greater than (>) less than (<)
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
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
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
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.
H 0 and H a are contradictory.
by Marco Taboga , PhD
In a test of hypothesis , a sample of data is used to decide whether to reject or not to reject a hypothesis about the probability distribution from which the sample was extracted.
The hypothesis is called the null hypothesis, or simply "the null".
Table of contents
How is the null hypothesis tested, example 1 - proportion of defective items, measurement, test statistic, critical region, interpretation, example 2 - reliability of a production plant, rejection and failure to reject, not rejecting and accepting are not the same thing, failure to reject can be due to lack of power, rejections are easier to interpret, but be careful, takeaways - how to (and not to) formulate a null hypothesis, more examples, more details, best practices in science, keep reading the glossary.
Formulating null hypotheses and subjecting them to statistical testing is one of the workhorses of the scientific method.
Scientists in all fields make conjectures about the phenomena they study, translate them into null hypotheses and gather data to test them.
This process resembles a trial:
the defendant (the null hypothesis) is accused of being guilty (wrong);
evidence (data) is gathered in order to prove the defendant guilty (reject the null);
if there is evidence beyond any reasonable doubt, the defendant is found guilty (the null is rejected);
otherwise, the defendant is found not guilty (the null is not rejected).
Keep this analogy in mind because it helps to better understand statistical tests, their limitations, use and misuse, and frequent misinterpretation.
Before collecting the data:
we decide how to summarize the relevant characteristics of the sample data in a single number, the so-called test statistic ;
we derive the probability distribution of the test statistic under the hypothesis that the null is true (the data is regarded as random; therefore, the test statistic is a random variable);
we decide what probability of incorrectly rejecting the null we are willing to tolerate (the level of significance , or size of the test ); the level of significance is typically a small number, such as 5% or 1%.
we choose one or more intervals of values (collectively called rejection region) such that the probability that the test statistic falls within these intervals is equal to the desired level of significance; the rejection region is often a tail of the distribution of the test statistic (one-tailed test) or the union of the left and right tails (two-tailed test).
Then, the data is collected and used to compute the value of the test statistic.
A decision is taken as follows:
if the test statistic falls within the rejection region, then the null hypothesis is rejected;
otherwise, it is not rejected.
We now make two examples of practical problems that lead to formulate and test a null hypothesis.
A new method is proposed to produce light bulbs.
The proponents claim that it produces less defective bulbs than the method currently in use.
To check the claim, we can set up a statistical test as follows.
We keep the light bulbs on for 10 consecutive days, and then we record whether they are still working at the end of the test period.
The probability that a light bulb produced with the new method is still working at the end of the test period is the same as that of a light bulb produced with the old method.
100 light bulbs are tested:
50 of them are produced with the new method (group A)
the remaining 50 are produced with the old method (group B).
The final data comprises 100 observations of:
an indicator variable which is equal to 1 if the light bulb is still working at the end of the test period and 0 otherwise;
a categorical variable that records the group (A or B) to which each light bulb belongs.
We use the data to compute the proportions of working light bulbs in groups A and B.
The proportions are estimates of the probabilities of not being defective, which are equal for the two groups under the null hypothesis.
We then compute a z-statistic (see here for details) by:
taking the difference between the proportion in group A and the proportion in group B;
standardizing the difference:
we subtract the expected value (which is zero under the null hypothesis);
we divide by the standard deviation (it can be derived analytically).
The distribution of the z-statistic can be approximated by a standard normal distribution .
We decide that the level of confidence must be 5%. In other words, we are going to tolerate a 5% probability of incorrectly rejecting the null hypothesis.
The critical region is the right 5%-tail of the normal distribution, that is, the set of all values greater than 1.645 (see the glossary entry on critical values if you are wondering how this value was obtained).
If the test statistic is greater than 1.645, then the null hypothesis is rejected; otherwise, it is not rejected.
A rejection is interpreted as significant evidence that the new production method produces less defective items; failure to reject is interpreted as insufficient evidence that the new method is better.
A production plant incurs high costs when production needs to be halted because some machinery fails.
The plant manager has decided that he is not willing to tolerate more than one halt per year on average.
If the expected number of halts per year is greater than 1, he will make new investments in order to improve the reliability of the plant.
A statistical test is set up as follows.
The reliability of the plant is measured by the number of halts.
The number of halts in a year is assumed to have a Poisson distribution with expected value equal to 1 (using the Poisson distribution is common in reliability testing).
The manager cannot wait more than one year before taking a decision.
There will be a single datum at his disposal: the number of halts observed during one year.
The number of halts is used as a test statistic. By assumption, it has a Poisson distribution under the null hypothesis.
The manager decides that the probability of incorrectly rejecting the null can be at most 10%.
A Poisson random variable with expected value equal to 1 takes values:
larger than 1 with probability 26.42%;
larger than 2 with probability 8.03%.
Therefore, it is decided that the critical region will be the set of all values greater than or equal to 3.
If the test statistic is strictly greater than or equal to 3, then the null is rejected; otherwise, it is not rejected.
A rejection is interpreted as significant evidence that the production plant is not reliable enough (the average number of halts per year is significantly larger than tolerated).
Failure to reject is interpreted as insufficient evidence that the plant is unreliable.
This section discusses the main problems that arise in the interpretation of the outcome of a statistical test (reject / not reject).
When the test statistic does not fall within the critical region, then we do not reject the null hypothesis.
Does this mean that we accept the null? Not really.
In general, failure to reject does not constitute, per se, strong evidence that the null hypothesis is true .
Remember the analogy between hypothesis testing and a criminal trial. In a trial, when the defendant is declared not guilty, this does not mean that the defendant is innocent. It only means that there was not enough evidence (not beyond any reasonable doubt) against the defendant.
In turn, lack of evidence can be due:
either to the fact that the defendant is innocent ;
or to the fact that the prosecution has not been able to provide enough evidence against the defendant, even if the latter is guilty .
This is the very reason why courts do not declare defendants innocent, but they use the locution "not guilty".
In a similar fashion, statisticians do not say that the null hypothesis has been accepted, but they say that it has not been rejected.
To better understand why failure to reject does not in general constitute strong evidence that the null hypothesis is true, we need to use the concept of statistical power .
