probability of obtaining test results at least as extreme as the results actually observed, under the assumption that the null hypothesis is correct
In null-hypothesis significance testing, the p-value is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct. A … Wikipedia
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Wikipedia
en.wikipedia.org › wiki › P_value
p-value - Wikipedia
July 17, 2026 - In null-hypothesis significance testing, the p-value is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct. A very small p-value means that such an extreme observed outcome would be very unlikely ...
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Going to start off with some relevant definitions first Dependent variable — the thing that’s being measured, a response variable (ie. heart rate) Independent variable — the thing that’s being manipulated or set by the researchers; the variable that is hypothesized to cause a change in the dependent variable (ie. a drug treatment) Population — the group being tested. Important to note that the conclusion can only be generalized to the population of the study. If the experiment (“sample population”) only includes men of Asian descent aged 45 and over, then the conclusion cannot be assumed to extend to men of other backgrounds, women, young men, children, etc. The alternative hypothesis is the research question in the form of a true/false statement (This drug affects heart rate). The null hypothesis is the “blank.” It assumes there is no relation between the independent and dependent variables (This drug has no effect on heart rate). With no evidence, we default that the null hypothesis is true. The experiment aims to disprove the null hypothesis in favor of the alternative.* The p-value is the probability of getting the observed result under the assumption that the null hypothesis is true — that there is no relation between the variables. A small p-value means that it would be very unlikely to observe this result by random chance; therefore, it is likely that something is causing it. In a well-designed experiment, the cause can be attributed to the independent variable. *Just because a result is not significant, does not necessarily mean that the null hypothesis is definitively true, it just means we did not find evidence to say otherwise. Same goes for the alternative. Just because a result is significant, does not mean it is the end-all explanation. We just have evidence to support the conclusion. That’s not a go-ahead for all you conspiracy theorists out there to say “Gotcha!” If the results can be observed time and time again, then that’s more and more evidence to support the explanation.
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Let's say you want to understand if the temperature of the day relates to how many times a day my dog farts. My null hypothesis is: the days temperate does not effect how much my dog farts. Ie that any relation is just chance. My aim (Alternative hypothesis) is to reject that statement, so I can prove that the temperature DOES effect my dog's farts. I want 95% confidence to prove my aim. So I need 5% confidence (p value) I can reject my null hypothesis. Say I run this test and record the data for a year. Plug in all the values, and get a result that says it's a 50:50 that these are related. Sadly then, I cannot reject my null hypothesis, and cannot then prove that the temperature and my dogs farts are related.
People also ask

Does a p-value tell you whether your alternative hypothesis is true?
No. The p-value only tells you how likely the data you have observed is to have occurred under the null hypothesis. · If the p-value is below your threshold of significance (typically < 0.05), then you can reject the null hypothesis, but this does not necessarily mean that your alternative hypothesis is true.
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scribbr.com
scribbr.com › home › understanding p values | definition and examples
Understanding P-values | Definition and Examples
What is a p-value?
Ap-value, or probability value, is a number describing how likely it is that your data would have occurred under the null hypothesis of your statistical test.
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scribbr.com
scribbr.com › home › understanding p values | definition and examples
Understanding P-values | Definition and Examples
How do you calculate a p-value?
P-values are usually automatically calculated by the program you use to perform your statistical test. They can also be estimated using p-value tables for the relevant test statistic. · P-values are calculated from the null distribution of the test statistic. They tell you how often a test statistic is expected to occur under the null hypothesis of the statistical test, based on where it falls in the null distribution. · If the test statistic is far from the mean of the null distribution, then the p-value will be small, showing that the test statistic is not likely to have occurred under the n
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scribbr.com
scribbr.com › home › understanding p values | definition and examples
Understanding P-values | Definition and Examples
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PubMed Central
pmc.ncbi.nlm.nih.gov › articles › PMC137449
Statistics review 3: Hypothesis testing and P values - PMC
The 'P ' stands for probability, and measures how likely it is that any observed difference between groups is due to chance. In other words, the P value is the probability of seeing the observed difference, or greater, just by chance if the null hypothesis is true.
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Penn State Statistics
online.stat.psu.edu › statprogram › reviews › statistical-concepts › hypothesis-testing › p-value-approach
S.3.2 Hypothesis Testing (P-Value Approach) | STAT ONLINE
The P-value approach involves determining "likely" or "unlikely" by determining the probability — assuming the null hypothesis was true — of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed.
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ABPI Schools
abpischools.org.uk › topics › statistics › the-null-hypothesis-and-the-p-value
The null hypothesis and the p-value
In simpler terms, a p-value is used as a ‘cut-off point’ in terms of accepting or rejecting the null hypothesis.
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Scribbr
scribbr.com › home › understanding p values | definition and examples
Understanding P-values | Definition and Examples
June 22, 2023 - Alternative hypothesis (HA or H1): there is a difference in longevity between the two groups. ... The p value, or probability value, tells you how likely it is that your data could have occurred under the null hypothesis.
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Towards Data Science
towardsdatascience.com › home › data science › null hypothesis and the p-value
Null Hypothesis and the P-Value | Towards Data Science
November 13, 2019 - Null Hypothesis -> The Air Quality Index for Bangalore on 8th November 2019 at 6 PM is 162. This statement could be wrong. The people who published this value did a bunch of tests with their tools and came up with this value at the end of the test. But you might have your own tools to measure the quality of the air, or you may feel the air looks too clean to have such a high value.
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UCLA School of Law
libguides.law.ucla.edu › c.php
Statistical Significance and p-values - Working with Quantitative Data - LibGuides at UCLA School of Law - Hugh & Hazel Darling Law Library
3 weeks ago - In a hypothesis test, we produce a p-value. The p-value is the probability that we obtained an estimate as large as we did by random chance, under the assumption that the null hypothesis is true.
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WMed
wmed.edu › sites › default › files › P-VALUES SIMPLIFIED.pdf pdf
P-VALUES SIMPLIFIED Preface
In the following discussion we sometimes refer to the null hypothesis as being true, when in fact, we do not know and are not testing if it is true. ... The term p-value is an abbreviation for Probability Value.
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GraphPad
graphpad.com › quickcalcs › pvalue1
P value calculator
P values (or probability values) are used in hypothesis testing to represent the chance that, assuming the null hypothesis is true, you could observe the result in your study or one even more extreme.
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NCBI
ncbi.nlm.nih.gov › books › NBK557421
Hypothesis Testing, P Values, Confidence Intervals ... - NCBI
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numiqo
numiqo.com › tutorial › p-value
p-value: A Beginner’s Guide
If the null hypothesis applies in your population, for example that the salary of men and women does not differ, then there will typically be some difference in the sample, such as a difference of EUR 300 or more per month. The p-value tells you how likely a result at least this extreme would be if there were no difference in the population.
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Reddit
reddit.com › r/explainlikeimfive › eli5: what is p-value in statistics?
r/explainlikeimfive on Reddit: ELI5: What is p-value in statistics?
September 24, 2024 -

