A p-value is used to decide whether hypothesis test results are statistically significant or not. Once it is calculated from analyzing test data, it is compared to the selected alpha level – if lower than the alpha level, the results are deemed to be statistically significant; if higher, the results are deemed to not be statistically significant.
A p-value is expressed as a number between 0 and 1.
This Khan Academy video further explains how they apply to hypothesis tests, in-depth:
While the p-value is a standard method for finding the key measurement of one’s results, there is a mix of opinions on whether it’s actually the ideal solution.
Geoff Cumming — Emeritus Professor at La Trobe University in Melbourne, Australia — explains his dislike of p-values in hypothesis testing in the following video:
But then, Jeff Leek and Rafa Irizarry do not agree, and their article lists a number of useful pieces of information about the p-value. To summarize (the full list, with explanations, is available in the linked article):
- They’re easy to calculate.
- They’re easy to understand.
- They have simple, universal properties.
- Their calibration is within useful error rates.
- They can be used in correlation with multiple tests.
- They’re reproducible.
Frequently Asked Questions About P-Values
What is the difference between an alpha level and a p-value? (PDF)
This is a fundamental but often confusing question in hypothesis testing. Here’s a clear breakdown of the difference between alpha level and p-value:
- Alpha Level (α): This is the threshold you set before your test; it represents the probability of making a Type I error—that is, rejecting the null hypothesis when it’s actually true. Common values are 0.05, 0.01, or 0.10.
- p-value: This is the probability that the observed data (or something more extreme) could occur under the null hypothesis. It’s calculated from your sample data after the test is conducted.
Key Difference:
- Alpha is the benchmark you compare against.
- p-value is the result you get from your experiment.
If the p-value is less than or equal to α, you reject the null hypothesis; otherwise, you fail to reject it.
For more detailed insights on hypothesis testing, including alpha and p-values, visit our article on Hypothesis Testing.
Hope this clears it up!
What is a p-value in simple terms?
A p-value is the probability of getting results at least as extreme as your observed data, assuming the null hypothesis is true. It’s a tool used to decide whether to reject the null hypothesis.
What does a p-value of 0.05 mean?
A p-value of 0.05 means there’s a 5% chance the observed results occurred by random chance. If your p-value is below 0.05, it typically indicates statistical significance.
Is a lower p-value better?
Yes. A lower p-value means the results are less likely due to random chance and more likely to reflect a true effect, increasing your confidence in rejecting the null hypothesis.
What is considered a significant p-value?
A p-value is considered statistically significant if it’s below a set threshold (usually 0.05). This suggests strong evidence against the null hypothesis.
Can a p-value be greater than 1?
No. P-values range between 0 and 1. A p-value above 1 is not valid and usually indicates a calculation error.
What’s the difference between p-value and alpha?
The p-value is the calculated probability from your test. Alpha (typically 0.05) is the significance level you choose before testing. If p ≤ alpha, you reject the null hypothesis.
What does a p-value of 0.01 mean?
A p-value of 0.01 means there’s only a 1% chance the observed results happened by random chance. It’s stronger evidence against the null hypothesis than a p-value of 0.05.
Can p-values be negative?
No. P-values can’t be negative. They represent a probability, which ranges from 0 to 1.
Does a p-value prove causation?
No. A p-value can suggest a relationship between variables, but it does not prove causation. Other factors and study design must be considered.
How is a p-value calculated?
A p-value is calculated using a statistical test (like t-test or chi-square) based on the difference between observed and expected data under the null hypothesis.
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Comments (2)
Ciao! your work is extraordinary. Best 6 sigma training. In this page the pdf is no longer available. Can you add it again?
Massimo
Hi Massimo,
I was unable to find the PDF, but I did dramatically enhance this page with many FAQs which should help.
Best, Ted.