May 8, 2025 - 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 ...

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Null & Alternative Hypotheses - Statistics Resources - LibGuides at National University

“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.

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Null hypothesis

statistical concept

{\textstyle H_{0}} ) is the claim in scientific research that the effect being studied does not exist. The null hypothesis can also be described as the hypothesis in which no relationship exists … Wikipedia

Wikipedia

en.wikipedia.org › wiki › Null_hypothesis

Null hypothesis - Wikipedia

3 weeks ago - 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.

Basic definitions

Terminology

Technical description

Principle

Goals of null hypothesis tests

Choice of the null hypothesis

History of statistical tests

Top answer

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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.

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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.

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).

Khan Academy

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Examples of null and alternative hypotheses (video)

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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.

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

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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”)}

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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.

Psychstat

advstats.psychstat.org › book › hypothesis › index.php

Null hypothesis testing -- Advanced Statistics using R

If the $p$ value is small enough, we reject the null. In the significance testing approach of Ronald Fisher, a null hypothesis is rejected on the basis of data that are significantly unlikely if the null is true. However, the null hypothesis is never accepted or proved. This is analogous to a criminal trial: The defendant is assumed to be innocent (null is not rejected) until proven guilty (null is rejected) beyond a reasonable doubt (to a statistically ...

Towards Data Science

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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.

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.

Lumen Learning

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Null and Alternative Hypotheses | Introduction to Statistics

The null statement must always contain some form of equality (=, ≤ or ≥) Always write the alternative hypothesis, typically denoted with Ha or H1, 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. H0 and Ha are contradictory. ... OpenStax, Statistics, Null and Alternative Hypotheses.

Wikipedia

en.wikipedia.org › wiki › Null_distribution

Null distribution - Wikipedia

August 26, 2025 - In statistical hypothesis testing, the null distribution is the probability distribution of the test statistic when the null hypothesis is true. For example, in an F-test, the null distribution is an F-distribution.

Examples of application

Obtaining the null distribution

Null distribution with large sample size

BYJUS

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Null Hypothesis Definition

April 25, 2022 - 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.