Statistics LibreTexts
stats.libretexts.org › bookshelves › applied statistics › an introduction to psychological statistics (foster et al.) › 7: introduction to hypothesis testing
7.3: The Null Hypothesis - Statistics LibreTexts
January 8, 2024 - In general, the null hypothesis is the idea that nothing is going on: there is no effect of our treatment, no relation between our variables, and no difference in our sample mean from what we expected about the population mean.
Biztory
biztory.com › blog › 7-things-you-should-know-about-null-values
7 Things to know about NULL values - Biztory | Biztory
October 25, 2025 - The implications of believing that your NULL values are missing completely at random can catastrophic for the validity of your analysis. Just to illustrate this, I once saw a dataset where everybody under 18 had a salary NULL. Ignoring those rows would massively increase the mean age of the whole dataset. ... Also noteworthy: In some cases, especially when data is missing not a random, a boolean column indicating if something is NULL might be a good feature for a statistical ...
Where do NULL values come from in datasets and how to handle them?
It is fine to have null values in data sets. If something can be NULL you are saying, it’s okay to not have it. You just need to make sure that when operating on something that could be null you are checking before operating on it. If(possiblyNullValue) {console.log(“it’s not null”)} More on reddit.com
6
2
June 8, 2024How does NULL distribution is calculated and how p value is calculated for test vs null?
Your description of the null hypothesis is good. When calculating p-values, non-normal distributions don't need to be converted to the normal distribution. Calculating p-values involves calculating the area under the curve of a statistical distribution within a specific range. This range will typically be between your observed test statistic and infinity (although will sometimes be between your observed test statistic and 0). For example, if you observe an F statistic of 3.5, your p-value might be equal to the area under the curve of the F distribution for values >= 3.5. This principle applies to whatever statistical distribution you are interested in. More on reddit.com
4
2
April 19, 2023terminology - what is null hypothesis in a simple term? - Cross Validated
So when your value "fits in" the ... is, the null hypothesis. If your value is very extreme then you conclude that probably your value does not come from that distribution and you have yo reject your initial hypothesis/assumptions. Probably is not a very precise explanation but I think the intuition is there. ... Find the answer to your question by asking. Ask question ... See similar questions with these tags. 307 What is the meaning of p values and t values in statistical ... More on stats.stackexchange.com
Null hypothesis and Alternative Hypothesis
Hi! So, yours is actually a sophisticated question that masquerades as a simple one, so I'll try to answer this in a way that conveys the concept while perhaps alluding to some of its problems. At its heart, the null hypothesis is a sort of "straw man" that is defined by a researcher at the beginning of an experiment that usually represents a state of affairs that would be expected to occur if the researcher's proposal were false. Note that a null hypothesis is entirely imaginary, and it has nothing to do with the actual state of the world. It is contrived, usually to show that the actual state of the world is inconsistent with the null hypothesis. Suppose a researcher is trying to determine whether the heights of men and women are different. A suitable null hypothesis might be that the difference of the two population averages (height of men and height of women) is equal to zero. Then the researcher would conduct his or her experiment by measuring the heights of many men and women. When it comes time to draw a statistical conclusion, he or she will compute the probability that the observed data (the set of heights) could have come from the null hypothesis (i.e., a world where there is no difference). This probability is called a "p-value". Conceptually, this is similar to a "proof by contradiction," in which we assert that, if the probability is very small that the data could have originated from the null hypothesis, it must not be true. This is what is meant by "rejecting the null hypothesis". It is different from a proof by contradiction because rejecting the null proves nothing, except perhaps that the null is unlikely to be the source of the observed data. It doesn't prove that the true difference is 5 inches, or 1 inch, or anything. Because of this, rejecting the null hypothesis is in NO WAY equivalent to accepting an alternative hypothesis. Usually, in the course of an experiment, we observe a result (such as the observed height difference, perhaps it is ~5 inches) that, once we reject, replaces the hypothesized value of 0 under the null. However, we DON'T know anything about the probability that our observed value is "correct", which is why we never say that we have "accepted" an alternative. I actually hesitate to discuss an "alternative" hypothesis because most researchers never state one and it