprehensive employee training programs lead to higher job satisfaction.
• Eating Before Bed and Sleep Quality : Consuming heavy meals before bed negatively affects sleep quality.
• Financial Incentives and Employee Performance : Offering financial incentives increases employee performance.
• Parental Attachment and Emotional Well-being : Strong parental attachment fosters better emotional well-being in children.
• Social Interaction and Mental Well-being : Frequent social interaction correlates with improved mental health.
• Education and Crime Rates : Higher education levels result in lower crime rates within communities.
• Diet and Acne : A diet high in dairy products exacerbates acne.
• Leadership Style and Employee Motivation : Autocratic leadership style hampers employee motivation.
• Urban Green Spaces and Stress Reduction : Access to urban green spaces lowers stress levels.
• Sleep Duration and Athletic Performance : Adequate sleep duration enhances athletic performance.
• Financial Literacy and Investment Success : Individuals with high financial literacy make more successful investments.
• Team Collaboration and Project Success : Effective team collaboration leads to more successful project outcomes.
• Media Exposure and Body Image : Increased media exposure contributes to negative body image perceptions.
• Gender Representation and Film Success : Movies with more balanced gender representation achieve higher box office success. …
• Meditation and Anxiety Reduction : Regular meditation practice reduces symptoms of anxiety.
• Cognitive Training and Memory Enhancement : Cognitive training programs improve memory retention.
• Positive Affirmations and Self-Confidence : Repeating positive affirmations enhances self-confidence.
• Physical Fitness and Longevity : Being physically fit is linked to increased lifespan.
• Parental Guidance and Online Safety : Strong parental guidance promotes responsible online behavior in children.
• Artificial Intelligence and Job Displacement : Increased AI integration leads to more job displacement.
• Public Transportation Usage and Air Quality : Increased public transportation usage improves air quality in cities.
• Social Support and Addiction Recovery : Strong social support networks aid in addiction recovery.
• Gender Diversity and Company Performance : Companies with diverse gender representation outperform others.
• Mindfulness Meditation and Pain Management : Mindfulness meditation reduces perception of pain.
• Music Therapy and Autism : Music therapy improves social interaction skills in children with autism.
• Social Media Usage and Academic Performance : Excessive social media usage negatively impacts academic performance.
• Employee Engagement and Organizational Success : Higher employee engagement leads to greater organizational success.
• Healthy Eating and Longevity : A diet rich in fruits and vegetables contributes to a longer lifespan.
• Gender Stereotypes and Career Choice : Gender stereotypes influence career choices among young adults.
• Environmental Conservation Efforts and Biodiversity : Increased conservation efforts positively affect biodiversity.
• Volunteerism and Personal Well-being : Engaging in volunteer activities enhances personal well-being.
• Artificial Intelligence and Customer Service : AI-driven customer service improves user satisfaction.

Alternative Hypothesis Statement Examples in Research

In alternative research hypothesis propel investigations beyond the null. Examples span diverse fields, revealing the direction researchers expect their findings to take.

• Effect of Music on Concentration : Listening to classical music enhances concentration during study.
• Green Tea and Weight Loss : Green tea consumption leads to more significant weight loss than water intake.
• Parental Involvement and Academic Achievement : Active parental involvement boosts student academic achievement.
• Social Media Usage and Self-Esteem : Frequent social media use correlates with lower self-esteem.

Alternative Hypothesis Statement Examples in Business Research

Business research thrives on alternative hypotheses. Dive into these business-oriented examples that challenge null assumptions.

• Marketing Campaign Impact : Marketing campaign A generates higher conversion rates than campaign B.
• Employee Training and Productivity : Comprehensive employee training enhances workplace productivity.
• Work-Life Balance and Employee Satisfaction : Improved work-life balance increases employee job satisfaction.
• Customer Service Channel Effectiveness : Online chat support results in higher customer satisfaction compared to phone support.
• Branding Influence on Purchase Intent : Strong brand presence leads to increased purchase intent.

Directional Alternative Hypothesis Statement Examples

Directional hypothesis add clarity to research expectations. Explore these examples that predict specific outcomes.

• Exercise Frequency and Heart Health : Engaging in physical activity five times a week improves heart health.

Alternative Hypothesis Statement Examples in Psychology

Psychological studies benefit from well-crafted alternative hypotheses. These psychology hypothesis examples delve into the realm of human behavior and cognition.

• Mindfulness Meditation and Anxiety Reduction : Regular mindfulness practice reduces symptoms of anxiety.

Alternative Null Hypothesis Statement Examples

Explore alternative null hypothesis —statements asserting the absence of specific effects or differences.

• Coffee Consumption and Weight Gain : Increased coffee consumption does not lead to weight gain.
• Smartphone Usage and Sleep Quality : Using smartphones before bed does not impact sleep quality.
• Music Genre and Study Performance : Studying with rock music does not affect academic performance.
• Green Spaces and Stress Reduction : Access to green spaces does not decrease stress levels.
• Team Diversity and Project Success : Team diversity does not influence project success rates.

Alternative Hypothesis Statement Examples in Medical Research

Medical research relies on robust alternative hypotheses to drive scientific inquiry. These examples explore hypotheses in the realm of healthcare.

• Exercise and Diabetes Prevention : Regular exercise decreases the risk of developing type 2 diabetes.
• Medication A and Blood Pressure Reduction : Medication A leads to greater reduction in blood pressure compared to medication B.
• Nutritional Intake and Heart Disease : Higher intake of fruits and vegetables lowers the risk of heart disease.
• Stress Reduction Techniques and Anxiety Levels : Practicing stress reduction techniques decreases anxiety levels.
• Alternative Medicine and Pain Management : Alternative medicine therapies alleviate chronic pain more effectively than traditional treatments.

Alternative Hypothesis Statement Examples in Education Research

Education research thrives on alternative hypotheses to investigate innovative approaches. Explore examples that challenge conventional notions.

• Technology Integration and Student Engagement : Integrating technology enhances student engagement in the classroom.
• Project-Based Learning and Knowledge Retention : Project-based learning improves long-term knowledge retention.
• Teacher Professional Development and Student Performance : Effective teacher professional development positively impacts student academic performance.
• Inclusive Classroom Environment and Learning Outcomes : Inclusive classrooms lead to better learning outcomes for diverse students.
• Feedback Frequency and Writing Improvement : Frequent feedback results in greater improvement in student writing skills.

These examples showcase the pivotal role of alternative hypotheses across various disciplines, serving as the driving force behind scientific exploration and advancement.

What is the Alternative Hypothesis Formula?

The alternative hypothesis, denoted as “Ha” or “H1,” represents the assertion researchers aim to support through evidence. It stands in contrast to the null hypothesis (Ho), which suggests no effect or relationship. The formula for the alternative hypothesis varies based on the nature of the study:

• Directional Hypothesis : For studies with an expected direction, the formula takes the form of a prediction. For instance, “The new drug increases patient recovery rates.”
• Non-Directional Hypothesis : For exploratory studies, the formula reflects the possibility of any difference or effect. For example, “There is a difference in recovery rates between the two drugs.”

How do you start an Alternative Hypothesis?

Starting an alternative simple hypothesis involves framing a clear research statement that highlights the anticipated effect, relationship, or difference. To begin:

• Identify the Research Question: Determine the specific aspect you intend to explore or compare.
• Formulate a Hypothesis: Craft a statement that directly addresses the expected outcome.
• Include Variables: Introduce the relevant variables and their predicted connection.
• Be Clear and Specific: Ensure the alternative hypothesis is concise and unambiguous.

Is the Alternative Hypothesis a Claim or Statement?

The alternative hypothesis is both a claim and a statement. It claims that there is a measurable effect, relationship, or difference in the variables being studied. It is also a statement that researchers work to validate through evidence.

How do you write an Alternative Hypothesis Statement? – Step by Step Guide

Creating a robust alternative hypothesis statement involves structured steps:

• Identify Variables : Clearly define the independent and dependent variables in your study.
• State Expected Effect : Express the anticipated impact, relationship, or difference between variables.
• Be Precise : Use specific language to convey the exact nature of the expected outcome.
• Include Direction (if applicable) : If your hypothesis is directional, specify the expected direction.
• Avoid Ambiguity : Make sure your statement is clear and leaves no room for confusion.

Tips for Writing an Alternative Hypothesis Statement

• Be Specific : Clearly define the variables and the predicted relationship.
• Use Measurable Terms : Incorporate quantifiable terms to indicate the magnitude of the effect.
• Testability : Ensure the hypothesis can be tested empirically.
• Conciseness : Keep the statement concise and to the point.
• Alignment with Research Question : Ensure the hypothesis directly answers your research question.
• Avoid Value Judgments : Avoid value judgments or personal biases in the hypothesis.
• Review Literature : Consult existing literature to align your hypothesis with prior research.

Crafting a strong alternative hypothesis statement is essential for guiding your research and forming the basis for causual hypothesis testing. It directs the focus of your investigation and lays the foundation for drawing meaningful conclusions.

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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 .

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9.1 Null and Alternative Hypotheses

The actual test begins by considering two hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.

H 0 : The null hypothesis: It is a statement of no difference between the variables—they are not related. This can often be considered the status quo and as a result if you cannot accept the null it requires some action.

H a : The alternative hypothesis: It is a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0 . This is usually what the researcher is trying to prove.

Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.

After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are "reject H 0 " if the sample information favors the alternative hypothesis or "do not reject H 0 " or "decline to reject H 0 " if the sample information is insufficient to reject the null hypothesis.

Mathematical Symbols Used in H 0 and H a :

H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers (including one of the co-authors in research work) use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.

Example 9.1

H 0 : No more than 30% of the registered voters in Santa Clara County voted in the primary election. p ≤ .30 H a : More than 30% of the registered voters in Santa Clara County voted in the primary election. p > 30

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses.

Example 9.2

We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are: H 0 : μ = 2.0 H a : μ ≠ 2.0

We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• H 0 : μ __ 66
• H a : μ __ 66

Example 9.3

We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are: H 0 : μ ≥ 5 H a : μ < 5

We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• H 0 : μ __ 45
• H a : μ __ 45

Example 9.4

In an issue of U. S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%. State the null and alternative hypotheses. H 0 : p ≤ 0.066 H a : p > 0.066

On a state driver’s test, about 40% pass the test on the first try. We want to test if more than 40% pass on the first try. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• H 0 : p __ 0.40
• H a : p __ 0.40

Collaborative Exercise

Bring to class a newspaper, some news magazines, and some Internet articles . In groups, find articles from which your group can write null and alternative hypotheses. Discuss your hypotheses with the rest of the class.

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Understanding Hypothesis Testing

Hypothesis testing involves formulating assumptions about population parameters based on sample statistics and rigorously evaluating these assumptions against empirical evidence. This article sheds light on the significance of hypothesis testing and the critical steps involved in the process.

What is Hypothesis Testing?

A hypothesis is an assumption or idea, specifically a statistical claim about an unknown population parameter. For example, a judge assumes a person is innocent and verifies this by reviewing evidence and hearing testimony before reaching a verdict.

Hypothesis testing is a statistical method that is used to make a statistical decision using experimental data. Hypothesis testing is basically an assumption that we make about a population parameter. It evaluates two mutually exclusive statements about a population to determine which statement is best supported by the sample data. 

To test the validity of the claim or assumption about the population parameter:

• A sample is drawn from the population and analyzed.
• The results of the analysis are used to decide whether the claim is true or not.

Example: You say an average height in the class is 30 or a boy is taller than a girl. All of these is an assumption that we are assuming, and we need some statistical way to prove these. We need some mathematical conclusion whatever we are assuming is true.

Defining Hypotheses

• Null hypothesis (H 0 ): In statistics, the null hypothesis is a general statement or default position that there is no relationship between two measured cases or no relationship among groups. In other words, it is a basic assumption or made based on the problem knowledge. Example : A company’s mean production is 50 units/per da H 0 : [Tex]\mu [/Tex] = 50.
• Alternative hypothesis (H 1 ): The alternative hypothesis is the hypothesis used in hypothesis testing that is contrary to the null hypothesis.  Example: A company’s production is not equal to 50 units/per day i.e. H 1 : [Tex]\mu [/Tex] [Tex]\ne [/Tex] 50.

Key Terms of Hypothesis Testing

• Level of significance : It refers to the degree of significance in which we accept or reject the null hypothesis. 100% accuracy is not possible for accepting a hypothesis, so we, therefore, select a level of significance that is usually 5%. This is normally denoted with  [Tex]\alpha[/Tex] and generally, it is 0.05 or 5%, which means your output should be 95% confident to give a similar kind of result in each sample.
• P-value: The P value , or calculated probability, is the probability of finding the observed/extreme results when the null hypothesis(H0) of a study-given problem is true. If your P-value is less than the chosen significance level then you reject the null hypothesis i.e. accept that your sample claims to support the alternative hypothesis.
• Test Statistic: The test statistic is a numerical value calculated from sample data during a hypothesis test, used to determine whether to reject the null hypothesis. It is compared to a critical value or p-value to make decisions about the statistical significance of the observed results.
• Critical value : The critical value in statistics is a threshold or cutoff point used to determine whether to reject the null hypothesis in a hypothesis test.
• Degrees of freedom: Degrees of freedom are associated with the variability or freedom one has in estimating a parameter. The degrees of freedom are related to the sample size and determine the shape.

Why do we use Hypothesis Testing?

Hypothesis testing is an important procedure in statistics. Hypothesis testing evaluates two mutually exclusive population statements to determine which statement is most supported by sample data. When we say that the findings are statistically significant, thanks to hypothesis testing. 

One-Tailed and Two-Tailed Test

One tailed test focuses on one direction, either greater than or less than a specified value. We use a one-tailed test when there is a clear directional expectation based on prior knowledge or theory. The critical region is located on only one side of the distribution curve. If the sample falls into this critical region, the null hypothesis is rejected in favor of the alternative hypothesis.