The power of a test is the probability (calculated ex-ante, i.e., before observing the data) that the null will be rejected when another hypothesis (called the alternative hypothesis ) is true.
Let's consider the first of the two examples above (the production of light bulbs).
In that example, the null hypothesis is: the probability that a light bulb is defective does not decrease after introducing a new production method.
Let's make the alternative hypothesis that the probability of being defective is 1% smaller after changing the production process (assume that a 1% decrease is considered a meaningful improvement by engineers).
How much is the ex-ante probability of rejecting the null if the alternative hypothesis is true?
If this probability (the power of the test) is small, then it is very likely that we will not reject the null even if it is wrong.
If we use the analogy with criminal trials, low power means that most likely the prosecution will not be able to provide sufficient evidence, even if the defendant is guilty.
Thus, in the case of lack of power, failure to reject is almost meaningless (it was anyway highly likely).
This is why, before performing a test, it is good statistical practice to compute its power against a relevant alternative .
If the power is found to be too small, there are usually remedies. In particular, statistical power can usually be increased by increasing the sample size (see, e.g., the lecture on hypothesis tests about the mean ).
As we have explained above, interpreting a failure to reject the null hypothesis is not always straightforward. Instead, interpreting a rejection is somewhat easier.
When we reject the null, we know that the data has provided a lot of evidence against the null. In other words, it is unlikely (how unlikely depends on the size of the test) that the null is true given the data we have observed.
There is an important caveat though. The null hypothesis is often made up of several assumptions, including:
the main assumption (the one we are testing);
other assumptions (e.g., technical assumptions) that we need to make in order to set up the hypothesis test.
For instance, in Example 2 above (reliability of a production plant), the main assumption is that the expected number of production halts per year is equal to 1. But there is also a technical assumption: the number of production halts has a Poisson distribution.
It must be kept in mind that a rejection is always a joint rejection of the main assumption and all the other assumptions .
Therefore, we should always ask ourselves whether the null has been rejected because the main assumption is wrong or because the other assumptions are violated.
In the case of Example 2 above, is a rejection of the null due to the fact that the expected number of halts is greater than 1 or is it due to the fact that the distribution of the number of halts is very different from a Poisson distribution?
When we suspect that a rejection is due to the inappropriateness of some technical assumption (e.g., assuming a Poisson distribution in the example), we say that the rejection could be due to misspecification of the model .
The right thing to do when these kind of suspicions arise is to conduct so-called robustness checks , that is, to change the technical assumptions and carry out the test again.
In our example, we could re-run the test by assuming a different probability distribution for the number of halts (e.g., a negative binomial or a compound Poisson - do not worry if you have never heard about these distributions).
If we keep obtaining a rejection of the null even after changing the technical assumptions several times, the we say that our rejection is robust to several different specifications of the model .
What are the main practical implications of everything we have said thus far? How does the theory above help us to set up and test a null hypothesis?
What we said can be summarized in the following guiding principles:
A test of hypothesis is like a criminal trial and you are the prosecutor . You want to find evidence that the defendant (the null hypothesis) is guilty. Your job is not to prove that the defendant is innocent. If you find yourself hoping that the defendant is found not guilty (i.e., the null is not rejected) then something is wrong with the way you set up the test. Remember: you are the prosecutor.
Compute the power of your test against one or more relevant alternative hypotheses. Do not run a test if you know ex-ante that it is unlikely to reject the null when the alternative hypothesis is true.
Beware of technical assumptions that you add to the main assumption you want to test. Make robustness checks in order to verify that the outcome of the test is not biased by model misspecification.
More examples of null hypotheses and how to test them can be found in the following lectures.
Where the example is found | Null hypothesis |
---|---|
The mean of a normal distribution is equal to a certain value | |
The variance of a normal distribution is equal to a certain value | |
A vector of parameters estimated by MLE satisfies a set of linear or non-linear restrictions | |
A regression coefficient is equal to a certain value |
The lecture on Hypothesis testing provides a more detailed mathematical treatment of null hypotheses and how they are tested.
This lecture on the null hypothesis was featured in Stanford University's Best practices in science .
Previous entry: Normal equations
Next entry: Parameter
Please cite as:
Taboga, Marco (2021). "Null hypothesis", Lectures on probability theory and mathematical statistics. Kindle Direct Publishing. Online appendix. https://www.statlect.com/glossary/null-hypothesis.
Most of the learning materials found on this website are now available in a traditional textbook format.
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A null hypothesis is a statistical concept suggesting no significant difference or relationship between measured variables. It’s the default assumption unless empirical evidence proves otherwise.
The null hypothesis states no relationship exists between the two variables being studied (i.e., one variable does not affect the other).
The null hypothesis is the statement that a researcher or an investigator wants to disprove.
Testing the null hypothesis can tell you whether your results are due to the effects of manipulating the dependent variable or due to random chance.
Null hypotheses (H0) start as research questions that the investigator rephrases as statements indicating no effect or relationship between the independent and dependent variables.
It is a default position that your research aims to challenge or confirm.
There is no significant difference in weight loss between individuals who exercise daily and those who do not.
Research Question | Null Hypothesis |
---|---|
Do teenagers use cell phones more than adults? | Teenagers and adults use cell phones the same amount. |
Do tomato plants exhibit a higher rate of growth when planted in compost rather than in soil? | Tomato plants show no difference in growth rates when planted in compost rather than soil. |
Does daily meditation decrease the incidence of depression? | Daily meditation does not decrease the incidence of depression. |
Does daily exercise increase test performance? | There is no relationship between daily exercise time and test performance. |
Does the new vaccine prevent infections? | The vaccine does not affect the infection rate. |
Does flossing your teeth affect the number of cavities? | Flossing your teeth has no effect on the number of cavities. |
We reject the null hypothesis when the data provide strong enough evidence to conclude that it is likely incorrect. This often occurs when the p-value (probability of observing the data given the null hypothesis is true) is below a predetermined significance level.
If the collected data does not meet the expectation of the null hypothesis, a researcher can conclude that the data lacks sufficient evidence to back up the null hypothesis, and thus the null hypothesis is rejected.
Rejecting the null hypothesis means that a relationship does exist between a set of variables and the effect is statistically significant ( p > 0.05).
If the data collected from the random sample is not statistically significance , then the null hypothesis will be accepted, and the researchers can conclude that there is no relationship between the variables.
You need to perform a statistical test on your data in order to evaluate how consistent it is with the null hypothesis. A p-value is one statistical measurement used to validate a hypothesis against observed data.
Calculating the p-value is a critical part of null-hypothesis significance testing because it quantifies how strongly the sample data contradicts the null hypothesis.
The level of statistical significance is often expressed as a p -value between 0 and 1. The smaller the p-value, the stronger the evidence that you should reject the null hypothesis.
Usually, a researcher uses a confidence level of 95% or 99% (p-value of 0.05 or 0.01) as general guidelines to decide if you should reject or keep the null.
When your p-value is less than or equal to your significance level, you reject the null hypothesis.
In other words, smaller p-values are taken as stronger evidence against the null hypothesis. Conversely, when the p-value is greater than your significance level, you fail to reject the null hypothesis.
In this case, the sample data provides insufficient data to conclude that the effect exists in the population.
Because you can never know with complete certainty whether there is an effect in the population, your inferences about a population will sometimes be incorrect.
When you incorrectly reject the null hypothesis, it’s called a type I error. When you incorrectly fail to reject it, it’s called a type II error.
The reason we do not say “accept the null” is because we are always assuming the null hypothesis is true and then conducting a study to see if there is evidence against it. And, even if we don’t find evidence against it, a null hypothesis is not accepted.
A lack of evidence only means that you haven’t proven that something exists. It does not prove that something doesn’t exist.
It is risky to conclude that the null hypothesis is true merely because we did not find evidence to reject it. It is always possible that researchers elsewhere have disproved the null hypothesis, so we cannot accept it as true, but instead, we state that we failed to reject the null.
One can either reject the null hypothesis, or fail to reject it, but can never accept it.
We can never prove with 100% certainty that a hypothesis is true; We can only collect evidence that supports a theory. However, testing a hypothesis can set the stage for rejecting or accepting this hypothesis within a certain confidence level.
The null hypothesis is useful because it can tell us whether the results of our study are due to random chance or the manipulation of a variable (with a certain level of confidence).
A null hypothesis is rejected if the measured data is significantly unlikely to have occurred and a null hypothesis is accepted if the observed outcome is consistent with the position held by the null hypothesis.
Rejecting the null hypothesis sets the stage for further experimentation to see if a relationship between two variables exists.
Hypothesis testing is a critical part of the scientific method as it helps decide whether the results of a research study support a particular theory about a given population. Hypothesis testing is a systematic way of backing up researchers’ predictions with statistical analysis.
It helps provide sufficient statistical evidence that either favors or rejects a certain hypothesis about the population parameter.
The null (H0) and alternative (Ha or H1) hypotheses are two competing claims that describe the effect of the independent variable on the dependent variable. They are mutually exclusive, which means that only one of the two hypotheses can be true.
While the null hypothesis states that there is no effect in the population, an alternative hypothesis states that there is statistical significance between two variables.
The goal of hypothesis testing is to make inferences about a population based on a sample. In order to undertake hypothesis testing, you must express your research hypothesis as a null and alternative hypothesis. Both hypotheses are required to cover every possible outcome of the study.
The alternative hypothesis is the complement to the null hypothesis. The null hypothesis states that there is no effect or no relationship between variables, while the alternative hypothesis claims that there is an effect or relationship in the population.
It is the claim that you expect or hope will be true. The null hypothesis and the alternative hypothesis are always mutually exclusive, meaning that only one can be true at a time.
One major problem with the null hypothesis is that researchers typically will assume that accepting the null is a failure of the experiment. However, accepting or rejecting any hypothesis is a positive result. Even if the null is not refuted, the researchers will still learn something new.
We can either reject or fail to reject a null hypothesis, but never accept it. If your test fails to detect an effect, this is not proof that the effect doesn’t exist. It just means that your sample did not have enough evidence to conclude that it exists.
We can’t accept a null hypothesis because a lack of evidence does not prove something that does not exist. Instead, we fail to reject it.
Failing to reject the null indicates that the sample did not provide sufficient enough evidence to conclude that an effect exists.
If the p-value is greater than the significance level, then you fail to reject the null hypothesis.
A hypothesis test can either contain an alternative directional hypothesis or a non-directional alternative hypothesis. A directional hypothesis is one that contains the less than (“<“) or greater than (“>”) sign.
A nondirectional hypothesis contains the not equal sign (“≠”). However, a null hypothesis is neither directional nor non-directional.
A null hypothesis is a prediction that there will be no change, relationship, or difference between two variables.
The directional hypothesis or nondirectional hypothesis would then be considered alternative hypotheses to the null hypothesis.
Gill, J. (1999). The insignificance of null hypothesis significance testing. Political research quarterly , 52 (3), 647-674.
Krueger, J. (2001). Null hypothesis significance testing: On the survival of a flawed method. American Psychologist , 56 (1), 16.
Masson, M. E. (2011). A tutorial on a practical Bayesian alternative to null-hypothesis significance testing. Behavior research methods , 43 , 679-690.
Nickerson, R. S. (2000). Null hypothesis significance testing: a review of an old and continuing controversy. Psychological methods , 5 (2), 241.
Rozeboom, W. W. (1960). The fallacy of the null-hypothesis significance test. Psychological bulletin , 57 (5), 416.
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A null hypothesis is a general assertion or default position that there is no relationship or effect between two measured phenomena.
It’s a critical part of statistics, data analysis, and the scientific method . This concept forms the basis of testing statistical significance and allows researchers to be objective in their conclusions.
A null hypothesis helps to eliminate biases and ensures that the observed results are not due to chance. The rejection or failure to reject the null hypothesis helps in guiding the course of research.
The null hypothesis, often denoted as H 0 , is the hypothesis in a statistical test which proposes no statistical significance exists in a set of observed data.
It hypothesizes that any kind of difference or importance you see in a data set is due to chance.
Null hypotheses are typically proposed to be negated or disproved by statistical tests, paving way for the acceptance of an alternate hypothesis.
