# Hypothesis Testing in Equivalence and Noninferiority Trials

Computational physics and science, algorithms; Representation of numbers, machine precision, series summation; Errors, uncertainties, round offs, recursion relations method; Visualization of data; Non-thermal Monte Carlo techniques, random numbers and sequences, random walk problems, application to radio-active decay; Numerical Integration and Differentiation, Higher Dimensional Integration, Quantum Monte-Carlo methods; Function optimization, steepest descent, conjugate gradient, Golden ratio search, Variational Methods in Quantum mechanics; Matrix computing, system of equations, eigenvalue problems, large matrices, linear algebra packages; Data fitting: Lagrange interpolation, cubic splines, least-squares method, singular value decomposition; Ordinary differential equations: Euler's rule, Runge-Kutta methods, solving for equations of motion, non-linear oscillations with and without forcing, precision considerations, energy and momentum conservations; Quantum eigenvalue problem for a particle in a box; Time series analysis in Physics, Fourier analysis, discrete Fourier transforms, sampling and aliasing effects, Fast Fourier Transforms; Molecular Dynamics, non-interacting gas in a box, extracting thermodynamic variables from simulations; Introduction to high-performance computing hardware and parallel computing: distributed memory programming, parallelizing strategy, high level view of message passing, high throughput computing models.

## 22/12/2017 · Equivalence Trials Hypotheses ..

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### In Equivalence Hypothesis Testing the null ..

Blackwelder (Controlled Clinical Trials 1982; 3: 345-353) proposes a solution. If a differencebetween the two treatments, call it D, is specified that practically represents equivalence, then thenull hypothesis can be restated to include the specified difference. In other words, that: Ps isgreater than or equal to Pn + D. Rejection of this hypothesis implies that the difference betweenthe standard and novel treatments is less than or equal to D, indicating equivalence.

### Sample size based on null hypothesis of non-equivalence

This equivalence of confidence intervals and statistical significance is a well-known corollary of statistical first principles, and we will not explain it further here. But we stress that confidence intervals do not represent an advance on null hypothesis testing, if they are interpreted only in relation to positive and negative values or, equivalently, the zero or null value.

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### Hypothesis and Equivalence Testing - WinSPC

Overview of optical communications; Planar optical wave guides, modes and the eigenvalue equation, single-mode and multimode fiber; Group velocity and material dispersion, inter-modal and intra-modal dispersion, attenuation, pulse dispersion, fiber bandwidth, dispersion management; wavelength division multiplexing (WDM) concepts, Signal degradation, attenuation, dispersion and its compensation; Optical sources, semiconductor lasers and light emitting diodes, structure, spectral and temporal properties, modulation schemes; Photo-detectors, structure, operation, quantum efficiency, responsivity, spectral and temporal response; Detection schemes, coherent and non-coherent detection, performance analysis; WDM components, splitters, isolators, circulators, fiber Bragg gratings (FBG), Fabry-Perot and thin-film filters; Optical amplifiers, erbium doped fiber amplifiers

### depending on the goals of the study, ..

Data visualization, elements of data analysis, linear and non-linear regression. General Physics and Optics: determination of Hall effect coefficient in n and p-type semiconductors, determination of electrical resistivity of a semiconductor using the 4-probe method, characteristics of a diode laser, Fabry-Perot etalon, Michelson and Mach-Zehnder interferometery, To visualize fine-splitting structure and verification of Bohr magneton value by Zeeman effect, characteristics of wave guides (optical fiber), determination of e/h ratio from Josephson junction experiments. Electronics: Characteristics of FET & MOSFET, Experiments using OPAMP (IC-741) VIZ. (Inverting & non-inverting amplifier, Comparator, Summing and Differential Amplifier, Integrator & Differentiator, Frequency characteristics of various kind of filters), Introduction to logic gates and digital electronics, Study of Frequency and Amplitude modulation. Incubate student led experiments in consultation with a faculty/expert.

### Sample Size for an Equivalence Study

Frequency response of RLC circuits; Power factor improvement; Power measurement in balanced and unbalanced three phase circuits; Modeling the magnetic system by an equivalent electric circuit; Performance of single phase induction motor; Speed control of stepper motor. Diode clipper, clamper and rectifier circuits; Transistor amplifier and oscillator; Operational amplifier circuits; Combinational digital circuits; Sequential digital circuits.