doesn't matter for the purposes of null hypothesis significance testing (NHST). It is just the name given to the conclusion drawn by the researchers after they have rejected their null hypothesis. Philosophically, there is an adage that data can never be used to prove an assertion, only to disprove one. It includes an analogy about a turkey concluding that he is loved by his human family and is proven wrong upon being slaughtered on Thanksgiving. I'll include a link if I can find it. Now, think about this: The concept of rejecting a null hypothesis probably seems very reasonable as long as we are careful not to overinterpret it, and this is how NHST was performed for decades. But consider - what is the probability that the null hypothesis is true in the first place? In other words, how likely is it that the difference between mens' and womens' heights is equal to zero? I propose that the probability is exactly zero, and if you disagree then I will find a ruler small enough to prove me correct. The difference can never be equal to exactly zero (even though this is the "straw man" that our experiment refutes), so we are effectively testing against a hypothesis that can never be true. Rejecting a hypothesis we already know to be false tells us nothing important ("the data are unlikely to have come from this state that cannot be true"). And since every null hypothesis is imaginary, it is suggested that any null hypothesis can be rejected with enough statistical power (read:sample size). Often a "significant" result says more about a study's sample size than it does about the study's findings, even though the language used in papers/media suggests to readers that the findings are more "important" or "likely to be correct". This has, in part, led to a reproducibility crisis in the sciences and, for some, an undermining of subject-matter-experts' trust in the use of applied statistics. More on reddit.com
20
19
January 5, 2021Videos
04:33
What is a Null Hypothesis? (4 Minute Easy Explanation) - YouTube
04:29
What's a null hypothesis? // How to write a null hypothesis - YouTube
Examples of null and alternative hypotheses (video)
04:29
Hypothesis testing. Null vs alternative - YouTube
05:00
Hypothesis Testing - Introductory Statistics; null hypothesis; ...
15:54
Null Hypothesis, p-Value, Statistical Significance, Type 1 Error ...
Reddit
reddit.com › r/step1 › help with uworld concept on null values
r/step1 on Reddit: Help with UWorld concept on null values
July 3, 2021 -
QID: 10672
95% confidence interval was -2.7 to -1.3
There was an overall change in systolic blood pressure of -2.2
This test is saying the results are statistically significant, but -2.2 falls between the confidence intervals? UWorld's explanation doesn't make much sense to me.
Drawn it out below:
https://i.imgur.com/Pshs4x0.jpg
Open Textbook BC
opentextbc.ca › researchmethods › chapter › understanding-null-hypothesis-testing
Understanding Null Hypothesis Testing – Research Methods in Psychology – 2nd Canadian Edition
October 13, 2015 - But how low must the p value be before the sample result is considered unlikely enough to reject the null hypothesis? In null hypothesis testing, this criterion is called α (alpha) and is almost always set to .05. If there is less than a 5% chance of a result as extreme as the sample result if the null hypothesis were true, then the null hypothesis is rejected. When this happens, the result is said to be statistically ...
Investopedia
investopedia.com › terms › n › null_hypothesis.asp
Understanding Null Hypothesis in Investment Analysis
May 7, 2007 - ... A null hypothesis is a foundational concept in statistics that assumes there is no real relationship or effect in the data being analyzed, and that any variations or trends are simply the result of random fluctuation rather than a true ...
Colostate
psy652.colostate.edu › modules › m16-nhst.html
Null Hypothesis Significance Testing – Foundations in Data Science
Null (\(H_0\)): the “nothing to see here” position. Alternative (\(H_A\)): the claim that something interesting is happening. ... Compare the sample result to what \(H_0\) predicts, turning that gap into a test statistic and p-value.
ABPI Schools
abpischools.org.uk › topics › statistics › the-null-hypothesis-and-the-p-value
The null hypothesis and the p-value
Accepting the null hypothesis means that there is no significant difference between the samples (there is no difference between heart rate before and after exercise) while rejecting the null hypothesis means that there is a significant difference (there is a difference in heart rate before exercise compared to after exercise). But how do we know when to reject a null hypothesis, and when to accept it? All statistical tests that are discussed here incorporate the probability value (p-value).
National University
resources.nu.edu › statsresources › hypothesis
Null & Alternative Hypotheses - Statistics Resources - LibGuides at National University
1 month ago - “Null” meaning “nothing.” This hypothesis states that there is no difference between groups or no relationship between variables. The null hypothesis is a presumption of status quo or no change. Alternative Hypothesis (Ha) – This is also known as the claim.