Importantly, a null hypothesis cannot be proven true; it can only be supported or rejected with confidence.
Should evidence – via statistical analysis – contradict the null hypothesis, it is rejected in favor of an alternative hypothesis. In essence, the null hypothesis is a tool to challenge and disprove that there is no effect or relationship between variables.
I like to show this video to my students which outlines a null hypothesis really clearly and engagingly, using real life studies by research students! The into explains it really well:
“There’s an idea in science called the null hypothesis and it works like this: when you’re setting out to prove a theory, your default answer should be “it’s not going to work” and you have to convince the world otherwise through clear results”
Here’s the full video:
An alternative hypothesis is the direct contrast to the null hypothesis. It posits that there is a statistically significant relationship or effect between the variables being observed.
If the null hypothesis is rejected based on the test data, the alternative hypothesis is accepted.
Importantly, while the null hypothesis is typically a statement of ‘no effect’ or ‘no difference,’ the alternative hypothesis states that there is an effect or difference.
Comprehension Checkpoint: How does the null hypothesis help to ensure that research is objective and unbiased?
A statement of no effect or no relationship | A statement that suggests there is an effect or relationship | |
H | H or H | |
The average time to recover using Drug A is the same as with Drug B | The average time to recover using Drug A is less than with Drug B | |
No statistical significance between observed data | Statistical significance exists between observed data | |
The observed result is due to chance | The observed result is due to the effect or relationship |
The null hypothesis plays a critical role in numerous research settings, promoting objectivity and ensuring findings aren’t due to random chance.
In all these areas, the null hypothesis helps minimize bias, enabling researchers to support their findings with statistically significant data. It forms the backbone of many scientific research methodologies , promoting a disciplined approach to uncovering new knowledge.
See More Hypothesis Examples Here
The null hypothesis is a cornerstone of statistical analysis and empirical research. It serves as a starting point for investigations, providing a baseline premise that the observed effects are due to chance. By understanding and applying the concept of the null hypothesis, researchers can test the validity of their assumptions, making their findings more robust and reliable. In essence, the null hypothesis ensures that the scientific exploration remains objective, systematic, and free from unintended bias.
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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.
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.
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.
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.
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.
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.
In mathematics, Statistics deals with the study of research and surveys on the numerical data. For taking surveys, we have to define the hypothesis. Generally, there are two types of hypothesis. One is a null hypothesis, and another is an alternative hypothesis .
In probability and statistics, the null hypothesis is a comprehensive statement or default status that there is zero happening or nothing happening. For example, there is no connection among groups or no association between two measured events. It is generally assumed here that the hypothesis is true until any other proof has been brought into the light to deny the hypothesis. Let us learn more here with definition, symbol, principle, types and example, in this article.
Table of contents:
The null hypothesis is a kind of hypothesis which explains the population parameter whose purpose is to test the validity of the given experimental data. This hypothesis is either rejected or not rejected based on the viability of the given population or sample . In other words, the null hypothesis is a hypothesis in which the sample observations results from the chance. It is said to be a statement in which the surveyors wants to examine the data. It is denoted by H 0 .
In statistics, the null hypothesis is usually denoted by letter H with subscript ‘0’ (zero), such that H 0 . It is pronounced as H-null or H-zero or H-nought. At the same time, the alternative hypothesis expresses the observations determined by the non-random cause. It is represented by H 1 or H a .
The principle followed for null hypothesis testing is, collecting the data and determining the chances of a given set of data during the study on some random sample, assuming that the null hypothesis is true. In case if the given data does not face the expected null hypothesis, then the outcome will be quite weaker, and they conclude by saying that the given set of data does not provide strong evidence against the null hypothesis because of insufficient evidence. Finally, the researchers tend to reject that.
Here, the hypothesis test formulas are given below for reference.
The formula for the null hypothesis is:
H 0 : p = p 0
The formula for the alternative hypothesis is:
H a = p >p 0 , < p 0 ≠ p 0
The formula for the test static is:
Remember that, p 0 is the null hypothesis and p – hat is the sample proportion.
Also, read:
There are different types of hypothesis. They are:
Simple Hypothesis
It completely specifies the population distribution. In this method, the sampling distribution is the function of the sample size.
Composite Hypothesis
The composite hypothesis is one that does not completely specify the population distribution.
Exact Hypothesis
Exact hypothesis defines the exact value of the parameter. For example μ= 50
Inexact Hypothesis
This type of hypothesis does not define the exact value of the parameter. But it denotes a specific range or interval. For example 45< μ <60
Sometimes the null hypothesis is rejected too. If this hypothesis is rejected means, that research could be invalid. Many researchers will neglect this hypothesis as it is merely opposite to the alternate hypothesis. It is a better practice to create a hypothesis and test it. The goal of researchers is not to reject the hypothesis. But it is evident that a perfect statistical model is always associated with the failure to reject the null hypothesis.
The null hypothesis says there is no correlation between the measured event (the dependent variable) and the independent variable. We don’t have to believe that the null hypothesis is true to test it. On the contrast, you will possibly assume that there is a connection between a set of variables ( dependent and independent).
The null hypothesis is rejected using the P-value approach. If the P-value is less than or equal to the α, there should be a rejection of the null hypothesis in favour of the alternate hypothesis. In case, if P-value is greater than α, the null hypothesis is not rejected.
Now, let us discuss the difference between the null hypothesis and the alternative hypothesis.
|
| |
1 | The null hypothesis is a statement. There exists no relation between two variables | Alternative hypothesis a statement, there exists some relationship between two measured phenomenon |
2 | Denoted by H | Denoted by H |
3 | The observations of this hypothesis are the result of chance | The observations of this hypothesis are the result of real effect |
4 | The mathematical formulation of the null hypothesis is an equal sign | The mathematical formulation alternative hypothesis is an inequality sign such as greater than, less than, etc. |
Here, some of the examples of the null hypothesis are given below. Go through the below ones to understand the concept of the null hypothesis in a better way.
If a medicine reduces the risk of cardiac stroke, then the null hypothesis should be “the medicine does not reduce the chance of cardiac stroke”. This testing can be performed by the administration of a drug to a certain group of people in a controlled way. If the survey shows that there is a significant change in the people, then the hypothesis is rejected.