One-Tailed Test

There are two types of one-tailed test:

• Left-Tailed (Left-Sided) Test: The alternative hypothesis asserts that the true parameter value is less than the null hypothesis. Example: H 0 ​: [Tex]\mu \geq 50 [/Tex] and H 1 : [Tex]\mu < 50 [/Tex]
• Right-Tailed (Right-Sided) Test : The alternative hypothesis asserts that the true parameter value is greater than the null hypothesis. Example: H 0 : [Tex]\mu \leq50 [/Tex] and H 1 : [Tex]\mu > 50 [/Tex]

Two-Tailed Test

A two-tailed test considers both directions, greater than and less than a specified value.We use a two-tailed test when there is no specific directional expectation, and want to detect any significant difference.

Example: H 0 : [Tex]\mu = [/Tex] 50 and H 1 : [Tex]\mu \neq 50 [/Tex]

To delve deeper into differences into both types of test: Refer to link

What are Type 1 and Type 2 errors in Hypothesis Testing?

In hypothesis testing, Type I and Type II errors are two possible errors that researchers can make when drawing conclusions about a population based on a sample of data. These errors are associated with the decisions made regarding the null hypothesis and the alternative hypothesis.

• Type I error: When we reject the null hypothesis, although that hypothesis was true. Type I error is denoted by alpha( [Tex]\alpha [/Tex] ).
• Type II errors : When we accept the null hypothesis, but it is false. Type II errors are denoted by beta( [Tex]\beta [/Tex] ).

How does Hypothesis Testing work?

Step 1: define null and alternative hypothesis.

State the null hypothesis ( [Tex]H_0 [/Tex] ), representing no effect, and the alternative hypothesis ( [Tex]H_1 [/Tex] ​), suggesting an effect or difference.

We first identify the problem about which we want to make an assumption keeping in mind that our assumption should be contradictory to one another, assuming Normally distributed data.

Step 2 – Choose significance level

Select a significance level ( [Tex]\alpha [/Tex] ), typically 0.05, to determine the threshold for rejecting the null hypothesis. It provides validity to our hypothesis test, ensuring that we have sufficient data to back up our claims. Usually, we determine our significance level beforehand of the test. The p-value is the criterion used to calculate our significance value.

Step 3 – Collect and Analyze data.

Gather relevant data through observation or experimentation. Analyze the data using appropriate statistical methods to obtain a test statistic.

Step 4-Calculate Test Statistic

The data for the tests are evaluated in this step we look for various scores based on the characteristics of data. The choice of the test statistic depends on the type of hypothesis test being conducted.

There are various hypothesis tests, each appropriate for various goal to calculate our test. This could be a Z-test , Chi-square , T-test , and so on.

• Z-test : If population means and standard deviations are known. Z-statistic is commonly used.
• t-test : If population standard deviations are unknown. and sample size is small than t-test statistic is more appropriate.
• Chi-square test : Chi-square test is used for categorical data or for testing independence in contingency tables
• F-test : F-test is often used in analysis of variance (ANOVA) to compare variances or test the equality of means across multiple groups.

We have a smaller dataset, So, T-test is more appropriate to test our hypothesis.

T-statistic is a measure of the difference between the means of two groups relative to the variability within each group. It is calculated as the difference between the sample means divided by the standard error of the difference. It is also known as the t-value or t-score.

Step 5 – Comparing Test Statistic:

In this stage, we decide where we should accept the null hypothesis or reject the null hypothesis. There are two ways to decide where we should accept or reject the null hypothesis.

Method A: Using Crtical values

Comparing the test statistic and tabulated critical value we have,

• If Test Statistic>Critical Value: Reject the null hypothesis.
• If Test Statistic≤Critical Value: Fail to reject the null hypothesis.

Note: Critical values are predetermined threshold values that are used to make a decision in hypothesis testing. To determine critical values for hypothesis testing, we typically refer to a statistical distribution table , such as the normal distribution or t-distribution tables based on.

Method B: Using P-values

We can also come to an conclusion using the p-value,

• If the p-value is less than or equal to the significance level i.e. ( [Tex]p\leq\alpha [/Tex] ), you reject the null hypothesis. This indicates that the observed results are unlikely to have occurred by chance alone, providing evidence in favor of the alternative hypothesis.
• If the p-value is greater than the significance level i.e. ( [Tex]p\geq \alpha[/Tex] ), you fail to reject the null hypothesis. This suggests that the observed results are consistent with what would be expected under the null hypothesis.

Note : The p-value is the probability of obtaining a test statistic as extreme as, or more extreme than, the one observed in the sample, assuming the null hypothesis is true. To determine p-value for hypothesis testing, we typically refer to a statistical distribution table , such as the normal distribution or t-distribution tables based on.

Step 7- Interpret the Results

At last, we can conclude our experiment using method A or B.

Calculating test statistic

To validate our hypothesis about a population parameter we use statistical functions . We use the z-score, p-value, and level of significance(alpha) to make evidence for our hypothesis for normally distributed data .

1. Z-statistics:

When population means and standard deviations are known.

[Tex]z = \frac{\bar{x} – \mu}{\frac{\sigma}{\sqrt{n}}}[/Tex]

• [Tex]\bar{x} [/Tex] is the sample mean,
• μ represents the population mean, 
• σ is the standard deviation
• and n is the size of the sample.

2. T-Statistics

T test is used when n<30,

t-statistic calculation is given by:

[Tex]t=\frac{x̄-μ}{s/\sqrt{n}} [/Tex]

• t = t-score,
• x̄ = sample mean
• μ = population mean,
• s = standard deviation of the sample,
• n = sample size

3. Chi-Square Test

Chi-Square Test for Independence categorical Data (Non-normally distributed) using:

[Tex]\chi^2 = \sum \frac{(O_{ij} – E_{ij})^2}{E_{ij}}[/Tex]

• [Tex]O_{ij}[/Tex] is the observed frequency in cell [Tex]{ij} [/Tex]
• i,j are the rows and columns index respectively.
• [Tex]E_{ij}[/Tex] is the expected frequency in cell [Tex]{ij}[/Tex] , calculated as : [Tex]\frac{{\text{{Row total}} \times \text{{Column total}}}}{{\text{{Total observations}}}}[/Tex]

Real life Examples of Hypothesis Testing

Let’s examine hypothesis testing using two real life situations,

Case A: D oes a New Drug Affect Blood Pressure?

Imagine a pharmaceutical company has developed a new drug that they believe can effectively lower blood pressure in patients with hypertension. Before bringing the drug to market, they need to conduct a study to assess its impact on blood pressure.

• Before Treatment: 120, 122, 118, 130, 125, 128, 115, 121, 123, 119
• After Treatment: 115, 120, 112, 128, 122, 125, 110, 117, 119, 114

Step 1 : Define the Hypothesis

• Null Hypothesis : (H 0 )The new drug has no effect on blood pressure.
• Alternate Hypothesis : (H 1 )The new drug has an effect on blood pressure.

