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Related Concept Videos

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the others.
¹H NMR Signal Multiplicity: Splitting Patterns01:13

¹H NMR Signal Multiplicity: Splitting Patterns

When protons A and X are coupled, their nuclear spin energy levels are slightly modified. This is because the energy required to excite proton A to a spin state parallel to proton X is slightly different from the energy required for it to become anti-parallel to spin X. Consequently, there are two possible excitation frequencies for A (A1 and A2), depending on the spin state of X, and vice versa. The mutual nature of coupling implies that the difference between frequencies A1 and A2, indicated...
¹H NMR: Complex Splitting01:13

¹H NMR: Complex Splitting

A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied first.
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must have a...
Upsampling01:22

Upsampling

Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
Bulk Modulus01:21

Bulk Modulus

The bulk modulus is a scientific term used to describe a material's resistance to uniform compression. It is the proportionality constant that links a change in pressure to the resulting relative volume change.

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Related Experiment Video

Updated: May 22, 2026

Evaluation of Synaptic Multiplicity Using Whole-cell Patch-clamp Electrophysiology
10:52

Evaluation of Synaptic Multiplicity Using Whole-cell Patch-clamp Electrophysiology

Published on: April 23, 2019

Multiplicity adjustment for composite binary endpoints.

Geraldine Rauch1, M Kieser

  • 1Institute of Medical Biometry and Informatics, University of Heidelberg, Heidelberg, Germany. rauch@imbi.uni-heidelberg.de

Methods of Information in Medicine
|April 25, 2012
PubMed
Summary
This summary is machine-generated.

This study introduces a new statistical method for clinical trials using composite endpoints. The approach enhances power for analyzing both composite and individual outcomes, potentially reducing sample size requirements.

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Area of Science:

  • Biostatistics
  • Clinical Trial Design
  • Statistical Methods

Background:

  • Binary composite outcome measures are increasingly utilized as primary endpoints in clinical trials.
  • Composite endpoints combine multiple events into a single variable, but may mask individual component effects.
  • Evaluating individual components separately alongside the composite is recommended in scientific literature.

Purpose of the Study:

  • To define an adequate multiple test procedure for composite endpoints.
  • To allow confirmatory interpretation of individual components when effects are large.
  • To focus on the composite outcome while enabling component-level insights.

Main Methods:

  • Determined the correlation matrix for multiple binary endpoints, including a composite endpoint and its components.
  • Utilized normal approximation test statistics for rates, assuming multinomial distribution for components.
  • Calculated adjusted local significance levels based on the correlation structure.
  • Illustrated the approach with two clinical trial examples.

Main Results:

  • Developed an adequate multiple test procedure for assessing composite and component outcomes.
  • The procedure leverages the correlation structure between the composite and its components.
  • Achieved this using an approximate multivariate normal distribution with minimal power loss compared to composite-only analyses.

Conclusions:

  • Incorporating correlation under null hypotheses increases global power for composite and component analyses.
  • The proposed method may allow confirmatory analysis of composite and components without significantly increasing sample size.
  • This offers a more informative approach than simple Bonferroni adjustments.