Few more examples are:
1). Are there is 100% chance of getting affected by dengue?
Ans: There could be chances of getting affected by dengue but not 100%.
2). Do teenagers are using mobile phones more than grown-ups to access the internet?
Ans: Age has no limit on using mobile phones to access the internet.
3). Does having apple daily will not cause fever?
Ans: Having apple daily does not assure of not having fever, but increases the immunity to fight against such diseases.
4). Do the children more good in doing mathematical calculations than grown-ups?
Ans: Age has no effect on Mathematical skills.
In many common applications, the choice of the null hypothesis is not automated, but the testing and calculations may be automated. Also, the choice of the null hypothesis is completely based on previous experiences and inconsistent advice. The choice can be more complicated and based on the variety of applications and the diversity of the objectives.
The main limitation for the choice of the null hypothesis is that the hypothesis suggested by the data is based on the reasoning which proves nothing. It means that if some hypothesis provides a summary of the data set, then there would be no value in the testing of the hypothesis on the particular set of data.
What is meant by the null hypothesis.
In Statistics, a null hypothesis is a type of hypothesis which explains the population parameter whose purpose is to test the validity of the given experimental data.
Hypothesis testing is defined as a form of inferential statistics, which allows making conclusions from the entire population based on the sample representative.
The null hypothesis is either accepted or rejected in terms of the given data. If P-value is less than α, then the null hypothesis is rejected in favor of the alternative hypothesis, and if the P-value is greater than α, then the null hypothesis is accepted in favor of the alternative hypothesis.
The importance of the null hypothesis is that it provides an approximate description of the phenomena of the given data. It allows the investigators to directly test the relational statement in a research study.
If the result of the chi-square test is bigger than the critical value in the table, then the data does not fit the model, which represents the rejection of the null hypothesis.
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Null Hypothesis , often denoted as H 0, is a foundational concept in statistical hypothesis testing. It represents an assumption that no significant difference, effect, or relationship exists between variables within a population. It serves as a baseline assumption, positing no observed change or effect occurring. The null is t he truth or falsity of an idea in analysis.
In this article, we will discuss the null hypothesis in detail, along with some solved examples and questions on the null hypothesis.
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Null hypothesis symbol, formula of null hypothesis, types of null hypothesis, null hypothesis examples, principle of null hypothesis, how do you find null hypothesis, null hypothesis in statistics, null hypothesis and alternative hypothesis, null hypothesis and alternative hypothesis examples, null hypothesis – practice problems.
Null Hypothesis in statistical analysis suggests the absence of statistical significance within a specific set of observed data. Hypothesis testing, using sample data, evaluates the validity of this hypothesis. Commonly denoted as H 0 or simply “null,” it plays an important role in quantitative analysis, examining theories related to markets, investment strategies, or economies to determine their validity.
Null Hypothesis represents a default position, often suggesting no effect or difference, against which researchers compare their experimental results. The Null Hypothesis, often denoted as H 0 asserts a default assumption in statistical analysis. It posits no significant difference or effect, serving as a baseline for comparison in hypothesis testing.
The null Hypothesis is represented as H 0 , the Null Hypothesis symbolizes the absence of a measurable effect or difference in the variables under examination.
Certainly, a simple example would be asserting that the mean score of a group is equal to a specified value like stating that the average IQ of a population is 100.
The Null Hypothesis is typically formulated as a statement of equality or absence of a specific parameter in the population being studied. It provides a clear and testable prediction for comparison with the alternative hypothesis. The formulation of the Null Hypothesis typically follows a concise structure, stating the equality or absence of a specific parameter in the population.
H 0 : μ 1 = μ 2
This asserts that there is no significant difference between the means of two populations or groups.
H 0 : p 1 − p 2 = 0
This suggests no significant difference in proportions between two populations or conditions.
H 0 : σ 1 = σ 2
This states that there’s no significant difference in variances between groups or populations.
H 0 : Variables are independent
This asserts that there’s no association or relationship between categorical variables.
Null Hypotheses vary including simple and composite forms, each tailored to the complexity of the research question. Understanding these types is pivotal for effective hypothesis testing.
The Equality Null Hypothesis, also known as the Simple Null Hypothesis, is a fundamental concept in statistical hypothesis testing that assumes no difference, effect or relationship between groups, conditions or populations being compared.
In some studies, the focus might be on demonstrating that a new treatment or method is not significantly worse than the standard or existing one.
The concept of a superiority null hypothesis comes into play when a study aims to demonstrate that a new treatment, method, or intervention is significantly better than an existing or standard one.
In certain statistical tests, such as chi-square tests for independence, the null hypothesis assumes no association or independence between categorical variables.
In tests like ANOVA (Analysis of Variance), the null hypothesis suggests that there’s no difference in population means across different groups.
The principle of the null hypothesis is a fundamental concept in statistical hypothesis testing. It involves making an assumption about the population parameter or the absence of an effect or relationship between variables.
In essence, the null hypothesis (H 0 ) proposes that there is no significant difference, effect, or relationship between variables. It serves as a starting point or a default assumption that there is no real change, no effect or no difference between groups or conditions.
The null hypothesis is usually formulated to be tested against an alternative hypothesis (H 1 or H [Tex]\alpha [/Tex] ) which suggests that there is an effect, difference or relationship present in the population.
Rejecting the Null Hypothesis occurs when statistical evidence suggests a significant departure from the assumed baseline. It implies that there is enough evidence to support the alternative hypothesis, indicating a meaningful effect or difference. Null Hypothesis rejection occurs when statistical evidence suggests a deviation from the assumed baseline, prompting a reconsideration of the initial hypothesis.
Identifying the Null Hypothesis involves defining the status quotient, asserting no effect and formulating a statement suitable for statistical analysis.
The Null Hypothesis is rejected when statistical tests indicate a significant departure from the expected outcome, leading to the consideration of alternative hypotheses. It occurs when statistical evidence suggests a deviation from the assumed baseline, prompting a reconsideration of the initial hypothesis.