I have actually been studying and using statistics a lot in my career, but I still struggle with finding a simply way to explain what exactly is p-value.

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You can see a pattern due to random luck and you could misinterpret it to suggest some underlying factor that isn’t really there. P-value measures how likely (or unlikely) it would be for this particular result to appear just by random chance. The smaller it is, the more likely that the result is meaningful and not just lucky. Imagine you give a drug to 2 people who are moderately sick, and they both get better. It’s totally possible they both got lucky and would have gotten better anyways without the drug. It’s going to be really hard to tell with only 2 people, so if you analyze the P value you would find it’s likely high, indicating there is a large chance you just got lucky and you can’t take any meaningful lessons from that study. However if you don’t give 1000 people a drug, and find only 20% get better on their own, then you do give 1000 people a drug and 80% get better, that’s a very strong pattern outside the “random luck” behavior you were able to observe. So if you analyzed that P value it would likely be small, indicating it was more likely that the drug really did cause this result, and it wasn’t just luck.
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Say I have a coin and i want to know "is this coin fair?" I toss the coin 100 times and it comes up heads 60 times and tails 40 times. Intuitively this seems kind of close to fair, but also a bit skewed. Was this just random variance? Or is this a large enough sample size that a 60-40 split is alarming? P values give a way to reason about this scenario by asking "if the coin is fair, how unlikely is this result?" It turns out that in this case it's about a 2.8% chance of getting 60 or more heads (and similarly for 60 or more tails). It's at this point that people tend to misinterpret p values. The statement people want to be able to make is "there is a 2.8% chance that this coin is fair," but p values do not allow you to make that statement, at least on their own. The p value only says "if the coin is fair then you'd see this result 2.8% of the time." Turning a p value into the probability that some hypothesis is correct generally requires knowing some unknowable information. In this toy example that information would be the probability that coins are fair which may be knowable for the right setup, but for more real-world applications it could be something like "the probability that another subatomic particle exists with XYZ properties" (where that probability is either 0 or 1, but we don't know which). This makes p values somewhat frustrating since they're so close to making the statement we want, and yet getting that final inch is out of reach. What p values are very well equipped for is stopping you from publishing results as significant if it turns out you just got lucky. If you took a threshold of p < 0.05 then you might declare that the coin is unfair, but with a more stringent threshold like p < 0.01 you'd declare the test to be inconclusive. With a threshold of p < 0.05 what you're saying is that you're OK with calling 1 in 20 fair coins weighted, regardless of how any weighted coins get judged. Different disciplines tend to set p value thresholds at different levels, based on the available data collection. For example, particle physicists like to aim for p < 1/1,000,000 or lower.
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BachelorPrint
bachelorprint.com › home › statistics › hypothesis testing › the p-value – definition, calculation & example
The P-Value ~ Definition, Calculation & Example
October 16, 2025 - The p-value is used in hypothesis testing to determine whether the null hypothesis can be rejected or accepted. Therefore, the probability value is compared to the significance level.
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PubMed Central
pmc.ncbi.nlm.nih.gov › articles › PMC5804470
P-value: What is and what is not - PMC
The p-value is the probability of the observed data given that the null hypothesis is true, which is a probability that measures the consistency between the data and the hypothesis being tested if, and only if, the statistical model used to compute the p-value is correct (9).
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jitsi.cmu.edu
jitsi.cmu.edu.jm › home › calculating p-values: a comprehensive guide for informative and friendly understanding
Calculating p-Values: A Comprehensive Guide for Informative and Friendly Understanding
February 17, 2025 - This statistic quantifies the discrepancy between the observed data and what would be expected under the assumption of the null hypothesis being true. The p-value is then calculated, which represents the probability of obtaining a test statistic as extreme as, or more extreme than, the observed data, assuming the null hypothesis is true.
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Penn State Statistics
online.stat.psu.edu › statprogram › book › export › html › 529
S.3.2 Hypothesis Testing (P-Value Approach)
The P-value approach involves determining "likely" or "unlikely" by determining the probability — assuming the null hypothesis was true — of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed.