Use this Severity Calculator to easily calculate the severity criterion (SEV) and assess the strength of your statistical inferences. It helps determine whether observed differences in means or proportions have passed a severe test based on your data. Developed following the severe testing framework by Prof. Deborah Mayo and Prof. Aris Spanos, this tool ensures robust and reliable data analysis.
📊 Severity Calculator (SEV)
✅ SEV Calculation Result
What is “Severity” and “Severely Tested”?
In the context of statistical inference and error analysis, severity refers to the degree to which data have been subjected to a severe test—a test that would have likely revealed an error if the hypothesis were false. The concept of severity was developed by Prof. Deborah Mayo and Prof. Aris Spanos as part of the Severe Testing Philosophy, emphasizing the importance of evidence that genuinely tests and challenges a hypothesis rather than merely confirming it.
A result is said to be “severely tested” when it passes a stringent test—meaning the data provide strong evidence against possible errors. In simple terms, a hypothesis has been severely tested if, had it been false, the test would almost certainly have shown that. This approach ensures that statistical conclusions are not only valid but also robust against uncertainty, bias, and model misspecification.
In practice, the Severity Criterion (SEV) quantifies how strongly a hypothesis has withstood testing. It ranges from 0 to 1, where values closer to 1 indicate stronger severity and greater confidence in the result. A low severity value implies weak testing or insufficient evidence, while a high SEV value indicates a hypothesis that has survived an intense and rigorous evaluation.
Severity Formula:
SEV(H, x) = 1 − P(T(X) ≥ T(x); H1)
Where:
- SEV(H, x) – Severity of hypothesis H given data x
- T(X) – Test statistic under the null hypothesis
- T(x) – Observed value of the test statistic
- H1 – Alternative hypothesis
Using the Severity Calculator, analysts can compute this SEV value to evaluate the strength of evidence behind their findings. This helps ensure that any accepted hypothesis is not only statistically significant but also severely tested, providing a deeper understanding of reliability and validity in data-driven decision-making.
Severity Criterion
The Severity Criterion is a key concept in the Severe Testing Framework developed by Prof. Deborah Mayo and Prof. Aris Spanos. It measures how strongly the data support a hypothesis after undergoing a rigorous or severe test. In statistical terms, it quantifies the probability that the test would have produced less favorable evidence if the hypothesis were false, providing a direct measure of the test’s stringency and reliability.
A high Severity Criterion (SEV) value indicates that the hypothesis has survived a strong test and that the observed results are not due to chance. Conversely, a low SEV value suggests that the data have not been severely tested or that the evidence is insufficient to confidently support the hypothesis. This makes the Severity Criterion a crucial tool for ensuring error control and scientific rigor in data-driven analysis.
Severity Criterion Formula:
SEV(H, x) = 1 − P(T(X) ≥ T(x) | H1)
Where:
- SEV(H, x) – Severity of the hypothesis H given data x
- T(X) – Test statistic under the null hypothesis
- T(x) – Observed value of the test statistic
- H1 – Alternative hypothesis
The Severity Criterion is fundamental to evidence-based statistical inference. By using this formula, the Severity Calculator computes how well the data challenge or support a given hypothesis, helping researchers ensure that their conclusions are both valid and severely tested.
How to Interpret Severity
Understanding how to interpret the severity criterion (SEV) is essential for making meaningful conclusions about your data. The severity value represents how strongly a hypothesis has been tested and supported by the available evidence. It reflects the probability that the test would have found a discrepancy if the hypothesis were false — a direct indicator of test reliability and error control.
In simpler terms, a high SEV value (close to 1) means the data provide strong evidence that the hypothesis has passed a severe test. A low SEV (close to 0) suggests that the evidence is weak or inconclusive, and more testing or data may be needed. This interpretation helps analysts determine whether results are genuinely significant or just statistically coincidental.
Interpreting Severity Formula:
Interpretation ∝ SEV(H, x) = 1 − P(T(X) ≥ T(x) | H1)
Meaning: The higher the SEV(H, x) value, the more severe the test — indicating stronger evidence in favor of the hypothesis H. If SEV ≈ 1 → strong evidence; if SEV ≈ 0 → weak evidence.
To put it practically:
| SEV Range | Interpretation | Inference Strength |
|---|---|---|
| 0.80 – 1.00 | Strong severity – hypothesis is well supported | High confidence |
| 0.50 – 0.79 | Moderate severity – evidence is acceptable | Medium confidence |
| 0.00 – 0.49 | Low severity – weak or insufficient evidence | Low confidence |
The Severity Calculator uses this interpretation framework to help you evaluate how reliable your statistical results are. By combining the SEV formula and threshold ranges, users can make accurate and transparent decisions in data analysis and hypothesis testing.
Severity Calculator – Complete Guide
What is “Severity” and “Severely Tested”?
In the context of statistical inference and error analysis, severity refers to the degree to which data have been subjected to a severe test—a test that would have likely revealed an error if the hypothesis were false. The concept of severity was developed by Prof. Deborah Mayo and Prof. Aris Spanos as part of the Severe Testing Philosophy, emphasizing the importance of evidence that genuinely tests and challenges a hypothesis rather than merely confirming it.