In statistical hypothesis testing, researchers begin by stating the null hypothesis, often based on theoretical considerations or previous research. The null hypothesis is then tested against an alternative hypothesis (Ha), which represents the researcher’s claim or the hypothesis they seek to support.
The process of hypothesis testing involves collecting sample data and using statistical methods to assess the likelihood of observing the data if the null hypothesis were true. This assessment is typically done by calculating a test statistic, which measures the difference between the observed data and what would be expected under the null hypothesis.
In the realm of hypothesis testing, the null hypothesis (H 0 ) and alternative hypothesis (H₁ or Ha) play critical roles. The null hypothesis generally assumes no difference, effect, or relationship between variables, suggesting that any observed change or effect is due to random chance. Its counterpart, the alternative hypothesis, asserts the presence of a significant difference, effect, or relationship between variables, challenging the null hypothesis. These hypotheses are formulated based on the research question and guide statistical analyses.
The null hypothesis (H 0 ) serves as the baseline assumption in statistical testing, suggesting no significant effect, relationship, or difference within the data. It often proposes that any observed change or correlation is merely due to chance or random variation. Conversely, the alternative hypothesis (H 1 or Ha) contradicts the null hypothesis, positing the existence of a genuine effect, relationship or difference in the data. It represents the researcher’s intended focus, seeking to provide evidence against the null hypothesis and support for a specific outcome or theory. These hypotheses form the crux of hypothesis testing, guiding the assessment of data to draw conclusions about the population being studied.
Criteria | Null Hypothesis | Alternative Hypothesis |
---|---|---|
Definition | Assumes no effect or difference | Asserts a specific effect or difference |
Symbol | H | H (or Ha) |
Formulation | States equality or absence of parameter | States a specific value or relationship |
Testing Outcome | Rejected if evidence of a significant effect | Accepted if evidence supports the hypothesis |
Let’s envision a scenario where a researcher aims to examine the impact of a new medication on reducing blood pressure among patients. In this context:
Null Hypothesis (H 0 ): “The new medication does not produce a significant effect in reducing blood pressure levels among patients.”
Alternative Hypothesis (H 1 or Ha): “The new medication yields a significant effect in reducing blood pressure levels among patients.”
The null hypothesis implies that any observed alterations in blood pressure subsequent to the medication’s administration are a result of random fluctuations rather than a consequence of the medication itself. Conversely, the alternative hypothesis contends that the medication does indeed generate a meaningful alteration in blood pressure levels, distinct from what might naturally occur or by random chance.
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Example 1: A researcher claims that the average time students spend on homework is 2 hours per night.
Null Hypothesis (H 0 ): The average time students spend on homework is equal to 2 hours per night. Data: A random sample of 30 students has an average homework time of 1.8 hours with a standard deviation of 0.5 hours. Test Statistic and Decision: Using a t-test, if the calculated t-statistic falls within the acceptance region, we fail to reject the null hypothesis. If it falls in the rejection region, we reject the null hypothesis. Conclusion: Based on the statistical analysis, we fail to reject the null hypothesis, suggesting that there is not enough evidence to dispute the claim of the average homework time being 2 hours per night.
Example 2: A company asserts that the error rate in its production process is less than 1%.
Null Hypothesis (H 0 ): The error rate in the production process is 1% or higher. Data: A sample of 500 products shows an error rate of 0.8%. Test Statistic and Decision: Using a z-test, if the calculated z-statistic falls within the acceptance region, we fail to reject the null hypothesis. If it falls in the rejection region, we reject the null hypothesis. Conclusion: The statistical analysis supports rejecting the null hypothesis, indicating that there is enough evidence to dispute the company’s claim of an error rate of 1% or higher.
Q1. A researcher claims that the average time spent by students on homework is less than 2 hours per day. Formulate the null hypothesis for this claim?
Q2. A manufacturing company states that their new machine produces widgets with a defect rate of less than 5%. Write the null hypothesis to test this claim?
Q3. An educational institute believes that their online course completion rate is at least 60%. Develop the null hypothesis to validate this assertion?
Q4. A restaurant claims that the waiting time for customers during peak hours is not more than 15 minutes. Formulate the null hypothesis for this claim?
Q5. A study suggests that the mean weight loss after following a specific diet plan for a month is more than 8 pounds. Construct the null hypothesis to evaluate this statement?
The null hypothesis (H 0 ) and alternative hypothesis (H a ) are fundamental concepts in statistical hypothesis testing. The null hypothesis represents the default assumption, stating that there is no significant effect, difference, or relationship between variables. It serves as the baseline against which the alternative hypothesis is tested. In contrast, the alternative hypothesis represents the researcher’s hypothesis or the claim to be tested, suggesting that there is a significant effect, difference, or relationship between variables. The relationship between the null and alternative hypotheses is such that they are complementary, and statistical tests are conducted to determine whether the evidence from the data is strong enough to reject the null hypothesis in favor of the alternative hypothesis. This decision is based on the strength of the evidence and the chosen level of significance. Ultimately, the choice between the null and alternative hypotheses depends on the specific research question and the direction of the effect being investigated.
What does null hypothesis stands for.
The null hypothesis, denoted as H 0 , is a fundamental concept in statistics used for hypothesis testing. It represents the statement that there is no effect or no difference, and it is the hypothesis that the researcher typically aims to provide evidence against.
A null hypothesis is formed based on the assumption that there is no significant difference or effect between the groups being compared or no association between variables being tested. It often involves stating that there is no relationship, no change, or no effect in the population being studied.
In statistical hypothesis testing, if the p-value (the probability of obtaining the observed results) is lower than the chosen significance level (commonly 0.05), we reject the null hypothesis. This suggests that the data provides enough evidence to refute the assumption made in the null hypothesis.
In research, the null hypothesis represents the default assumption or position that there is no significant difference or effect. Researchers often try to test this hypothesis by collecting data and performing statistical analyses to see if the observed results contradict the assumption.
The null hypothesis (H0) is the default assumption that there is no significant difference or effect. The alternative hypothesis (H1 or Ha) is the opposite, suggesting there is a significant difference, effect or relationship.
Rejecting the null hypothesis implies that there is enough evidence in the data to support the alternative hypothesis. In simpler terms, it suggests that there might be a significant difference, effect or relationship between the groups or variables being studied.
