An inferential confidence interval method of establishing statistical equivalence that corrects Tryon's (2001)...

Area of Science:

• Statistics
• Psychometrics
• Data Analysis

Background:

• Null hypothesis statistical testing (NHST) is frequently misused to infer group equivalence.
• Failing to reject the null hypothesis (H-sub-0) does not provide evidence for equivalence.
• There is a need for robust statistical equivalence testing methods.

Purpose of the Study:

• To correct and extend W. W. Tryon's (2001) inferential confidence interval (ICI) reduction factor for statistical equivalence.
• To demonstrate the algebraic equivalence of the corrected ICI method with established two one-sided t-tests (TOST) for equivalence.
• To introduce hybrid confidence intervals as an improvement over traditional error bars for inferential clarity.

Main Methods:

• Correction and application of the inferential confidence interval (ICI) reduction factor.
• Algebraic comparison with the two one-sided t-tests (TOST) method (Schuirmann, 1987).
• Introduction and application of hybrid confidence intervals.

Main Results:

• The corrected ICI method is algebraically equivalent to the TOST method for testing statistical equivalence.
• The ICI method offers an intuitive graphical approach for inferring both statistical difference and equivalence.
• Identified conditions for 'trivial difference' (both tests passed) and 'statistical indeterminacy' (both tests failed).

Conclusions:

• The corrected ICI method provides a valid and intuitive approach to statistical equivalence testing.
• Hybrid confidence intervals are recommended as superior replacements for error bars, enhancing inferential capabilities.
• Accurate statistical inference requires appropriate tests for both difference and equivalence, not just NHST.