Statistics Notes: Percentage differences, symmetry, and natural logarithms

Statistics Notes: Percentage differences, symmetry, and natural logarithms.

Despite its wide use in statistics, the logarithmic transformation can make non-statisticians uncomfortable. This is a shame because logarithms have very useful properties, including a secret not widely known even among statisticians. The two familiar forms of logarithm are common logs, to base 10, and natural logs, to base e. Here we focus on natural logs (or “ln” for short), which have the fo...

Natural logarithms

Marusic et al. (J. Fluid Mech., vol. 716, 2013, R3) show the first clear evidence of universal logarithmic scaling emerging naturally (and simultaneously) in the mean velocity and the intensity of the streamwise velocity fluctuations about that mean in canonical turbulent flows near walls. These observations represent a significant advance in understanding of the behaviour of wall turbulence at...

Principles of Statistics for the Natural Sciences -Notes-

Radiative Electroweak Symmetry Breaking Beyond Leading Logarithms

The top-quark Yukawa coupling is too large to permit radiative electroweak symmetry breaking to occur for small values of y, the Higgs self-coupling, to leading-logarithm order. However, a large y solution leading to a viable Higgs mass of approximately 220GeV does exist, and differs from conventional symmetry breaking by an approximately five-fold enhancement of the Higgs self-coupling. This s...

Statistics notes: variables and parameters.

the course of low back pain in general practice: a one year follow up study. Ann Rheum Dis 1998;57:13-9. 16 Croft PR, Papageorgiou AC, Ferry S, Thomas E, Jayson MIV, Silman AJ. Psychological distress and low back pain: Evidence from a prospective study in the general population. Spine 1996;20:2731-7. 17 Papageorgiou AC, Macfarlane GJ, Thomas E, Croft PR, Jayson MIV, Silman AJ. Psychosocial fact...