New relevance and significance measures to replace p-values

Area of Science:

• Statistics
• Scientific Methodology

Background:

• The p-value is widely debated and often misinterpreted.
• Current methods frequently test unrealistic null hypotheses of zero effect.

Purpose of the Study:

• To propose a more meaningful approach to statistical inference.
• To introduce a quantitative measure of effect relevance.
• To offer a classification of results beyond significance testing.

Main Methods:

• Defining a relevance threshold for statistical effects.
• Developing a quantitative measure of relevance.
• Utilizing confidence intervals for relevance inference.
• Proposing a "secured relevance" metric.

Main Results:

• A natural quantitative measure of relevance emerges from a chosen threshold.
• Confidence intervals provide a basis for statistical inference on relevance.
• A classification system for results is proposed, enhancing interpretation.

Conclusions:

• Shifting focus from "significant/non-significant" to "relevant/non-relevant" improves scientific interpretation.
• The "secured relevance" offers a scientifically meaningful alternative to the p-value.