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 โ€ฆ Wikipedia
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Wikipedia
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p-value - Wikipedia
3 weeks ago - In null-hypothesis significance ... is correct. A very small p-value means that such an extreme observed outcome would be very unlikely under the null hypothesis. Even though reporting p-values of statistical tests is common practice in academic publications of many quantitative fields, misinterpretation and misuse of p-values is widespread and has been a major topic in mathematics and metascience. In 2016, the American Statistical Association (ASA) made a formal statement that "p-values ...
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Simply Psychology
simplypsychology.org โ€บ statistics โ€บ understanding p-values and statistical significance
Understanding P-Values and Statistical Significance
August 11, 2025 - It indicates strong evidence of ... Specifically, a p-value of 0.001 means there is only a 0.1% chance of obtaining a result at least as extreme as the one observed, assuming the null hypothesis is correct....
People also ask

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
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Understanding P-values | Definition and Examples
Can a non-significant p-value indicate that there is no effect or difference in the data?
No, a non-significant p-value does not necessarily indicate that there is no effect or difference in the data. It means that the observed data do not provide strong enough evidence to reject the null hypothesis.

There could still be a real effect or difference, but it might be smaller or more variable than the study was able to detect.

Other factors like sample size, study design, and measurement precision can influence the p-value. It's important to consider the entire body of evidence and not rely solely on p-values when interpreting research findings.
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simplypsychology.org
simplypsychology.org โ€บ statistics โ€บ understanding p-values and statistical significance
Understanding P-Values and Statistical Significance
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. ยท 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. ยท 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
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Understanding P-values | Definition and Examples
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Investopedia
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P-Value: What It Is, How to Calculate It, and Examples
October 3, 2025 - For example, the U.S. Census Bureau stipulates that any analysis with a p-value greater than 0.10 must be accompanied by a statement that the difference is not statistically different from zero.
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Scribbr
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Understanding P-values | Definition and Examples
June 22, 2023 - This is because the smaller your frame of reference, the greater the chance that you stumble across a statistically significant pattern completely by accident. P values are also often interpreted as supporting or refuting the alternative hypothesis. This is not the case. The p value can only tell you whether or not the null hypothesis is supported. It cannot tell you whether your alternative hypothesis is true, or why. If you want to know more about statistics, methodology, or research bias, make sure to check out some of our other articles with explanations and examples.
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PubMed Central
pmc.ncbi.nlm.nih.gov โ€บ articles โ€บ PMC4111019
P โ€“ VALUE, A TRUE TEST OF STATISTICAL SIGNIFICANCE? A CAUTIONARY NOTE - PMC
Both the Fisherian and Neyman-Pearson (N-P) schools did not uphold the practice of stating, โ€œP values of less than 0.05 were regarded as statistically significantโ€ or โ€œP-value was 0.02 and therefore there was statistically significant difference.โ€ These statements and many similar ...
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Statistics By Jim
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Interpreting P values - Statistics By Jim
June 17, 2025 - However, we cannot say that about an individual test and itโ€™s P-value. ... Hi, that is sort of correct. More correct would be to say that if you repeat an experiment on a population where the null is true, youโ€™d expect 5% (using alpha = 0.05) of the studies to be statistically significant (false positives).
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NCBI
ncbi.nlm.nih.gov โ€บ books โ€บ NBK557421
Hypothesis Testing, P Values, Confidence Intervals, and Significance - StatPearls - NCBI Bookshelf
March 13, 2023 - Conventionally, data yielding a p<0.05 or p<0.01 is considered statistically significant. While some have debated that the 0.05 level should be lowered, it is still universally practiced.[6] Hypothesis testing allows us to determine the size of the effect. Two examples of findings reported ...
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StatsDirect
statsdirect.com โ€บ help โ€บ basics โ€บ p_values.htm
P Values (Calculated Probability) and Hypothesis Testing - StatsDirect
When presenting P values some groups find it helpful to use the asterisk rating system as well as quoting the P value: ... Most authors refer to statistically significant as P < 0.05 and statistically highly significant as P < 0.001 (less than one in a thousand chance of being wrong).
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WMed
wmed.edu โ€บ sites โ€บ default โ€บ files โ€บ P-VALUES SIMPLIFIED.pdf pdf
P-VALUES SIMPLIFIED Preface
Accordingly, a large p-value lends support to the assertion of a correct null hypothesis. Hence, larger p-values result in failure to reject the null hypothesis. ***************************************************** Conversely, a small p-value means that there is a lesser chance that the data ...
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Penn State Statistics
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S.3.2 Hypothesis Testing (P-Value Approach) | STAT ONLINE
The P-value approach involves determining "likely" or "unlikely" by determining the probability โ€” assuming the null hypothesis was true โ€” of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed.
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Quizlet
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Exam 2 Flashcards | Quizlet
the alternative hypothesis includes ... correct about a p-value? Whether a small p-value provides evidence in favor of the alternative hypothesis depends on whether the test is one-sided or two-sided....
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PubMed Central
pmc.ncbi.nlm.nih.gov โ€บ articles โ€บ PMC5665734
What the P values really tell us - PMC
These methods include confidence, ... on estimation than testing. P values alone cannot confirm whether the researcher's argument is correct or not; P < 0.05 cannot ensure that the researchersโ€™ arguments are true....
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Reddit
reddit.com โ€บ r/statistics โ€บ [discussion] explain a p-value
r/statistics on Reddit: [Discussion] Explain a p-value
January 29, 2022 -

I was talking to a friend recently about stats, and p-values came up in the conversation. He has no formal training in methods/statistics and asked me to explain a p-value to him in the most easy to understand way possible. I was stumped lol. Of course I know what p-values mean (their pros/cons, etc), but I couldn't simplify it. The textbooks don't explain them well either.

How would you explain a p-value in a very simple and intuitive way to a non-statistician? Like, so simple that my beloved mother could understand.

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PubMed Central
pmc.ncbi.nlm.nih.gov โ€บ articles โ€บ PMC5804470
P-value: What is and what is not - PMC
As it is clearly mentioned in ASA statement, any effect (large or small) can produce a small or large p-value depending on the sample size or measurement precision, so conclusion about a hypothesis should not be based on p-value only, but also other aspects such as measurement precision, sample ...