Esri Support
support.esri.com › en-us › gis-dictionary › null-value
Null Value Definition | GIS Dictionary
... [statistics, mathematics] The absence of a recorded value for a field. A null value differs from a value of zero in that zero may represent the measure of an attribute, while a null value indicates that no measurement has been taken.
Scribbr
scribbr.com › home › null and alternative hypotheses | definitions & examples
Null & Alternative Hypotheses | Definitions, Templates & Examples
January 24, 2025 - 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 independent variable on the dependent variable.
Towards Data Science
towardsdatascience.com › home › latest › null hypothesis and the p-value
Null Hypothesis and the P-Value | Towards Data Science
January 23, 2025 - There is a correlation between frustration and aggression. Alternative hypothesis are represented as H1 or HA. I hope you understood this very confusing concept. Keeping the null hypothesis in mind, we’ll move on to P-value. ... In statistics, the p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct.
Reddit
reddit.com › r/learnprogramming › where do null values come from in datasets and how to handle them?
r/learnprogramming on Reddit: Where do NULL values come from in datasets and how to handle them?
June 8, 2024 -
My understanding is that NULL represents true absence of value or a total unknown value. This is not the same as empty which is a known value, or a string of zero length. I've worked with banking data and often see lots of NULL values in various fields but if NULL represents UNKNOWN does that mean something simply went wrong/error in the system or is it a legitimate value? Because otherwise I'd think putting empty there makes more sense.
Not really sure how to treat NULL values in these datasets, should I simply ignore them? What if I'm trying to transform the data (or preform joins) on these rows wouldn't NULL values throw all the calculations off?
How should I think about and handle NULL values as they come into my codebase?
Thanks
Top answer 1 of 3
4
It is fine to have null values in data sets. If something can be NULL you are saying, it’s okay to not have it. You just need to make sure that when operating on something that could be null you are checking before operating on it. If(possiblyNullValue) {console.log(“it’s not null”)}
2 of 3
3
NULL values can mean whatever you want them to mean, and different people have different opinions on how they should be used. Generally, the only way they will enter your database is because you insert them -- either explicitly by using NULL as a value in an INSERT statement, or implicitly, by not specifying a value for a column whose default is NULL. Probably the most common reason to use NULL is to represent an "optional" value. For instance, maybe in a banking application, you have a user table with a "social security number" field. Some of your users might be US residents who have an SSN, and others might be foreigners who don't. This could be considered a "true absence of value" because it's not the case that the person has an SSN which is "empty", they simply don't have one. It doesn't necessarily make sense to allow a "missing" or NULL value for every field, which is why databases allow you to easily declare which fields are nullable or non-nullable in your schema. Can you explain why you think using NULL would "throw all the calculations off"? It's true that NULL has different behavior than an empty string, but that might be exactly what you want. For instance, if you perform a join on the SSN field, you probably wouldn't want every possible pair of users with a missing SSN to be joined with each other. Two empty strings are considered "equal", but two NULL values are not.
Reddit
reddit.com › r/askstatistics › how does null distribution is calculated and how p value is calculated for test vs null?
r/AskStatistics on Reddit: How does NULL distribution is calculated and how p value is calculated for test vs null?
April 19, 2023 -
As I understood— The null distribution is a theoretical distribution of test statistics that would be obtained if the null hypothesis were true. In other words, it represents the distribution of test statistics that would be expected by chance, in the absence of any true effect or difference between groups. The null distribution can be calculated in different ways depending on the type of test being performed.
As each distributions i.e. t, χ2, F, have their own way to calculate statistic using tables, When we using software (e.g. R programming) to calculate p value for them, Does the software convert respect distribution to Normal distribution for calculating the p value?
Could someone explain the concept behind NULL distribution with an simulated example if possible?
Top answer 1 of 3
2
Your description of the null hypothesis is good. When calculating p-values, non-normal distributions don't need to be converted to the normal distribution. Calculating p-values involves calculating the area under the curve of a statistical distribution within a specific range. This range will typically be between your observed test statistic and infinity (although will sometimes be between your observed test statistic and 0). For example, if you observe an F statistic of 3.5, your p-value might be equal to the area under the curve of the F distribution for values >= 3.5. This principle applies to whatever statistical distribution you are interested in.