Step 2: Define the Significance level

Let’s consider the Significance level at 0.05, indicating rejection of the null hypothesis.

If the evidence suggests less than a 5% chance of observing the results due to random variation.

Step 3 : Compute the test statistic

Using paired T-test analyze the data to obtain a test statistic and a p-value.

The test statistic (e.g., T-statistic) is calculated based on the differences between blood pressure measurements before and after treatment.

t = m/(s/√n)

• m  = mean of the difference i.e X after, X before
• s  = standard deviation of the difference (d) i.e d i ​= X after, i ​− X before,
• n  = sample size,

then, m= -3.9, s= 1.8 and n= 10

we, calculate the , T-statistic = -9 based on the formula for paired t test

Step 4: Find the p-value

The calculated t-statistic is -9 and degrees of freedom df = 9, you can find the p-value using statistical software or a t-distribution table.

thus, p-value = 8.538051223166285e-06

Step 5: Result

• If the p-value is less than or equal to 0.05, the researchers reject the null hypothesis.
• If the p-value is greater than 0.05, they fail to reject the null hypothesis.

Conclusion: Since the p-value (8.538051223166285e-06) is less than the significance level (0.05), the researchers reject the null hypothesis. There is statistically significant evidence that the average blood pressure before and after treatment with the new drug is different.

Python Implementation of Case A

Let’s create hypothesis testing with python, where we are testing whether a new drug affects blood pressure. For this example, we will use a paired T-test. We’ll use the scipy.stats library for the T-test.

Scipy is a mathematical library in Python that is mostly used for mathematical equations and computations.

We will implement our first real life problem via python,

import numpy as np from scipy import stats # Data before_treatment = np . array ([ 120 , 122 , 118 , 130 , 125 , 128 , 115 , 121 , 123 , 119 ]) after_treatment = np . array ([ 115 , 120 , 112 , 128 , 122 , 125 , 110 , 117 , 119 , 114 ]) # Step 1: Null and Alternate Hypotheses # Null Hypothesis: The new drug has no effect on blood pressure. # Alternate Hypothesis: The new drug has an effect on blood pressure. null_hypothesis = "The new drug has no effect on blood pressure." alternate_hypothesis = "The new drug has an effect on blood pressure." # Step 2: Significance Level alpha = 0.05 # Step 3: Paired T-test t_statistic , p_value = stats . ttest_rel ( after_treatment , before_treatment ) # Step 4: Calculate T-statistic manually m = np . mean ( after_treatment - before_treatment ) s = np . std ( after_treatment - before_treatment , ddof = 1 ) # using ddof=1 for sample standard deviation n = len ( before_treatment ) t_statistic_manual = m / ( s / np . sqrt ( n )) # Step 5: Decision if p_value <= alpha : decision = "Reject" else : decision = "Fail to reject" # Conclusion if decision == "Reject" : conclusion = "There is statistically significant evidence that the average blood pressure before and after treatment with the new drug is different." else : conclusion = "There is insufficient evidence to claim a significant difference in average blood pressure before and after treatment with the new drug." # Display results print ( "T-statistic (from scipy):" , t_statistic ) print ( "P-value (from scipy):" , p_value ) print ( "T-statistic (calculated manually):" , t_statistic_manual ) print ( f "Decision: { decision } the null hypothesis at alpha= { alpha } ." ) print ( "Conclusion:" , conclusion )

T-statistic (from scipy): -9.0 P-value (from scipy): 8.538051223166285e-06 T-statistic (calculated manually): -9.0 Decision: Reject the null hypothesis at alpha=0.05. Conclusion: There is statistically significant evidence that the average blood pressure before and after treatment with the new drug is different.

In the above example, given the T-statistic of approximately -9 and an extremely small p-value, the results indicate a strong case to reject the null hypothesis at a significance level of 0.05. 

• The results suggest that the new drug, treatment, or intervention has a significant effect on lowering blood pressure.
• The negative T-statistic indicates that the mean blood pressure after treatment is significantly lower than the assumed population mean before treatment.

Case B : Cholesterol level in a population

Data: A sample of 25 individuals is taken, and their cholesterol levels are measured.

Cholesterol Levels (mg/dL): 205, 198, 210, 190, 215, 205, 200, 192, 198, 205, 198, 202, 208, 200, 205, 198, 205, 210, 192, 205, 198, 205, 210, 192, 205.

Populations Mean = 200

Population Standard Deviation (σ): 5 mg/dL(given for this problem)

Step 1: Define the Hypothesis

• Null Hypothesis (H 0 ): The average cholesterol level in a population is 200 mg/dL.
• Alternate Hypothesis (H 1 ): The average cholesterol level in a population is different from 200 mg/dL.

As the direction of deviation is not given , we assume a two-tailed test, and based on a normal distribution table, the critical values for a significance level of 0.05 (two-tailed) can be calculated through the z-table and are approximately -1.96 and 1.96.

The test statistic is calculated by using the z formula Z = [Tex](203.8 – 200) / (5 \div \sqrt{25}) [/Tex] ​ and we get accordingly , Z =2.039999999999992.

Step 4: Result

Since the absolute value of the test statistic (2.04) is greater than the critical value (1.96), we reject the null hypothesis. And conclude that, there is statistically significant evidence that the average cholesterol level in the population is different from 200 mg/dL

Python Implementation of Case B

import scipy.stats as stats import math import numpy as np # Given data sample_data = np . array ( [ 205 , 198 , 210 , 190 , 215 , 205 , 200 , 192 , 198 , 205 , 198 , 202 , 208 , 200 , 205 , 198 , 205 , 210 , 192 , 205 , 198 , 205 , 210 , 192 , 205 ]) population_std_dev = 5 population_mean = 200 sample_size = len ( sample_data ) # Step 1: Define the Hypotheses # Null Hypothesis (H0): The average cholesterol level in a population is 200 mg/dL. # Alternate Hypothesis (H1): The average cholesterol level in a population is different from 200 mg/dL. # Step 2: Define the Significance Level alpha = 0.05 # Two-tailed test # Critical values for a significance level of 0.05 (two-tailed) critical_value_left = stats . norm . ppf ( alpha / 2 ) critical_value_right = - critical_value_left # Step 3: Compute the test statistic sample_mean = sample_data . mean () z_score = ( sample_mean - population_mean ) / \ ( population_std_dev / math . sqrt ( sample_size )) # Step 4: Result # Check if the absolute value of the test statistic is greater than the critical values if abs ( z_score ) > max ( abs ( critical_value_left ), abs ( critical_value_right )): print ( "Reject the null hypothesis." ) print ( "There is statistically significant evidence that the average cholesterol level in the population is different from 200 mg/dL." ) else : print ( "Fail to reject the null hypothesis." ) print ( "There is not enough evidence to conclude that the average cholesterol level in the population is different from 200 mg/dL." )

Reject the null hypothesis. There is statistically significant evidence that the average cholesterol level in the population is different from 200 mg/dL.