A result is said to be “severely tested” when it passes a stringent test—meaning the data provide strong evidence against possible errors. In simple terms, a hypothesis has been severely tested if, had it been false, the test would almost certainly have shown that. This ensures statistical conclusions are not only valid but also robust against uncertainty, bias, and model misspecification.
In practice, the Severity Criterion (SEV) quantifies how strongly a hypothesis has withstood testing. It ranges from 0 to 1, where values closer to 1 indicate stronger severity and greater confidence in the result. A low severity value implies weak testing or insufficient evidence, while a high SEV value indicates a hypothesis that has survived an intense and rigorous evaluation.
Severity Formula:
SEV(H, x) = 1 − P(T(X) ≥ T(x); H1)
Where:
- SEV(H, x) – Severity of hypothesis H given data x
- T(X) – Test statistic under the null hypothesis
- T(x) – Observed value of the test statistic
- H1 – Alternative hypothesis
Using the Severity Calculator, analysts can compute this SEV value to evaluate the strength of evidence behind their findings. This ensures that accepted hypotheses are statistically significant and severely tested, providing reliable results for data-driven decision-making.
Severity Criterion
The Severity Criterion is a key concept in the Severe Testing Framework. It measures how strongly the data support a hypothesis after undergoing a rigorous or severe test. In statistical terms, it quantifies the probability that the test would have produced less favorable evidence if the hypothesis were false, providing a direct measure of the test’s stringency and reliability.
A high SEV value indicates that the hypothesis has survived a strong test and that the observed results are not due to chance. Conversely, a low SEV value suggests that the data have not been severely tested or that the evidence is insufficient to confidently support the hypothesis. This makes the Severity Criterion a crucial tool for ensuring error control and scientific rigor.
Severity Criterion Formula:
SEV(H, x) = 1 − P(T(X) ≥ T(x) | H1)
Where:
- SEV(H, x) – Severity of the hypothesis H given data x
- T(X) – Test statistic under the null hypothesis
- T(x) – Observed value of the test statistic
- H1 – Alternative hypothesis
The Severity Calculator computes how well the data challenge or support a given hypothesis, ensuring that conclusions are both valid and severely tested.
How to Interpret Severity
The severity value (SEV) represents how strongly a hypothesis has been tested and supported by the data. A high SEV (close to 1) means the hypothesis has passed a severe test, while a low SEV (close to 0) indicates weak evidence.
Interpreting Severity Formula:
Interpretation ∝ SEV(H, x) = 1 − P(T(X) ≥ T(x) | H1)
Meaning: Higher SEV → stronger evidence for the hypothesis; lower SEV → weaker evidence.
| SEV Range | Interpretation | Inference Strength |
|---|---|---|
| 0.80 – 1.00 | Strong severity – hypothesis is well supported | High confidence |
| 0.50 – 0.79 | Moderate severity – evidence is acceptable | Medium confidence |
| 0.00 – 0.49 | Low severity – weak or insufficient evidence | Low confidence |
Severity Calculator – Practical Examples
Here’s how to apply the Severity Calculator with example data to calculate and interpret SEV.
Example 1: Testing a Mean Difference
Test statistic: T(x) = 2.1, Probability under H₁: P(T(X) ≥ 2.1 | H₁) = 0.12
SEV(H, x) = 1 − 0.12 = 0.88
The SEV = 0.88 → strong evidence, hypothesis has passed a severe test.
Example Summary Table
| Example | T(x) | P(T(X) ≥ T(x) | H₁) | Calculated SEV | Interpretation |
|---|---|---|---|---|
| 1. Mean Difference Test | 2.1 | 0.12 | 0.88 | Strong evidence (High Severity) |
| 2. Proportion Test | 1.4 | 0.35 | 0.65 | Moderate evidence |
| 3. Variance Comparison | 0.9 | 0.55 | 0.45 | Weak evidence (Low Severity) |
The Severity Calculator ensures accurate computation of SEV values and helps interpret results using the severity framework, providing strong evidence for decision-making in statistical analysis.
Severity Calculator – Frequently Asked Questions (FAQ)
1. What is a Severity Calculator?
The Severity Calculator helps determine the severity criterion (SEV) of a hypothesis, showing how strongly the data have been severely tested. It quantifies the reliability of statistical evidence.
2. How is the severity (SEV) calculated?
SEV is calculated using the formula: SEV(H, x) = 1 − P(T(X) ≥ T(x) | H₁). It measures the probability that the test would detect a discrepancy if the hypothesis were false.
3. What does a high or low SEV value mean?
A high SEV value (close to 1) indicates the hypothesis has passed a strong, severe test and evidence is reliable. A low SEV (close to 0) suggests weak evidence or insufficient testing.
4. Can I use the calculator for any type of data?
Yes, the calculator works for continuous data, proportions, and means. It is flexible and adapts to different statistical tests while automatically computing the severity criterion.
5. Why is severity testing important?
Severity testing ensures your conclusions are robust and not due to chance. It allows researchers to evaluate the strength of evidence and decide whether to accept or reject hypotheses with confidence.
6. How do I interpret the results from the calculator?
The calculator outputs the SEV value and interpretation guidance. Typically, SEV ≥ 0.8 → strong evidence, SEV 0.5–0.79 → moderate evidence, SEV < 0.5 → weak evidence. This helps make informed statistical decisions.