2 of 3
2
Does the software convert respect distribution to Normal distribution for calculating the p value? No. It does each one in its own way. On occasions there may be a normal approximation of the null distribution that's involved for large sample sizes, but it's case-by-case basis, not the usual thing. For example, with a Wilcoxon-Mann-Whitney two sample test; the null distribution of the test statistic is discrete, but we can also look at a standardized version of the statistic [U - μ₀]/σ₀ (where μ₀ and σ₀ are the mean and standard deviation of the null distribution when H0 is true, and are both functions of the two sample sizes). Asymptotically (as both sample sizes go to infinity) the distribution of that standardized statistic will go to a standard normal distribution when H0 is true and at sufficiently large sample sizes a normal approximation will give perfectly useful approximations to any but the most extreme p-values (those may be inaccurate but given they should be be much smaller than anything you'd care to compare them with, it's not practically a big issue). Nevertheless when there are no ties, R uses the exact discrete distribution until the sample sizes are very large; it has a special function for doing that (and you can use that function directly, its pwilcox). By contrast an F statistic has an F distribution and R won't be using any normal approximation there. While I haven't checked, I presume it's converting the F to an inverse regularized incomplete beta (a beta quantile function) except when the denominator df are extremely large, when it might use the chi-squared instead. edit: just checked the help (you can do that for almost all the tests built into R; it usually documents exactly what functions - with references - it uses). It said this: For ‘pf’, via ‘pbeta’ (or for large ‘df2’, via ‘pchisq’). For ‘qf’, via ‘qchisq’ for large ‘df2’, else via ‘qbeta’. Yeah, so essentially exactly what I said. When distributions are simply and closely related (on which see the Wikipedia pages on the various distributions, which usually have a section pointing out the main such relationships), it makes sense not to have to get (or write from scratch) and then test a whole new function for the quantile function but to get a related one that's really well tested and stable and use it again. Much less scope for mistakes if your code is a couple of lines of simple transformation and a call to something you already know works. There's a number of those relationships that get used in practice for calculating p values Could someone explain the concept behind NULL distribution with an simulated example if possible? Sure. First thing is to forget p-values to start with -- they're not part of the Neyman-Pearson framework, you don't need them for anything in it. Indeed p-values are from Fisher's approach, although the concept - albeit less clearly expressed - is older. Everything is easier to explain without them and then we can bring them back in at the end if needed. You choose some test statistic that behaves differently when H0 is true and when H1 is true. What you want to do is picking the values of the test statistic that are most consistent with H1 (e.g. in the sense that they're much more likely to occur under H1 than under H0) and reject H0 when you are in that region (or those regions -- you might have several disjoint parts of the distribution that are like that). Clearly there's some boundary between the part where you reject and where you don't and the most usual convention includes the boundary in the rejection region (though that distinction doesn't matter for a continuously distributed statistic). You can move those boundaries to make the overall rejection region smaller or larger. Now under the usual framework we choose some type I error rate, alpha1. This allows us to fix our boundary. For the moment I'll assume we have our test statistic so that the rejection region is one side of a single boundary value (the critical value) and the non-rejection region is on the other side. For example, for a two-tailed t-test, we'd look at the distribution of |t|, the absolute value of t, and then the rejection region would be in the right tail only. (It can potentially get more complicated than that ... but this will cover almost every case of actual hypothesis tests in practice.) If you move the critical value further toward the "most strongly consistent with H1" parts, the rejection region is smaller, so the type I error rate is smaller, and if you move it out into the "less strongly consistent with H1" parts, the region is larger, the type I error rate is larger. You should get a collection of nested rejection regions, where any larger region has at least the type I error rate of any of the regions within it2. So given nested rejection regions, you then simply move your critical value to the least extreme value it would have without making the type I error rate exceed alpha. That way you reject the most cases you can without exceeding your type I error budget. This makes your power as high as you can given the test statistic being used. Often you don't literally move the critical value back and forth, because if you can calculate the inverse cdf (the quantile function) of the test statistic when H0 is true (i.e. the quantile function of the null distribution of the test statistic), then you can directly compute that critical value. However in some cases you don't have a neat inverse cdf to work with, and then you may in fact be engaged in searching for where the "tail" probability is no more than alpha (literal root-finding, in that you're solving F(T) - (1-⍺) = 0, which may involve binary section, for example, or some more sophisticated root-finder; 'vanilla' R offers Brent's algorithm via uniroot which is quite decent.) In some cases, it's not possible (or possible but difficult) to directly compute the density/pmf nor the cdf (let alone its inverse). In those cases it may be possible to simulate the distribution of the test statistic under the assumptions, for example by drawing samples that satisfy the assumptions and then computing the test statistic. By repeating that many times you can obtain an estimate of the cdf of the distribution of the test statistic when H0 is true, and so get critical values (and hence, p-values). Now that we know how to obtain critical values and alphas (either can be found from the other), let's define a p-value. The p-value is simply the smallest alpha for which you'd still reject H0. I'll try to think of a simple example to discuss, but if not I've at least covered the process in a reasonably general way.