Limitations of Hypothesis Testing

• Although a useful technique, hypothesis testing does not offer a comprehensive grasp of the topic being studied. Without fully reflecting the intricacy or whole context of the phenomena, it concentrates on certain hypotheses and statistical significance.
• The accuracy of hypothesis testing results is contingent on the quality of available data and the appropriateness of statistical methods used. Inaccurate data or poorly formulated hypotheses can lead to incorrect conclusions.
• Relying solely on hypothesis testing may cause analysts to overlook significant patterns or relationships in the data that are not captured by the specific hypotheses being tested. This limitation underscores the importance of complimenting hypothesis testing with other analytical approaches.

Hypothesis testing stands as a cornerstone in statistical analysis, enabling data scientists to navigate uncertainties and draw credible inferences from sample data. By systematically defining null and alternative hypotheses, choosing significance levels, and leveraging statistical tests, researchers can assess the validity of their assumptions. The article also elucidates the critical distinction between Type I and Type II errors, providing a comprehensive understanding of the nuanced decision-making process inherent in hypothesis testing. The real-life example of testing a new drug’s effect on blood pressure using a paired T-test showcases the practical application of these principles, underscoring the importance of statistical rigor in data-driven decision-making.

Frequently Asked Questions (FAQs)

1. what are the 3 types of hypothesis test.

There are three types of hypothesis tests: right-tailed, left-tailed, and two-tailed. Right-tailed tests assess if a parameter is greater, left-tailed if lesser. Two-tailed tests check for non-directional differences, greater or lesser.

2.What are the 4 components of hypothesis testing?

Null Hypothesis ( [Tex]H_o [/Tex] ): No effect or difference exists. Alternative Hypothesis ( [Tex]H_1 [/Tex] ): An effect or difference exists. Significance Level ( [Tex]\alpha [/Tex] ): Risk of rejecting null hypothesis when it’s true (Type I error). Test Statistic: Numerical value representing observed evidence against null hypothesis.

3.What is hypothesis testing in ML?

Statistical method to evaluate the performance and validity of machine learning models. Tests specific hypotheses about model behavior, like whether features influence predictions or if a model generalizes well to unseen data.

4.What is the difference between Pytest and hypothesis in Python?

Pytest purposes general testing framework for Python code while Hypothesis is a Property-based testing framework for Python, focusing on generating test cases based on specified properties of the code.

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• Published: 21 August 2024

Neoarchaean oxygen-based nitrogen cycle en route to the Great Oxidation Event

• Alice Pellerin   ORCID: orcid.org/0000-0001-6828-5899 1 ,
• Christophe Thomazo   ORCID: orcid.org/0000-0002-2475-0514 1 , 2 ,
• Magali Ader   ORCID: orcid.org/0000-0002-9239-1509 3 ,
• Camille Rossignol   ORCID: orcid.org/0000-0003-0082-4854 4 ,
• Eric Siciliano Rego 5 ,
• Vincent Busigny   ORCID: orcid.org/0000-0001-7556-0772 3 &
• Pascal Philippot   ORCID: orcid.org/0000-0002-8094-5834 6 , 7  

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• Element cycles
• Geochemistry

The nitrogen isotopic composition of sedimentary rocks (δ 15 N) can trace redox-dependent biological pathways and early Earth oxygenation 1 , 2 . However, there is no substantial change in the sedimentary δ 15 N record across the Great Oxidation Event about 2.45 billion years ago (Ga) 3 , a prominent redox change. This argues for a temporal decoupling between the emergence of the first oxygen-based oxidative pathways of the nitrogen cycle and the accumulation of atmospheric oxygen after 2.45 Ga (ref.  3 ). The transition between both states shows strongly positive δ 15 N values (10–50‰) in rocks deposited between 2.8 Ga and 2.6 Ga, but their origin and spatial extent remain uncertain 4 , 5 . Here we report strongly positive δ 15 N values (>30‰) in the 2.68-Gyr-old shallow to deep marine sedimentary deposit of the Serra Sul Formation 6 , Amazonian Craton, Brazil. Our findings are best explained by regionally variable extents of ammonium oxidation to N 2 or N 2 O tied to a cryptic oxygen cycle, implying that oxygenic photosynthesis was operating at 2.7 Ga. Molecular oxygen production probably shifted the redox potential so that an intermediate N cycle based on ammonium oxidation developed before nitrate accumulation in surface waters. We propose to name this period, when strongly positive nitrogen isotopic compositions are superimposed on the usual range of Precambrian δ 15 N values, the Nitrogen Isotope Event. We suggest that it marks the earliest steps of the biogeochemical reorganizations that led to the Great Oxidation Event.

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Data availability.

All data are available in the main text or the supplementary materials, and at https://doi.org/10.25666/DATAUBFC-2024-06-27 .

Ader, M. et al. Interpretation of the nitrogen isotopic composition of Precambrian sedimentary rocks: assumptions and perspectives. Chem. Geol. 429 , 93–110 (2016).

Article   ADS   CAS   Google Scholar  

Stüeken, E. E., Kipp, M. A., Koehler, M. C. & Buick, R. The evolution of Earth’s biogeochemical nitrogen cycle. Earth-Sci. Rev. 160 , 220–239 (2016).

Article   ADS   Google Scholar  

Lyons, T. W., Reinhard, C. T. & Planavsky, N. J. The rise of oxygen in Earth’s early ocean and atmosphere. Nature 506 , 307–315 (2014).

Article   ADS   CAS   PubMed   Google Scholar  

Thomazo, C., Ader, M. & Philippot, P. Extreme 15 N-enrichments in 2.72-Gyr-old sediments: evidence for a turning point in the nitrogen cycle. Geobiology 9 , 107–120 (2011).

Article   CAS   PubMed   Google Scholar  

Stüeken, E. E., Buick, R. & Schauer, A. J. Nitrogen isotope evidence for alkaline lakes on late Archean continents. Earth Planet. Sci. Lett. 411 , 1–10 (2015).

Rossignol, C. et al. Stratigraphy and geochronological constraints of the Serra Sul Formation (Carajás Basin, Amazonian Craton, Brazil). Precambrian Res. 351 , 105981 (2020).

Article   CAS   Google Scholar  

Altabet, M. A. & Francois, R. Sedimentary nitrogen isotopic ratio as a recorder for surface ocean nitrate utilization. Global Biogeochem. Cycles 8 , 103–116 (1994).

Zhang, X., Sigman, D. M., Morel, F. M. M. & Kraepiel, A. M. L. Nitrogen isotope fractionation by alternative nitrogenases and past ocean anoxia. Proc. Natl Acad. Sci. 111 , 4782–4787 (2014).

Article   ADS   CAS   PubMed   PubMed Central   Google Scholar  

Sigman, D. M., Karsh, K. L. & Casciotti, K. L. in Encyclopedia of Ocean Sciences 2nd edn (Steele, J. H.) 40–54 (Academic Press, 2009).

Möbius, J. Isotope fractionation during nitrogen remineralization (ammonification): implications for nitrogen isotope biogeochemistry. Geochim. Cosmochim. Acta 105 , 422–432 (2013).