Formulating a null hypothesis often involves considering the research question and assuming that no difference or effect exists. It should be a statement that can be tested through data collection and statistical analysis, typically stating no relationship or no change between variables or groups.
The null hypothesis is commonly symbolized as H 0 in statistical notation.
The null hypothesis serves as a starting point for hypothesis testing, enabling researchers to assess if there’s enough evidence to reject it in favor of an alternative hypothesis.
Rejecting the null hypothesis implies that there is sufficient evidence to support an alternative hypothesis, suggesting a significant effect or relationship between variables.
Various statistical tests, such as t-tests or chi-square tests, are employed to evaluate the validity of the Null Hypothesis in different scenarios.
Similar reads.
The alternative hypothesis.
Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and behavioral finance. Adam received his master's in economics from The New School for Social Research and his Ph.D. from the University of Wisconsin-Madison in sociology. He is a CFA charterholder as well as holding FINRA Series 7, 55 & 63 licenses. He currently researches and teaches economic sociology and the social studies of finance at the Hebrew University in Jerusalem.
A null hypothesis is a type of statistical hypothesis that proposes that no statistical significance exists in a set of given observations. Hypothesis testing is used to assess the credibility of a hypothesis by using sample data. Sometimes referred to simply as the “null,” it is represented as H 0 .
The null hypothesis, also known as “the conjecture,” is used in quantitative analysis to test theories about markets, investing strategies, and economies to decide if an idea is true or false.
Alex Dos Diaz / Investopedia
A gambler may be interested in whether a game of chance is fair. If it is, then the expected earnings per play come to zero for both players. If it is not, then the expected earnings are positive for one player and negative for the other.
To test whether the game is fair, the gambler collects earnings data from many repetitions of the game, calculates the average earnings from these data, then tests the null hypothesis that the expected earnings are not different from zero.
If the average earnings from the sample data are sufficiently far from zero, then the gambler will reject the null hypothesis and conclude the alternative hypothesis—namely, that the expected earnings per play are different from zero. If the average earnings from the sample data are near zero, then the gambler will not reject the null hypothesis, concluding instead that the difference between the average from the data and zero is explainable by chance alone.
A null hypothesis can only be rejected, not proven.
The null hypothesis assumes that any kind of difference between the chosen characteristics that you see in a set of data is due to chance. For example, if the expected earnings for the gambling game are truly equal to zero, then any difference between the average earnings in the data and zero is due to chance.
Analysts look to reject the null hypothesis because doing so is a strong conclusion. This requires evidence in the form of an observed difference that is too large to be explained solely by chance. Failing to reject the null hypothesis—that the results are explainable by chance alone—is a weak conclusion because it allows that while factors other than chance may be at work, they may not be strong enough for the statistical test to detect them.
An important point to note is that we are testing the null hypothesis because there is an element of doubt about its validity. Whatever information that is against the stated null hypothesis is captured in the alternative (alternate) hypothesis (H 1 ).
For the examples below, the alternative hypothesis would be:
In other words, the alternative hypothesis is a direct contradiction of the null hypothesis.
Here is a simple example: A school principal claims that students in her school score an average of seven out of 10 in exams. The null hypothesis is that the population mean is not 7.0. To test this null hypothesis, we record marks of, say, 30 students ( sample ) from the entire student population of the school (say, 300) and calculate the mean of that sample.
We can then compare the (calculated) sample mean to the (hypothesized) population mean of 7.0 and attempt to reject the null hypothesis. (The null hypothesis here—that the population mean is not 7.0—cannot be proved using the sample data. It can only be rejected.)
Take another example: The annual return of a particular mutual fund is claimed to be 8%. Assume that the mutual fund has been in existence for 20 years. The null hypothesis is that the mean return is not 8% for the mutual fund. We take a random sample of annual returns of the mutual fund for, say, five years (sample) and calculate the sample mean. We then compare the (calculated) sample mean to the (claimed) population mean (8%) to test the null hypothesis.
For the above examples, null hypotheses are:
For the purposes of determining whether to reject the null hypothesis (abbreviated H0), said hypothesis is assumed, for the sake of argument, to be true. Then the likely range of possible values of the calculated statistic (e.g., the average score on 30 students’ tests) is determined under this presumption (e.g., the range of plausible averages might range from 6.2 to 7.8 if the population mean is 7.0).
If the sample average is outside of this range, the null hypothesis is rejected. Otherwise, the difference is said to be “explainable by chance alone,” being within the range that is determined by chance alone.
As an example related to financial markets, assume Alice sees that her investment strategy produces higher average returns than simply buying and holding a stock . The null hypothesis states that there is no difference between the two average returns, and Alice is inclined to believe this until she can conclude contradictory results.
Refuting the null hypothesis would require showing statistical significance, which can be found by a variety of tests. The alternative hypothesis would state that the investment strategy has a higher average return than a traditional buy-and-hold strategy.
One tool that can determine the statistical significance of the results is the p-value. A p-value represents the probability that a difference as large or larger than the observed difference between the two average returns could occur solely by chance.
A p-value that is less than or equal to 0.05 often indicates whether there is evidence against the null hypothesis. If Alice conducts one of these tests, such as a test using the normal model, resulting in a significant difference between her returns and the buy-and-hold returns (the p-value is less than or equal to 0.05), she can then reject the null hypothesis and conclude the alternative hypothesis.
The analyst or researcher establishes a null hypothesis based on the research question or problem they are trying to answer. Depending on the question, the null may be identified differently. For example, if the question is simply whether an effect exists (e.g., does X influence Y?), the null hypothesis could be H 0 : X = 0. If the question is instead, is X the same as Y, the H 0 would be X = Y. If it is that the effect of X on Y is positive, H 0 would be X > 0. If the resulting analysis shows an effect that is statistically significantly different from zero, the null can be rejected.
In finance , a null hypothesis is used in quantitative analysis. It tests the premise of an investing strategy, the markets, or an economy to determine if it is true or false.
For instance, an analyst may want to see if two stocks, ABC and XYZ, are closely correlated. The null hypothesis would be ABC ≠ XYZ.