Minitab
support.minitab.com › en-us › minitab › help-and-how-to › statistics › basic-statistics › supporting-topics › basics › null-and-alternative-hypotheses
About the null and alternative hypotheses - Support - Minitab
The null hypothesis states that a population parameter (such as the mean, the standard deviation, and so on) is equal to a hypothesized value. The null hypothesis is often an initial claim that is based on previous analyses or specialized knowledge.
Wikipedia
en.wikipedia.org › wiki › Null_hypothesis
Null hypothesis - Wikipedia
February 6, 2026 - According to this view, the null hypothesis must be numerically exact—it must state that a particular quantity or difference is equal to a particular number. In classical science, it is most typically the statement that there is no effect of a particular treatment; in observations, it is typically that there is no difference between the value of a particular measured variable and that of a prediction. Most statisticians believe that it is valid to state direction as a part of null hypothesis, or as part of a null hypothesis/alternative hypothesis pair.
Optimizely
optimizely.com › optimization-glossary › null-hypothesis
What is a null hypothesis? - Optimizely
June 10, 2025 - The null hypothesis works within a framework of interconnected statistical concepts. When you create a null hypothesis, you simultaneously define the alternative hypothesis which states there is a significant difference or relationship between your variables and typically represents what you hope to prove. Hypothesis testing evaluates whether your data provides sufficient evidence to reject the null hypothesis. This relies on the p-value...
National Library of Medicine
nlm.nih.gov › oet › ed › stats › 02-700.html
Hypotheses - Finding and Using Health Statistics - NIH
In statistical analysis, two hypotheses are used. The null hypothesis, or H0, states that there is no statistical significance between two variables. The null is often the commonly accepted position and what scientists seek to find evidence against.
Top answer 1 of 3
5
Imagine someone proposes a research question, like 'electric car sales are increasing'. Now they must test it with a hypothesis test.
The null hypothesis can be thought of as the hypothesis of no change. For example, 'electric car sales are the same as last year'
The alternative hypothesis usually links to the research question. For example, 'electric car sales have increased since last year'
Now, we need evidence (data) to reject the null hypothesis, which would allow us to conclude that electric car sales are not the same as last year. If we did not have strong enough evidence to reject the null hypothesis, we can't say that it's necessarily true, we just conclude that we 'fail to reject the null hypothesis'.
2 of 3
1
The null hypothesis is the hypothesis you want to reject. Usually, but not always, it is "no change" or "no relationship" or something similar.
In statistical hypothesis inference testing, you test the null by gathering data and running a test (which kind depends on what data you have and what you are trying to show) and then seeing if the results are unlikely if the null is true. How unlikely they have to be is up to you, but common levels are 5% and 1%.
We then either reject the null (yippee!) or fail to reject (we don't accept it). This is similar to a criminal trial (at least in the US and many other places) where we can find the defendant "guilty" or "not guilty" but not "innocent". The prosecution has to prove its case.
In statistics, the researchers are the prosecution and they have to prove their case.
In my opinion, nulls other than the usual are not used enough and unconventional levels of doubt to reject are also not used enough. But that's an aside.
Statsig
statsig.com › perspectives › null-hypothesis-guide-experimentation
What is a null hypothesis? A guide for experimentation
February 25, 2025 - In reality, the p-value indicates the probability of observing data as extreme as yours, assuming H₀ is true. It doesn't directly tell you the chance that H₀ is correct. Misconception 2: Failing to reject H₀ means it's true. Not rejecting the null hypothesis doesn't confirm it's true—it just means there's not enough evidence against it. As highlighted in this Reddit post, absence of evidence isn't evidence of absence. Misconception 3: Statistical significance implies practical importance.