Mariotti, A. et al. Experimental determination of nitrogen kinetic isotope fractionation: some principles; illustration for the denitrification and nitrification processes. Plant Soil 62 , 413–430 (1981).

Dalsgaard, T. & Thamdrup, B. Factors controlling anaerobic ammonium oxidation with nitrite in marine sediments. Appl. Environ. Microbiol. 68 , 3802–3808 (2002).

Nishizawa, M., Sano, Y., Ueno, Y. & Maruyama, S. Speciation and isotope ratios of nitrogen in fluid inclusions from seafloor hydrothermal deposits at ∼ 3.5 Ga. Earth Planet. Sci. Lett. 254 , 332–344 (2007).

Marty, B., Zimmermann, L., Pujol, M., Burgess, R. & Philippot, P. Nitrogen isotopic composition and density of the Archean atmosphere. Science 342 , 101–104 (2013).

Stüeken, E. E., Buick, R., Guy, B. M. & Koehler, M. C. Isotopic evidence for biological nitrogen fixation by molybdenum-nitrogenase from 3.2 Gyr. Nature 520 , 666–669 (2015).

Article   ADS   PubMed   Google Scholar  

Kipp, M. A., Stüeken, E. E., Yun, M., Bekker, A. & Buick, R. Pervasive aerobic nitrogen cycling in the surface ocean across the Paleoproterozoic Era. Earth Planet. Sci. Lett. 500 , 117–126 (2018).

Koehler, M. C., Buick, R., Kipp, M. A., Stüeken, E. E. & Zaloumis, J. Transient surface ocean oxygenation recorded in the ∼ 2.66-Ga Jeerinah Formation, Australia. Proc. Natl Acad. Sci. 115 , 7711–7716 (2018).

Zerkle, A. L. et al. Onset of the aerobic nitrogen cycle during the Great Oxidation Event. Nature 542 , 465–467 (2017).

Garvin, J., Buick, R., Anbar, A. D., Arnold, G. L. & Kaufman, A. J. Isotopic evidence for an aerobic nitrogen cycle in the latest Archean. Science 323 , 1045–1048 (2009).

Godfrey, L. V. & Falkowski, P. G. The cycling and redox state of nitrogen in the Archaean ocean. Nat. Geosci. 2 , 725–729 (2009).

Beaumont, V. & Robert, F. Nitrogen isotope ratios of kerogens in Precambrian cherts: a record of the evolution of atmosphere chemistry? Precambrian Res. 96 , 63–82 (1999).

Jia, Y. & Kerrich, R. Nitrogen 15–enriched Precambrian kerogen and hydrothermal systems. Geochem. Geophys. Geosyst. 5 , Q07005 (2004).

Kerrich, R., Jia, Y., Manikyamba, C. & Naqvi, S. M. Secular variations of N-isotopes in terrestrial reservoirs and ore deposits. Geol. Soc. Am. Bull. 198 , 81–104 (2006).

Google Scholar  

Stüeken, E. E. et al. Environmental niches and metabolic diversity in Neoarchean lakes. Geobiology 15 , 767–783 (2017).

Article   PubMed   Google Scholar  

Hayes, J. M. in Early Life Earth, Nobel Symposium, No. 84 (ed. Bengston, S.) 220–236 (Columbia Univ. Press, 1994).

Awramik, S. M. & Buchheim, H. P. A giant, Late Archean lake system: the Meentheena Member (Tumbiana Formation; Fortescue Group), Western Australia. Precambrian Res. 174 , 215–240 (2009).

Rossignol, C. et al. Unraveling one billion years of geological evolution of the southeastern Amazonia Craton from detrital zircon analyses. Geosci. Front. 13 , 101202 (2021).

Article   Google Scholar  

Perelló, J., Zulliger, G., García, A. & Creaser, R. A. Revisiting the IOCG geology and age of Alemão in the Igarapé Bahia camp, Carajás province, Brazil. J. South Am. Earth Sci. 124 , 104273 (2023).

Tomkins, A. G. et al. Ancient micrometeorites suggestive of an oxygen-rich Archaean upper atmosphere. Nature 533 , 235–238 (2016).

Stüeken, E. E., Boocock, T. J., Robinson, A., Mikhail, S. & Johnson, B. W. Hydrothermal recycling of sedimentary ammonium into oceanic crust and the Archean ocean at 3.24 Ga. Geology 49 , 822–826 (2021).

Figueiredo e Silva, R. C., Lobato, L. M., Zucchetti, M., Hagemann, S. & Vennemann, T. Geotectonic signature and hydrothermal alteration of metabasalts under- and overlying the giant Serra Norte iron deposits, Carajás mineral Province. Ore Geol. Rev. 120 , 103407 (2020).

Martins, P. L. G. et al. Low paleolatitude of the Carajás Basin at ∼ 2.75 Ga: paleomagnetic evidence from basaltic flows in Amazonia. Precambrian Res. 365 , 106411 (2021).

Li, L., Lollar, B. S., Li, H., Wortmann, U. G. & Lacrampe-Couloume, G. Ammonium stability and nitrogen isotope fractionations for NH 4 + –NH 3(aq) –NH 3(gas) systems at 20–70 °C and pH of 2–13: applications to habitability and nitrogen cycling in low-temperature hydrothermal systems. Geochim. Cosmochim. Acta 84 , 280–296 (2012).

Halevy, I. & Bachan, A. The geologic history of seawater pH. Science 355 , 1069–1071 (2017).

Tesdal, J.-E., Galbraith, E. & Kienast, M. Nitrogen isotopes in bulk marine sediment: linking seafloor observations with subseafloor records. Biogeosciences 10 , 101–118 (2013).

Hoch, M. P., Fogel, M. L. & Kirchman, D. L. Isotope fractionation associated with ammonium uptake by a marine bacterium. Limnol. Oceanogr. 37 , 1447–1459 (1992).

Papineau, D. et al. High primary productivity and nitrogen cycling after the Paleoproterozoic phosphogenic event in the Aravalli Supergroup, India. Precambrian Res. 171 , 37–56 (2009).

Yang, J. et al. Ammonium availability in the Late Archaean nitrogen cycle. Nat. Geosci. 12 , 553–557 (2019).

Saitoh, M. et al. Nitrogen isotope record from a mid-oceanic paleo-atoll limestone to constrain the redox state of the Panthalassa ocean in the Capitanian (Late Guadalupian, Permian). Paleoceanogr. Paleoclimatol. 38 , e2022PA004573 (2023).

Canfield, D. E., Glazer, A. N. & Falkowski, P. G. The evolution and future of Earth’s nitrogen cycle. Science 330 , 192–196 (2010).

Mandernack, K. W., Mills, C. T., Johnson, C. A., Rahn, T. & Kinney, C. The δ 15 N and δ 18 O values of N 2 O produced during the co-oxidation of ammonia by methanotrophic bacteria. Chem. Geol. 267 , 96–107 (2009).