Statistical hypotheses are tested by a four-step process . The first is for the analyst to state the two hypotheses so that only one can be right. The second is to formulate an analysis plan, which outlines how the data will be evaluated. The third is to carry out the plan and physically analyze the sample data. The fourth and final step is to analyze the results and either reject the null hypothesis or claim that the observed differences are explainable by chance alone.
An alternative hypothesis is a direct contradiction of a null hypothesis. This means that if one of the two hypotheses is true, the other is false.
A null hypothesis states there is no difference between groups or relationship between variables. It is a type of statistical hypothesis and proposes that no statistical significance exists in a set of given observations. “Null” means nothing.
The null hypothesis is used in quantitative analysis to test theories about economies, investing strategies, and markets to decide if an idea is true or false. Hypothesis testing assesses the credibility of a hypothesis by using sample data. It is represented as H 0 and is sometimes simply known as “the null.”
Sage Publishing. “ Chapter 8: Introduction to Hypothesis Testing ,” Page 4.
Sage Publishing. “ Chapter 8: Introduction to Hypothesis Testing ,” Pages 4 to 7.
Sage Publishing. “ Chapter 8: Introduction to Hypothesis Testing ,” Page 7.
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H 0 (Null Hypothesis): Population parameter =, ≤, ≥ some value. H A (Alternative Hypothesis): Population parameter <, >, ≠ some value. Note that the null hypothesis always contains the equal sign. We interpret the hypotheses as follows: Null hypothesis: The sample data provides no evidence to support some claim being made by an individual.
To distinguish it from other hypotheses, the null hypothesis is written as H 0 (which is read as "H-nought," "H-null," or "H-zero"). A significance test is used to determine the likelihood that the results supporting the null hypothesis are not due to chance. A confidence level of 95% or 99% is common. Keep in mind, even if the confidence level is high, there is still a small chance the ...
It is one of two mutually exclusive hypotheses about a population in a hypothesis test. When your sample contains sufficient evidence, you can reject the null and conclude that the effect is statistically significant. Statisticians often denote the null hypothesis as H 0 or H A. Null Hypothesis H0: No effect exists in the population.
Revised on June 22, 2023. The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test: Null hypothesis (H0): There's no effect in the population. Alternative hypothesis (Ha or H1): There's an effect in the population. The effect is usually the effect of the ...
An example of the null hypothesis is that light color has no effect on plant growth. The null hypothesis (H 0) is the hypothesis that states there is no statistical difference between two sample sets. In other words, it assumes the independent variable does not have an effect on the dependent variable in a scientific experiment.
The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test: Null hypothesis (H0): There's no effect in the population. Alternative hypothesis (HA): There's an effect in the population. The effect is usually the effect of the independent variable on the dependent ...
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.
It is the opposite of your research hypothesis. The alternative hypothesis--that is, the research hypothesis--is the idea, phenomenon, observation that you want to prove. If you suspect that girls take longer to get ready for school than boys, then: Alternative: girls time > boys time. Null: girls time <= boys time.
Null Hypothesis Examples. "Hyperactivity is unrelated to eating sugar " is an example of a null hypothesis. If the hypothesis is tested and found to be false, using statistics, then a connection between hyperactivity and sugar ingestion may be indicated. A significance test is the most common statistical test used to establish confidence in a ...
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: a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.
Write a statistical null hypothesis as a mathematical equation, such as. μ 1 = μ 2 {\displaystyle \mu _ {1}=\mu _ {2}} if you're comparing group means. Adjust the format of your null hypothesis to match the statistical method you used to test it, such as using "mean" if you're comparing the mean between 2 groups.
Step 1: Figure out the hypothesis from the problem. The hypothesis is usually hidden in a word problem, and is sometimes a statement of what you expect to happen in the experiment. The hypothesis in the above question is "I expect the average recovery period to be greater than 8.2 weeks.". Step 2: Convert the hypothesis to math.
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.
The null hypothesis and the alternative hypothesis are types of conjectures used in statistical tests to make statistical inferences, which are formal methods of reaching conclusions and separating scientific claims from statistical noise.. The statement being tested in a test of statistical significance is called the null hypothesis. The test of significance is designed to assess the strength ...
In that example, the null hypothesis is: the probability that a light bulb is defective does not decrease after introducing a new production method. Let's make the alternative hypothesis that the probability of being defective is 1% smaller after changing the production process (assume that a 1% decrease is considered a meaningful improvement ...
When your p-value is less than or equal to your significance level, you reject the null hypothesis. In other words, smaller p-values are taken as stronger evidence against the null hypothesis. Conversely, when the p-value is greater than your significance level, you fail to reject the null hypothesis. In this case, the sample data provides ...
A null hypothesis is a general assertion or default position that there is no relationship or effect between two measured phenomena. It's a critical part of statistics, data analysis, and the scientific method. This concept forms the basis of testing statistical significance and allows researchers to be objective in their conclusions.
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 ...
A null hypothesis is a prediction that there is no relationship between variables. This is an important assumption for scientific inquiry as it requires any relationships between independent and dependent variables to be proven as opposed to assumed. The following are illustrative examples of a null hypothesis.
Examples; Null Hypothesis Definition. The null hypothesis is a kind of hypothesis which explains the population parameter whose purpose is to test the validity of the given experimental data. This hypothesis is either rejected or not rejected based on the viability of the given population or sample. In other words, the null hypothesis is a ...
A basic discussion on the null hypothesis, z-scores, and probability. Includes examples of the null hypothesis, one-tailed, and two-tailed tests. A coin is tossed and comes up tails ten times: is this just a random chance, or is an unfair coin being used? Learn when to reject the null hypothesis.
Null hypothesis, often denoted as H0, is a foundational concept in statistical hypothesis testing. It represents an assumption that no significant difference, effect, or relationship exists between variables within a population. Learn more about Null Hypothesis, its formula, symbol and example in this article
Null Hypothesis: A null hypothesis is a type of hypothesis used in statistics that proposes that no statistical significance exists in a set of given observations. The null hypothesis attempts to ...
Both are statistically significant, but the 0.001 example provides an even stronger case against the null hypothesis than the 0.04. The Bottom Line The p-value is used to measure the significance ...