Casciotti, K. L. Inverse kinetic isotope fractionation during bacterial nitrite oxidation. Geochim. Cosmochim. Acta 73 , 2061–2076 (2009).

Grotzinger, J. P. & Kasting, J. F. New constraints on Precambrian ocean composition. J. Geol. 101 , 235–243 (1993).

Pellerin, A. et al. Iron-mediated anaerobic ammonium oxidation recorded in the early Archean ferruginous ocean. Geobiology 21 , 277–289 (2023).

Bouyon, A. et al. Multiple sulfur isotope record from the Precambrian of South America shows an unusual trend. American Geophysical Union, Fall Meeting 2018, abstract #V31B-04 (2018).

Thomazo, C., Ader, M., Farquhar, J. & Philippot, P. Methanotrophs regulated atmospheric sulfur isotope anomalies during the Mesoarchean (Tumbiana Formation, Western Australia). Earth Planet. Sci. Lett. 279 , 65–75 (2009).

Ulloa, O., Canfield, D. E., DeLong, E. F., Letelier, R. M. & Stewart, F. J. Microbial oceanography of anoxic oxygen minimum zones. Proc. Natl Acad. Sci. 109 , 15996–16003 (2012).

Boocock, T. J., Mikhail, S., Prytulak, J., Di Rocco, T. & Stüeken, E. E. Nitrogen mass fraction and stable isotope ratios for fourteen geological reference materials: evaluating the applicability of elemental analyser versus sealed tube combustion methods. Geostand. Geoanalytical Res. 44 , 537–551 (2020).

Ader, M. et al. Ocean redox structure across the Late Neoproterozoic Oxygenation Event: a nitrogen isotope perspective. Earth Planet. Sci. Lett. 396 , 1–13 (2014).

Kendall, C. & Grim, E. Combustion tube method for measurement of nitrogen isotope ratios using calcium oxide for total removal of carbon dioxide and water. Anal. Chem. 62 , 526–529 (1990).

Busigny, V., Ader, M. & Cartigny, P. Quantification and isotopic analysis of nitrogen in rocks at the ppm level using sealed tube combustion technique: a prelude to the study of altered oceanic crust. Chem. Geol. 223 , 249–258 (2005).

Fraga-Ferreira, P. L. et al. The Nitrogen Cycle in an epeiric sea in the core of Gondwana Supercontinent: a study on the Ediacaran-Cambrian Bambuí Group, east-central Brazil. Front. Earth Sci. 9 , 692895 (2021).

Blake, T. S., Buick, R., Brown, S. J. A. & Barley, M. E. Geochronology of a Late Archaean flood basalt province in the Pilbara Craton, Australia: constraints on basin evolution, volcanic and sedimentary accumulation, and continental drift rates. Precambrian Res. 133 , 143–173 (2004).

Arndt, N. T., Nelson, D. R., Compston, W., Trendall, A. F. & Thorne, A. M. The age of the Fortescue Group, Hamersley Basin, Western Australia, from ion microprobe zircon U‐Pb results. Aust. J. Earth Sci. 38 , 261–281 (1991).

Kasbohm, J., Schoene, B., Maclennan, S. A., Evans, D. A. D. & Weiss, B. P. Paleogeography and high-precision geochronology of the Neoarchean Fortescue Group, Pilbara, Western Australia. Precambrian Res. 394 , 107114 (2023).

Martins, P. L. G. et al. Neoarchean magmatism in the southeastern Amazonian Craton, Brazil: petrography, geochemistry and tectonic significance of basalts from the Carajás Basin. Precambrian Res. 302 , 340–357 (2017).

Lepot, K., Benzerara, K., Brown, G. E. & Philippot, P. Microbially influenced formation of 2,724-million-year-old stromatolites. Nat. Geosci. 1 , 118–121 (2008).

Vasquez, M. L. & da Rosa-Costa, L. T. Geologia e Recursos Minerais do Estado do Pará (CPRM, 2008).

Rego, E. S. et al. Anoxygenic photosynthesis linked to Neoarchean iron formations in Carajás (Brazil). Geobiology 19 , 326–341 (2021).

Kamber, B. S., Webb, G. E. & Gallagher, M. The rare earth element signal in Archaean microbial carbonate: information on ocean redox and biogenicity. J. Geol. Soc. 171 , 745–763 (2014).

de Melo, G. H. C. et al. Evolution of the Igarapé Bahia Cu-Au deposit, Carajás Province (Brazil): early syngenetic chalcopyrite overprinted by IOCG mineralization. Ore Geol. Rev. 111 , 102993 (2019).

Dreher, A. M., Xavier, R. P. & Martini, S. L. Fragmental rocks of the Igarapé Bahia Cu-Au deposit, Carajas Mineral Province, Brazil. Rev. Bras. Geociências 35 , 359–368 (2005).

Dreher, A. M., Xavier, R. P., Taylor, B. E. & Martini, S. L. New geologic, fluid inclusion and stable isotope studies on the controversial Igarapé Bahia Cu–Au deposit, Carajás Province, Brazil. Miner. Deposita 43 , 161–184 (2008).

Galarza, M. A., Macambira, M. J. B. & Villas, R. N. Dating and isotopic characteristics (Pb and S) of the Fe oxide–Cu–Au–U–REE Igarapé Bahia ore deposit, Carajás mineral province, Pará state, Brazil. J. South Am. Earth Sci. 25 , 377–397 (2008).

Ronzê, P. C., Soares, A. D., dos Santos, M. & Barreira, C. F. in Hydrothermal Iron Oxide Copper-Gold & Related Deposits: A Global Perspective (ed. Porter, T. M.) 191–202 (PGC Publishing, 2000).

Coffey, J. M., Flannery, D. T., Walter, M. R. & George, S. C. Sedimentology, stratigraphy and geochemistry of a stromatolite biofacies in the 2.72 Ga Tumbiana Formation, Fortescue Group, Western Australia. Precambrian Res. 236 , 282–296 (2013).

Lowe, D. R. Sediment gravity flows; II, depositional models with special reference to the deposits of high-density turbidity currents. J. Sediment. Res. 52 , 279–297 (1982).

Mulder, T. & Alexander, J. The physical character of subaqueous sedimentary density flows and their deposits. Sedimentology 48 , 269–299 (2001).

Nemec, W. & Steel, R. J. Alluvial and coastal conglomerates: their significant features and some comments on gravelly mass-flow deposits. Sedimentology of Gravels and Conglomerates — Memoir 10, 1–31 (1984).

Postma, G., Kleverlaan, K. & Cartigny, M. J. B. Recognition of cyclic steps in sandy and gravelly turbidite sequences, and consequences for the Bouma facies model. Sedimentology 61 , 2268–2290 (2014).

Postma, G. & Cartigny, M. J. B. Supercritical and subcritical turbidity currents and their deposits—a synthesis. Geology 42 , 987–990 (2014).

Walker, R. G. Generalized facies models for resedimented conglomerates of turbidite association. Geol. Soc. Am. Bull. 86 , 737–748 (1975).

2.0.CO;2" data-track-item_id="10.1130/0016-7606(1975)86 2.0.CO;2" data-track-value="article reference" data-track-action="article reference" href="https://doi.org/10.1130%2F0016-7606%281975%2986%3C737%3AGFMFRC%3E2.0.CO%3B2" aria-label="Article reference 72" data-doi="10.1130/0016-7606(1975)86 2.0.CO;2">Article   ADS   Google Scholar  

Myrow, P. M. et al. Flat-pebble conglomerate: its multiple origins and relationship to metre-scale depositional cycles. Sedimentology 51 , 973–996 (2004).

Lehmann, M. F., Bernasconi, S. M., Barbieri, A. & McKenzie, J. A. Preservation of organic matter and alteration of its carbon and nitrogen isotope composition during simulated and in situ early sedimentary diagenesis. Geochim. Cosmochim. Acta 66 , 3573–3584 (2002).

Bebout, G. E. & Fogel, M. L. Nitrogen-isotope compositions of metasedimentary rocks in the Catalina Schist, California: implications for metamorphic devolatilization history. Geochim. Cosmochim. Acta 56 , 2839–2849 (1992).

Boyd, S. R. & Philippot, P. Precambrian ammonium biogeochemistry: a study of the Moine metasediments, Scotland. Chem. Geol. 144 , 257–268 (1998).

Haendel, D., Mühle, K., Nitzsche, H.-M., Stiehl, G. & Wand, U. Isotopic variations of the fixed nitrogen in metamorphic rocks. Geochim. Cosmochim. Acta 50 , 749–758 (1986).

Jia, Y. Nitrogen isotope fractionations during progressive metamorphism: a case study from the Paleozoic Cooma metasedimentary complex, southeastern Australia. Geochim. Cosmochim. Acta 70 , 5201–5214 (2006).

Ader, M., Boudou, J.-P., Javoy, M., Goffe, B. & Daniels, E. Isotope study on organic nitrogen of Westphalian anthracites from the Western Middle field of Pennsylvania (U.S.A.) and from the Bramsche Massif (Germany). Org. Geochem. 29 , 315–323 (1998).

Ader, M. et al. Nitrogen isotopic evolution of carbonaceous matter during metamorphism: methodology and preliminary results. Chem. Geol. 232 , 152–169 (2006).

Boudou, J.-P. et al. Organic nitrogen chemistry during low-grade metamorphism. Geochim. Cosmochim. Acta 72 , 1199–1221 (2008).

Stüeken, E. E., Zaloumis, J., Meixnerová, J. & Buick, R. Differential metamorphic effects on nitrogen isotopes in kerogen extracts and bulk rocks. Geochim. Cosmochim. Acta 217 , 80–94 (2017).

Stüeken, E. E., Gregory, D. D., Mukherjee, I. & McGoldrick, P. Sedimentary exhalative venting of bioavailable nitrogen into the early ocean. Earth Planet. Sci. Lett. 565 , 116963 (2021).

Cordani, U. G. et al. Tectonic map of South America=Mapa tectônico da América do Sul (Commission for the Geological Map of the World, 2016).

Vasquez, M. L., Sousa, C. S. & Carvalho, J. M. A. Mapa geológico e de recursos minerais do Estado do Pará, escala 1: 1.000. 000. Programa Geol. Bras. Belém CPRM (2008).

Machado, N., Lindenmayer, Z., Krogh, T. E. & Lindenmayer, D. U-Pb geochronology of Archean magmatism and basement reactivation in the Carajás area, Amazon shield, Brazil. Precambrian Res. 49 , 329–354 (1991).

Trendall, A. F., Basei, M. A. S., de Laeter, J. R. & Nelson, D. R. SHRIMP zircon U–Pb constraints on the age of the Carajás formation, Grão ParáGroup, Amazon Craton. J. South Am. Earth Sci. 11 , 265–277 (1998).

Rossignol, C. et al. Neoarchean environments associated with the emplacement of a large igneous province: insights from the Carajás Basin, Amazonia Craton. J. South Am. Earth Sci. 130 , 104574 (2023).

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Acknowledgements

For technical support, we would like to thank A.-L. Santoni and the GISMO platform (Université de Bourgogne, France) and G. Landais, R. Tchibinda, G. Bardoux and V. Rojas (Institut de Physique du Globe de Paris, France). Funding: Institut Universitaire de France (IUF) – project EVOLINES (C.T.); Observatoire des Sciences de l’Univers Terre Homme Environnement Temps Astronomie of Bourgogne-Franche-Comté (OSU THETA) – project NITROPAST (C.T.); Fundação de Amparo à Pesquisa do Estado de São Paulo, FAPESP projects 2019/16271-0, 2018/05892-0, 2015/16235-2, 2018/02645-2 and 2019/16066-7 (P.P.).

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Alice Pellerin & Christophe Thomazo

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Christophe Thomazo

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Conceptualization: A.P., C.T., M.A., P.P. Investigation: A.P. Funding acquisition: C.T., P.P. Supervision: C.T., M.A. Writing—original draft: A.P. Review and editing: A.P., C.T., M.A., V.B., E.S.R., C.R., P.P.

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Extended data figures and tables

Extended data fig. 1 sedimentological logs of the drill cores gt13 and gt16 with photographs of the main facies and sedimentary structures..

Arrows point to the stratigraphic top. Top left, conglomerate with oriented clasts and sandy matrix; middle left, alternations of siltstone and fine sandstone; bottom left and middle, syn-sedimentary, centimetric-scale faults within fine sandstone to siltstone. Top right, sandstone with wave ripples, framboidal pyrite (blue circles) and load casts; middle right, normally graded conglomerate with rounded quartz pebbles and sub-angular sedimentary clasts, grading to coarse sandstone; bottom right, flat-pebble conglomerate comprising elongated and deformed intraformational clasts.

Extended Data Fig. 2 Cross-plots for drill cores GT13 (orange) and GT16 (red).

TOC (wt%) versus TN (ppm); δ 15 N (‰ versus air) versus TN (ppm); δ 15 N (‰ versus air) versus TOC/TN ratio and δ 13 C org (‰ versus PDB) versus δ 15 N (‰ versus air).

Extended Data Fig. 3 Maps illustrating the location of the Carajás Basin.

a , Main tectonic elements of South America 84 . b , Geological map of the Carajás Basin 85 . c , Location of the drill cores.

Extended Data Fig. 4 Main sedimentary units of the Carajás Basin and age constraints.

1: ref.  86 ; 2,3: ref.  87 ; 4: ref.  88 ; 5: ref.  6 ; 6: ref.  28 .

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Pellerin, A., Thomazo, C., Ader, M. et al. Neoarchaean oxygen-based nitrogen cycle en route to the Great Oxidation Event. Nature (2024). https://doi.org/10.1038/s41586-024-07842-x

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Received : 31 August 2023

Accepted : 17 July 2024

Published : 21 August 2024

DOI : https://doi.org/10.1038/s41586-024-07842-x

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